[[960, 184, 3]] magic-state factory, T0·T1·T2·T3·T4·T5·T6·T7·T8·T9·T10·T11...

The circuit

The 212\times960 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.

output wires
check wires, measured and postselected

wire	0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| '
out 0 (193)	1111····················································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········································································································································································································································································································································································································································································································
out 1 (7)	····1111111·····················································································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 2 (7)	···········1111111··············································································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 3 (7)	··················1111111·······································································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 4 (7)	·························1111111································································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 5 (7)	································1111111·························································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 6 (7)	·······································1111111··················································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 7 (7)	··············································1111111···········································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 8 (7)	·····················································1111111····································································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 9 (7)	····························································1111111·····························································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 10 (7)	···································································1111111······················································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 11 (7)	··········································································1111111···············································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 12 (7)	·················································································1111111········································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 13 (7)	························································································1111111·································································································································································································································································································································································································································································································································································································································································································································································································································································································
out 14 (7)	·······························································································1111111··························································································································································································································································································································································································································································································································································································································································································································································································································································································
out 15 (7)	······································································································1111111···················································································································································································································································································································································································································································································································································································································································································································································································································································································
out 16 (253)	11··1111···1111···1111···1111···1111···1111···1111···1111···1111···1111···1111··········1111···1111··········1111111111·1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········································································································································································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········
out 17 (145)	·····················································1111··········11··11········1111··········11··11········111········································································································································································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········
out 18 (85)	····11··11········1111··········11··11········11··11····································1111····················11······························································································································································································································································································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···································································································································
out 19 (143)	····························································11··11········11··11·11··11········1111··········1··················································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···························································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········
out 20 (125)	1·111·1·1·111··11·11··11·11··11·1·1·1·11111···1111···11··11·1111···1·1·1·111··11·1·1·1·1·······1·1·1·11111········11···11·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···························································································································································································································································································································································································································································································································································································································································································································································
out 21 (61)	···········1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1········································································································································································································································································································································································································································································································································································································································································································································································································································································
out 22 (61)	·····11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1········································································································································································································································································································································································································································································································································································································································································································································································································································································
out 23 (187)	·························································································································1···1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11············1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11············1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···········································································································································································································································································································································································································································································································
out 24 (7)	····························································································································1111111·····························································································································································································································································································································································································································································································································································································································································································································································································································································
out 25 (7)	···································································································································1111111······················································································································································································································································································································································································································································································································································································································································································································································································································································
out 26 (7)	··········································································································································1111111···············································································································································································································································································································································································································································································································································································································································································································································································································································
out 27 (7)	·················································································································································1111111········································································································································································································································································································································································································································································································································································································································································································································································································································
out 28 (7)	························································································································································1111111·································································································································································································································································································································································································································································································································································································································································································································································································································
out 29 (7)	·······························································································································································1111111··························································································································································································································································································································································································································································································································································································································································································································································································································
out 30 (7)	······································································································································································1111111···················································································································································································································································································································································································································································································································································································································································································································································································································
out 31 (7)	·············································································································································································1111111············································································································································································································································································································································································································································································································································································································································································································································································································
out 32 (7)	····················································································································································································1111111·····································································································································································································································································································································································································································································································································································································································································································································································································
out 33 (7)	···························································································································································································1111111······························································································································································································································································································································································································································································································································································································································································································································································································
out 34 (7)	··································································································································································································1111111·······················································································································································································································································································································································································································································································································································································································································································································································································
out 35 (7)	·········································································································································································································1111111················································································································································································································································································································································································································································································································································································································································································································································································
out 36 (7)	················································································································································································································1111111·········································································································································································································································································································································································································································································································································································································································································································································································
out 37 (7)	·······················································································································································································································1111111··································································································································································································································································································································································································································································································································································································································································································································································
out 38 (7)	······························································································································································································································1111111···························································································································································································································································································································································································································································································································································································································································································································································
out 39 (187)	·························································································································1111·1·1·1·········1111·1··1·11·11··11··1111········1··1·11··1111·11··11···1111·11··11·1·1·1·1········11··111111111111··1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11············································································································································································································································································································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···········
out 40 (145)	·············································································································································································1111··········11··11········1111··········11··11········111·················································································································································································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11····································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···········
out 41 (85)	····························································································································11··11········1111··········11··11········11··11····································1111····················11·······································································································································································································································································································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···································································································································
out 42 (143)	····················································································································································································11··11········11··11·11··11········1111··········1···························································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11····························································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···········
out 43 (51)	····························································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1················································································································································································································································································································································································································································································································································································································································································································································
out 44 (61)	···································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1················································································································································································································································································································································································································································································································································································································································································································································
out 45 (61)	·····························································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1················································································································································································································································································································································································································································································································································································································································································································································
out 46 (125)	··················································································································································································································································111·1·1·11·1·1·11111···1·1·1·11111·····1111··1·11·11··1·11··1111·1111·····1111···1111···1111···1111·1111··············11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············································································································································································································································································································································································································································································································
out 47 (7)	····················································································································································································································································1111111·····································································································································································································································································································································································································································································································································································································································································································································
out 48 (7)	···························································································································································································································································1111111······························································································································································································································································································································································································································································································································································································································································································································
out 49 (7)	··································································································································································································································································1111111·······················································································································································································································································································································································································································································································································································································································································································································
out 50 (7)	·········································································································································································································································································1111111················································································································································································································································································································································································································································································································································································································································································································
out 51 (7)	················································································································································································································································································1111111·········································································································································································································································································································································································································································································································································································································································································································
out 52 (7)	·······················································································································································································································································································1111111··································································································································································································································································································································································································································································································································································································································································································
out 53 (7)	······························································································································································································································································································1111111···························································································································································································································································································································································································································································································································································································································································································
out 54 (7)	·····································································································································································································································································································1111111····················································································································································································································································································································································································································································································································································································································································································
out 55 (7)	············································································································································································································································································································1111111·············································································································································································································································································································································································································································································································································································································································································
out 56 (7)	···················································································································································································································································································································1111111······································································································································································································································································································································································································································································································································································································································································
out 57 (7)	··························································································································································································································································································································1111111·······························································································································································································································································································································································································································································································································································································································································
out 58 (7)	·································································································································································································································································································································1111111························································································································································································································································································································································································································································································································································································································································
out 59 (7)	········································································································································································································································································································································1111111·················································································································································································································································································································································································································································································································································································································································
out 60 (7)	···············································································································································································································································································································································1111111··········································································································································································································································································································································································································································································································································································································································
out 61 (7)	······················································································································································································································································································································································1111111···································································································································································································································································································································································································································································································································································································································
out 62 (121)	·····················································································································································································································································1·11·1·1·11·1········1·11·1·······11··11·1·1·1·1·11··1111··11········11··11···1111·11··11·11··11·1111···1111111111·································································································································································································································································································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············
out 63 (145)	·····································································································································································································································································································1111··········11··11········1111··········11··11········111························································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············
out 64 (85)	····················································································································································································································································11··11········1111··········11··11········11··11····································1111····················11··············································································································································································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····································································································································
out 65 (143)	············································································································································································································································································································11··11········11··11·11··11········1111··········1··································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····························································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············
out 66 (51)	····················································································································································································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1························································································································································································································································································································································································································································································································································································································
out 67 (61)	···························································································································································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1························································································································································································································································································································································································································································································································································································································
out 68 (61)	·····················································································································································································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1························································································································································································································································································································································································································································································································································································································
out 69 (63)	········································································································································································································································································································································································111···1111···1111··1·11·11111····1·11·11··1·111··1·11··1111··11··111·1·1·11·1·1·1·1·11·111··11·1·1·1·1··1111············································································································································································································································································································································································································································································································
out 70 (7)	············································································································································································································································································································································································1111111·············································································································································································································································································································································································································································································································································································································
out 71 (7)	···················································································································································································································································································································································································1111111······································································································································································································································································································································································································································································································································································································
out 72 (7)	··························································································································································································································································································································································································1111111·······························································································································································································································································································································································································································································································································································································
out 73 (7)	·································································································································································································································································································································································································1111111························································································································································································································································································································································································································································································································································································
out 74 (7)	········································································································································································································································································································································································································1111111·················································································································································································································································································································································································································································································································································································
out 75 (7)	···············································································································································································································································································································································································································1111111··········································································································································································································································································································································································································································································································································································
out 76 (7)	······················································································································································································································································································································································································································1111111···································································································································································································································································································································································································································································································································································
out 77 (7)	·····························································································································································································································································································································································································································1111111····························································································································································································································································································································································································································································································································································
out 78 (7)	····································································································································································································································································································································································································································1111111·····················································································································································································································································································································································································································································································································································
out 79 (7)	···········································································································································································································································································································································································································································1111111··············································································································································································································································································································································································································································································································································
out 80 (7)	··················································································································································································································································································································································································································································1111111·······································································································································································································································································································································································································································································································································
out 81 (7)	·························································································································································································································································································································································································································································1111111································································································································································································································································································································································································································································································································
out 82 (7)	································································································································································································································································································································································································································································1111111·························································································································································································································································································································································································································································································································
out 83 (7)	·······································································································································································································································································································································································································································································1111111··················································································································································································································································································································································································································································································································
out 84 (7)	··············································································································································································································································································································································································································································································1111111···········································································································································································································································································································································································································································································································
out 85 (121)	·············································································································································································································································································································································································1·11·1·1·11·1········1·11·1·······11··11·1·1·1·1·11··1111··11········11··11···1111·11··11·11··11·1111···1111111111···············································································································································································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1
out 86 (145)	·····························································································································································································································································································································································································································1111··········11··11········1111··········11··11········111······································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1······························································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1
out 87 (85)	············································································································································································································································································································································································11··11········1111··········11··11········11··11····································1111····················11····························································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1························································································································
out 88 (143)	····································································································································································································································································································································································································································11··11········11··11·11··11········1111··········1················1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1······················································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1
out 89 (51)	············································································································································································································································································································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1································································································································································································································································································································································································································································································
out 90 (61)	···················································································································································································································································································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1································································································································································································································································································································································································································································································
out 91 (61)	·············································································································································································································································································································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1································································································································································································································································································································································································································································································
out 92 (63)	································································································································································································································································································································································································································································································111···1111···1111··1·11·11111····1·11·11··1·111··1·11··1111··11··111·1·1·11·1·1·1·1·11·111··11·1·1·1·1··1111····················································································································································································································································································································································································
out 93 (7)	····································································································································································································································································································································································································································································································1111111·····················································································································································································································································································································································································································································································
out 94 (7)	···········································································································································································································································································································································································································································································································1111111··············································································································································································································································································································································································································································································
out 95 (7)	··················································································································································································································································································································································································································································································································1111111·······································································································································································································································································································································································································································································
out 96 (7)	·························································································································································································································································································································································································································································································································1111111································································································································································································································································································································································································································································
out 97 (7)	································································································································································································································································································································································································································································································································1111111·························································································································································································································································································································································································································································
out 98 (7)	·······································································································································································································································································································································································································································································································································1111111··················································································································································································································································································································································································································································
out 99 (7)	··············································································································································································································································································································································································································································································································································1111111···········································································································································································································································································································································································································································
out 100 (7)	·····················································································································································································································································································································································································································································································································································1111111····································································································································································································································································································································································································································
out 101 (7)	····························································································································································································································································································································································································································································································································································1111111·····························································································································································································································································································································································································································
out 102 (7)	···································································································································································································································································································································································································································································································································································1111111······················································································································································································································································································································································································································
out 103 (7)	··········································································································································································································································································································································································································································································································································································1111111···············································································································································································································································································································································································································
out 104 (7)	·················································································································································································································································································································································································································································································································································································1111111········································································································································································································································································································································································································
out 105 (7)	························································································································································································································································································································································································································································································································································································1111111·································································································································································································································································································································································································
out 106 (7)	·······························································································································································································································································································································································································································································································································································································1111111··························································································································································································································································································································································································
out 107 (7)	······································································································································································································································································································································································································································································································································································································1111111···················································································································································································································································································································································································
out 108 (121)	·····································································································································································································································································································································································································································································································1·11·1·1·11·1········1·11·1·······11··11·1·1·1·1·11··1111··11········11··11···1111·11··11·11··11·1111···1111111111······················································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1
out 109 (145)	·····················································································································································································································································································································································································································································································································································1111··········11··11········1111··········11··11········111·············1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1·····························································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1
out 110 (85)	····································································································································································································································································································································································································································································································11··11········1111··········11··11········11··11····································1111····················11···································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1························································································································
out 111 (125)	······································································································································································································································································································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··11·11··11·11··11··1111·1111···1111····1·11·1········1·11·1·1·1·····················································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1
out 112 (51)	····································································································································································································································································································································································································································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1········································································································································································································································································································································································
out 113 (61)	···········································································································································································································································································································································································································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1········································································································································································································································································································································································
out 114 (61)	·····································································································································································································································································································································································································································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1········································································································································································································································································································································································
out 115 (63)	························································································································································································································································································································································································································································································································································································································111···1111···1111··1·11·11111····1·11·11··1·111··1·11··1111··11··111·1·1·11·1·1·1·1·11·111··11·1·1·1·1··1111····························································································································································································································································
out 116 (7)	····························································································································································································································································································································································································································································································································································································································1111111·····························································································································································································································································································································································
out 117 (7)	···································································································································································································································································································································································································································································································································································································································1111111······················································································································································································································································································································································
out 118 (7)	··········································································································································································································································································································································································································································································································································································································································1111111···············································································································································································································································································································································
out 119 (7)	·················································································································································································································································································································································································································································································································································································································································1111111········································································································································································································································································································································
out 120 (7)	························································································································································································································································································································································································································································································································································································································································1111111·································································································································································································································································································································
out 121 (7)	·······························································································································································································································································································································································································································································································································································································································································1111111··························································································································································································································································································································
out 122 (7)	······································································································································································································································································································································································································································································································································································································································································1111111···················································································································································································································································································································
out 123 (7)	·············································································································································································································································································································································································································································································································································································································································································1111111············································································································································································································································································································
out 124 (7)	····················································································································································································································································································································································································································································································································································································································································································1111111·····································································································································································································································································································
out 125 (7)	···························································································································································································································································································································································································································································································································································································································································································1111111······························································································································································································································································································
out 126 (7)	··································································································································································································································································································································································································································································································································································································································································································1111111·······················································································································································································································································································
out 127 (7)	·········································································································································································································································································································································································································································································································································································································································································································1111111················································································································································································································································································
out 128 (7)	················································································································································································································································································································································································································································································································································································································································································································1111111·········································································································································································································································································
out 129 (7)	·······················································································································································································································································································································································································································································································································································································································································································································1111111··································································································································································································································································
out 130 (7)	······························································································································································································································································································································································································································································································································································································································································································································1111111···························································································································································································································································
out 131 (121)	·····························································································································································································································································································································································································································································································································································································································1·11·1·1·11·1········1·11·1·······11··11·1·1·1·1·11··1111··11········11··11···1111·11··11·11··11·1111···1111111111·····························································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11
out 132 (131)	·····························································································································································································································································································································································································································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11··11··111111···11··11·11··11··1·11·11111···1··1·11··1111·11·111·11·1····························································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11
out 133 (85)	····························································································································································································································································································································································································································································································································································································································11··11········1111··········11··11········11··11····································1111····················11··········1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11························································································································
out 134 (125)	······························································································································································································································································································································································································································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··11·11··11·11··11··1111·1111···1111····1·11·1········1·11·1·1·1····························································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11
out 135 (51)	····························································································································································································································································································································································································································································································································································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1················································································································································································································································
out 136 (61)	···································································································································································································································································································································································································································································································································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1················································································································································································································································
out 137 (61)	·····························································································································································································································································································································································································································································································································································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1················································································································································································································································
out 138 (63)	················································································································································································································································································································································································································································································································································································································································································································································111···1111···1111··1·11·11111····1·11·11··1·111··1·11··1111··11··111·1·1·11·1·1·1·1·11·111··11·1·1·1·1··1111····································································································································
out 139 (7)	····················································································································································································································································································································································································································································································································································································································································································································································1111111·····································································································································································································································
out 140 (7)	···························································································································································································································································································································································································································································································································································································································································································································································1111111······························································································································································································································
out 141 (7)	··································································································································································································································································································································································································································································································································································································································································································································································1111111·······················································································································································································································
out 142 (7)	·········································································································································································································································································································································································································································································································································································································································································································································································1111111················································································································································································································
out 143 (7)	················································································································································································································································································································································································································································································································································································································································································································································································1111111·········································································································································································································
out 144 (7)	·······················································································································································································································································································································································································································································································································································································································································································································································································1111111··································································································································································································
out 145 (7)	······························································································································································································································································································································································································································································································································································································································································································································································································1111111···························································································································································································
out 146 (7)	·····································································································································································································································································································································································································································································································································································································································································································································································································1111111····················································································································································································
out 147 (7)	············································································································································································································································································································································································································································································································································································································································································································································································································1111111·············································································································································································
out 148 (7)	···················································································································································································································································································································································································································································································································································································································································································································································································································1111111······································································································································································
out 149 (7)	··························································································································································································································································································································································································································································································································································································································································································································································································································1111111·······························································································································································
out 150 (7)	·································································································································································································································································································································································································································································································································································································································································································································································································································1111111························································································································································
out 151 (7)	········································································································································································································································································································································································································································································································································································································································································································································································································································1111111·················································································································································
out 152 (7)	···············································································································································································································································································································································································································································································································································································································································································································································································································································1111111··········································································································································
out 153 (7)	······················································································································································································································································································································································································································································································································································································································································································································································································································································1111111···································································································································
out 154 (121)	·····················································································································································································································································································································································································································································································································································································································································································································································1·11·1·1·11·1········1·11·1·······11··11·1·1·1·1·11··1111··11········11··11···1111·11··11·11··11·1111···1111111111·····1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·
out 155 (131)	·····················································································································································································································································································································································································································································································································································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11··11··111111···11··11·11··11··1·11·11111···1··1·11··1111·11·111·11·1····1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·
out 156 (63)	······················································································································································································································································································································································································································································································································································································································································································································································1111·1111··········1·1·1·1·1·11·11111···11··11··1·11·1·1·11·11·1·1·1·1·11·11·1·1·1··1111·1··1·11·1·11·1·11·1·11·11························································································································
out 157 (125)	······················································································································································································································································································································································································································································································································································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··11·11··11·11··11··1111·1111···1111····1·11·1········1·11·1·1·1····1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·
out 158 (51)	····················································································································································································································································································································································································································································································································································································································································································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1························································································································
out 159 (61)	···························································································································································································································································································································································································································································································································································································································································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1························································································································
out 160 (61)	·····················································································································································································································································································································································································································································································································································································································································································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1························································································································
out 161 (63)	········································································································································································································································································································································································································································································································································································································································································································································································································································································111···1111···1111··1·11·11111····1·11·11··1·111··1·11··1111··11··111·1·1·11·1·1·1·1·11·111··11·1·1·1·1··1111············
out 162 (7)	············································································································································································································································································································································································································································································································································································································································································································································································································································································1111111·············································································································
out 163 (7)	···················································································································································································································································································································································································································································································································································································································································································································································································································································································1111111······································································································
out 164 (7)	··························································································································································································································································································································································································································································································································································································································································································································································································································································································1111111·······························································································
out 165 (7)	·································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111························································································
out 166 (7)	········································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111·················································································
out 167 (7)	···············································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111··········································································
out 168 (7)	······················································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111···································································
out 169 (7)	·····························································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111····························································
out 170 (7)	····································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111·····················································
out 171 (7)	···········································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111··············································
out 172 (7)	··················································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111·······································
out 173 (7)	·························································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111································
out 174 (7)	································································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111·························
out 175 (7)	·······································································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111··················
out 176 (7)	··············································································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111···········
out 177 (59)	············································································································································································································································································································································································································································································································································································································································································································································································································································································11··11········1··1·11··1111···1111·1111·····1111·1111···1·1·1·1··1111·1··1·1111··11··1·11·111··11···1111··11·····1··
out 178 (65)	············································································································································································································································································································································································································································································································································································································································································································································································································································································11··11·1111···1·1·1·11111····11··11·1·11·1·1·11·11111···1··1·111111···1··1·111·1·1·1·11··111··1·111111····1····1·111
out 179 (63)	··············································································································································································································································································································································································································································································································································································································································································································································································································································································1111·1111··········1·1·1·1·1·11·11111···11··11··1·11·1·1·11·11·1·1·1·1·11·11·1·1·1··1111·1··1·11·1·11·1·11·1·11·11
out 180 (55)	············································································································································································································································································································································································································································································································································································································································································································································································································································································1·1·1·111··11··11··111·1·1·1········11··11·11··111111···········1·11·1·11··11········11··11·1·11·111··11·11···1·1111
out 181 (51)	············································································································································································································································································································································································································································································································································································································································································································································································································································································1111·····1111········1·1·1·1··1111···1111········1·1·1·1··1111·1··1·11········11··11·1·11·1·1·11·11··1·11·····11···1
out 182 (61)	···················································································································································································································································································································································································································································································································································································································································································································································································································································································1·1·1·111··11·1·1·1·11··1·111111···1·1·1·11·1·1·11·1·1·11·1·1·11·1·1·1·1·11·111··11··1·11·111··11··11··1·1··1
out 183 (61)	·············································································································································································································································································································································································································································································································································································································································································································································································································································································11··1111··11···1111··1·11·1·11··11·······11··11·1··1·111··1·111111···1·1·1·1··1111·1·1·1·11111···1·1·1·1···11·11··1
check 184 (126)	1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···························································································································································································································································································································································································································································································································································································································································································································································
check 185 (126)	·1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···································································································································································································································································································································································································································································································································································································································
check 186 (126)	11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····························································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········································································································································································································································································································································································································································································································
check 187 (126)	······1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1········································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···················································································································································································································································································································································································
check 188 (126)	·····1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1································································································································································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···························································································································································································································································
check 189 (126)	····1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11························································································································································································································································································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···································································································································
check 190 (126)	····1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·················································································································································································································································································································································································································································································································································································································································································································································1·11·1·11·11111···11··11··11··111··1·1111··11·1111····11··1111··11···1111·11··11·11··11··1·11·11111····11··11···········
check 191 (126)	·························································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11············1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···································································································································································································································································································································································································································································································································································································································
check 192 (126)	························································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11·····································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···········································································································································································································································································································································································································································································································
check 193 (126)	······························································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1·················································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···················································································································································································································································································································································································
check 194 (126)	·····························································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1·········································································································································································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···························································································································································································································································
check 195 (126)	····························································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11·································································································································································································································································································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···································································································································
check 196 (126)	····························································································································1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1··························································································································································································································································································································································································································································································································································································································1111111····1·11·1··1111·11··11··11··111111···1·1·1·11111···1111···11··11·1111···1111····11··1111··11·1··1·11···········
check 197 (126)	················································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············································································································································································································································································································································································································································································································
check 198 (126)	······················································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1························································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····················································································································································································································································································································································································
check 199 (126)	·····················································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1················································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····························································································································································································································································
check 200 (126)	····················································································································································································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11········································································································································································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11····································································································································
check 201 (126)	····················································································································································································································································1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·································································································································································································································································································································································································································································································11·11··1·111··1·111·1·1·1·1·11·11·1·1·11·1·1·111··11·1·1·1·1·1·11·1·1·11·11··1·11·11··111111···1··1·1111··11············
check 202 (126)	··············································································································································································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1······1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1········································································································································································································································································································································································
check 203 (126)	·············································································································································································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1······························································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1················································································································································································································································
check 204 (126)	············································································································································································································································································································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11······················································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1························································································································
check 205 (126)	············································································································································································································································································································································································1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1···············································································································································································································································································································································································1111·1··1·111111···11··11···1111··1·11·11111····11··111·1·1·1·11··111111·····1111·1111···1·1·1·1·······11·11·1·1·1
check 206 (126)	·····································································································································································································································································································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1·····1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1················································································································································································································································
check 207 (126)	····································································································································································································································································································································································································································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11·····························································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1························································································································
check 208 (126)	····································································································································································································································································································································································································································································································1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1······················································································································································································································································1·11·11·1·1·1··1111·1··1·11·1·11·1·11··1111··11·1··1·111111··········11··11·1·1·1·11111····1·11·1··1111···1111·11·1
check 209 (126)	····························································································································································································································································································································································································································································································································································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11····1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11························································································································
check 210 (126)	····························································································································································································································································································································································································································································································································································································································1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·····························································································································1111···1111···1111···1·1·1·11··1·111111···········1·11·1·1·11·11·1·1·1·1·11·11·1·1·111··11·1··1·11·1·11·1·111··11·11
check 211 (126)	····················································································································································································································································································································································································································································································································································································································································································································································1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·····1··1·11·1·11·11··1·11·11··11··1111···1111·1··1·111··1·11·11··11··1111··1·11·11111···1··1·11·······11··11·1··11111·1·

The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.

Figures of merit

inputs n960Noisy T states per run.

outputs k184

distance d3Exact, proved and witnessed here.

error coefficient A_{3}18,032Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.

wires N212

checks r28

V_{\mathrm{ex}}184T states per run. CCZ counts as two.

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.5037Overhead per extractable T state. Lower is better.

\gamma = \log(n/k)/\log d1.5037Overhead per output qubit.

\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.

T-countnot computedMinimal T-count of the output gate. Not computable at this width.

phase-polynomial degreenot computedMinimised over changes of output basis.

effective width184Rank of the output rows modulo the check rows.

Output gate

184 T0 CS0 CCZon 184 output wires

As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}\cdot \mathrm{T}_{77}\cdot \mathrm{T}_{78}\cdot \mathrm{T}_{79}\cdot \mathrm{T}_{80}\cdot \mathrm{T}_{81}\cdot \mathrm{T}_{82}\cdot \mathrm{T}_{83}\cdot \mathrm{T}_{84}\cdot \mathrm{T}_{85}\cdot \mathrm{T}_{86}\cdot \mathrm{T}_{87}\cdot \mathrm{T}_{88}\cdot \mathrm{T}_{89}\cdot \mathrm{T}_{90}\cdot \mathrm{T}_{91}\cdot \mathrm{T}_{92}\cdot \mathrm{T}_{93}\cdot \mathrm{T}_{94}\cdot \mathrm{T}_{95}\cdot \mathrm{T}_{96}\cdot \mathrm{T}_{97}\cdot \mathrm{T}_{98}\cdot \mathrm{T}_{99}\cdot \mathrm{T}_{100}\cdot \mathrm{T}_{101}\cdot \mathrm{T}_{102}\cdot \mathrm{T}_{103}\cdot \mathrm{T}_{104}\cdot \mathrm{T}_{105}\cdot \mathrm{T}_{106}\cdot \mathrm{T}_{107}\cdot \mathrm{T}_{108}\cdot \mathrm{T}_{109}\cdot \mathrm{T}_{110}\cdot \mathrm{T}_{111}\cdot \mathrm{T}_{112}\cdot \mathrm{T}_{113}\cdot \mathrm{T}_{114}\cdot \mathrm{T}_{115}\cdot \mathrm{T}_{116}\cdot \mathrm{T}_{117}\cdot \mathrm{T}_{118}\cdot \mathrm{T}_{119}\cdot \mathrm{T}_{120}\cdot \mathrm{T}_{121}\cdot \mathrm{T}_{122}\cdot \mathrm{T}_{123}\cdot \mathrm{T}_{124}\cdot \mathrm{T}_{125}\cdot \mathrm{T}_{126}\cdot \mathrm{T}_{127}\cdot \mathrm{T}_{128}\cdot \mathrm{T}_{129}\cdot \mathrm{T}_{130}\cdot \mathrm{T}_{131}\cdot \mathrm{T}_{132}\cdot \mathrm{T}_{133}\cdot \mathrm{T}_{134}\cdot \mathrm{T}_{135}\cdot \mathrm{T}_{136}\cdot \mathrm{T}_{137}\cdot \mathrm{T}_{138}\cdot \mathrm{T}_{139}\cdot \mathrm{T}_{140}\cdot \mathrm{T}_{141}\cdot \mathrm{T}_{142}\cdot \mathrm{T}_{143}\cdot \mathrm{T}_{144}\cdot \mathrm{T}_{145}\cdot \mathrm{T}_{146}\cdot \mathrm{T}_{147}\cdot \mathrm{T}_{148}\cdot \mathrm{T}_{149}\cdot \mathrm{T}_{150}\cdot \mathrm{T}_{151}\cdot \mathrm{T}_{152}\cdot \mathrm{T}_{153}\cdot \mathrm{T}_{154}\cdot \mathrm{T}_{155}\cdot \mathrm{T}_{156}\cdot \mathrm{T}_{157}\cdot \mathrm{T}_{158}\cdot \mathrm{T}_{159}\cdot \mathrm{T}_{160}\cdot \mathrm{T}_{161}\cdot \mathrm{T}_{162}\cdot \mathrm{T}_{163}\cdot \mathrm{T}_{164}\cdot \mathrm{T}_{165}\cdot \mathrm{T}_{166}\cdot \mathrm{T}_{167}\cdot \mathrm{T}_{168}\cdot \mathrm{T}_{169}\cdot \mathrm{T}_{170}\cdot \mathrm{T}_{171}\cdot \mathrm{T}_{172}\cdot \mathrm{T}_{173}\cdot \mathrm{T}_{174}\cdot \mathrm{T}_{175}\cdot \mathrm{T}_{176}\cdot \mathrm{T}_{177}\cdot \mathrm{T}_{178}\cdot \mathrm{T}_{179}\cdot \mathrm{T}_{180}\cdot \mathrm{T}_{181}\cdot \mathrm{T}_{182}\cdot \mathrm{T}_{183}

As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100+101+102+103+104+105+106+107+108+109+110+111+112+113+114+115+116+117+118+119+120+121+122+123+124+125+126+127+128+129+130+131+132+133+134+135+136+137+138+139+140+141+142+143+144+145+146+147+148+149+150+151+152+153+154+155+156+157+158+159+160+161+162+163+164+165+166+167+168+169+170+171+172+173+174+175+176+177+178+179+180+181+182+183 (output wires per term, separated by +)

This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.

Clifford correction

With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 200 single-wire gates and 449 \mathrm{CZ} gates: \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{Z} on output 16, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{S}^\dagger on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25 and 625 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

All 649 correction gates

\mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{Z} on output 16, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{S}^\dagger on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{S} on output 26, \mathrm{S} on output 27, \mathrm{S} on output 28, \mathrm{S} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{S} on output 32, \mathrm{S} on output 33, \mathrm{S} on output 34, \mathrm{S} on output 35, \mathrm{S} on output 36, \mathrm{S} on output 37, \mathrm{S} on output 38, \mathrm{S}^\dagger on output 39, \mathrm{Z} on output 41, \mathrm{S} on output 42, \mathrm{S}^\dagger on output 43, \mathrm{Z} on output 44, \mathrm{Z} on output 45, \mathrm{Z} on output 46, \mathrm{S} on output 47, \mathrm{S} on output 48, \mathrm{S} on output 49, \mathrm{S} on output 50, \mathrm{S} on output 51, \mathrm{S} on output 52, \mathrm{S} on output 53, \mathrm{S} on output 54, \mathrm{S} on output 55, \mathrm{S} on output 56, \mathrm{S} on output 57, \mathrm{S} on output 58, \mathrm{S} on output 59, \mathrm{S} on output 60, \mathrm{S} on output 61, \mathrm{Z} on output 64, \mathrm{S} on output 65, \mathrm{S}^\dagger on output 66, \mathrm{Z} on output 67, \mathrm{Z} on output 68, \mathrm{S} on output 69, \mathrm{S} on output 70, \mathrm{S} on output 71, \mathrm{S} on output 72, \mathrm{S} on output 73, \mathrm{S} on output 74, \mathrm{S} on output 75, \mathrm{S} on output 76, \mathrm{S} on output 77, \mathrm{S} on output 78, \mathrm{S} on output 79, \mathrm{S} on output 80, \mathrm{S} on output 81, \mathrm{S} on output 82, \mathrm{S} on output 83, \mathrm{S} on output 84, \mathrm{Z} on output 87, \mathrm{S} on output 88, \mathrm{S}^\dagger on output 89, \mathrm{Z} on output 90, \mathrm{Z} on output 91, \mathrm{S} on output 92, \mathrm{S} on output 93, \mathrm{S} on output 94, \mathrm{S} on output 95, \mathrm{S} on output 96, \mathrm{S} on output 97, \mathrm{S} on output 98, \mathrm{S} on output 99, \mathrm{S} on output 100, \mathrm{S} on output 101, \mathrm{S} on output 102, \mathrm{S} on output 103, \mathrm{S} on output 104, \mathrm{S} on output 105, \mathrm{S} on output 106, \mathrm{S} on output 107, \mathrm{Z} on output 110, \mathrm{Z} on output 111, \mathrm{S}^\dagger on output 112, \mathrm{Z} on output 113, \mathrm{Z} on output 114, \mathrm{S} on output 115, \mathrm{S} on output 116, \mathrm{S} on output 117, \mathrm{S} on output 118, \mathrm{S} on output 119, \mathrm{S} on output 120, \mathrm{S} on output 121, \mathrm{S} on output 122, \mathrm{S} on output 123, \mathrm{S} on output 124, \mathrm{S} on output 125, \mathrm{S} on output 126, \mathrm{S} on output 127, \mathrm{S} on output 128, \mathrm{S} on output 129, \mathrm{S} on output 130, \mathrm{S}^\dagger on output 132, \mathrm{Z} on output 133, \mathrm{Z} on output 134, \mathrm{S}^\dagger on output 135, \mathrm{Z} on output 136, \mathrm{Z} on output 137, \mathrm{S} on output 138, \mathrm{S} on output 139, \mathrm{S} on output 140, \mathrm{S} on output 141, \mathrm{S} on output 142, \mathrm{S} on output 143, \mathrm{S} on output 144, \mathrm{S} on output 145, \mathrm{S} on output 146, \mathrm{S} on output 147, \mathrm{S} on output 148, \mathrm{S} on output 149, \mathrm{S} on output 150, \mathrm{S} on output 151, \mathrm{S} on output 152, \mathrm{S} on output 153, \mathrm{S}^\dagger on output 155, \mathrm{S} on output 156, \mathrm{Z} on output 157, \mathrm{S}^\dagger on output 158, \mathrm{Z} on output 159, \mathrm{Z} on output 160, \mathrm{S} on output 161, \mathrm{S} on output 162, \mathrm{S} on output 163, \mathrm{S} on output 164, \mathrm{S} on output 165, \mathrm{S} on output 166, \mathrm{S} on output 167, \mathrm{S} on output 168, \mathrm{S} on output 169, \mathrm{S} on output 170, \mathrm{S} on output 171, \mathrm{S} on output 172, \mathrm{S} on output 173, \mathrm{S} on output 174, \mathrm{S} on output 175, \mathrm{S} on output 176, \mathrm{S}^\dagger on output 177, \mathrm{S} on output 179, \mathrm{S} on output 180, \mathrm{S}^\dagger on output 181, \mathrm{Z} on output 182, \mathrm{Z} on output 183, \mathrm{S} on check 184, \mathrm{S} on check 185, \mathrm{S} on check 186, \mathrm{S} on check 187, \mathrm{S} on check 188, \mathrm{S} on check 189, \mathrm{S} on check 190, \mathrm{S} on check 191, \mathrm{S} on check 192, \mathrm{S} on check 193, \mathrm{S} on check 194, \mathrm{S} on check 195, \mathrm{S} on check 196, \mathrm{S} on check 197, \mathrm{S} on check 198, \mathrm{S} on check 199, \mathrm{S} on check 200, \mathrm{S} on check 201, \mathrm{S} on check 202, \mathrm{S} on check 203, \mathrm{S} on check 204, \mathrm{S} on check 205, \mathrm{S} on check 206, \mathrm{S} on check 207, \mathrm{S} on check 208, \mathrm{S} on check 209, \mathrm{S} on check 210, \mathrm{S} on check 211, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 39, \mathrm{CZ} on output 0, output 41, \mathrm{CZ} on output 0, output 43, \mathrm{CZ} on output 0, output 45, \mathrm{CZ} on output 0, output 62, \mathrm{CZ} on output 0, output 64, \mathrm{CZ} on output 0, output 66, \mathrm{CZ} on output 0, output 68, \mathrm{CZ} on output 0, output 85, \mathrm{CZ} on output 0, output 87, \mathrm{CZ} on output 0, output 89, \mathrm{CZ} on output 0, output 91, \mathrm{CZ} on output 0, check 184, \mathrm{CZ} on output 0, check 185, \mathrm{CZ} on output 0, check 186, \mathrm{CZ} on output 16, output 17, \mathrm{CZ} on output 16, output 21, \mathrm{CZ} on output 16, output 39, \mathrm{CZ} on output 16, output 41, \mathrm{CZ} on output 16, output 43, \mathrm{CZ} on output 16, output 45, \mathrm{CZ} on output 16, output 62, \mathrm{CZ} on output 16, output 64, \mathrm{CZ} on output 16, output 66, \mathrm{CZ} on output 16, output 68, \mathrm{CZ} on output 16, output 177, \mathrm{CZ} on output 16, output 179, \mathrm{CZ} on output 16, output 181, \mathrm{CZ} on output 16, output 183, \mathrm{CZ} on output 16, check 186, \mathrm{CZ} on output 16, check 188, \mathrm{CZ} on output 16, check 189, \mathrm{CZ} on output 16, check 190, \mathrm{CZ} on output 17, output 21, \mathrm{CZ} on output 17, output 131, \mathrm{CZ} on output 17, output 133, \mathrm{CZ} on output 17, output 135, \mathrm{CZ} on output 17, output 137, \mathrm{CZ} on output 17, output 177, \mathrm{CZ} on output 17, output 179, \mathrm{CZ} on output 17, output 181, \mathrm{CZ} on output 17, output 183, \mathrm{CZ} on output 17, check 187, \mathrm{CZ} on output 17, check 188, \mathrm{CZ} on output 17, check 189, \mathrm{CZ} on output 18, output 22, \mathrm{CZ} on output 18, output 154, \mathrm{CZ} on output 18, output 156, \mathrm{CZ} on output 18, output 158, \mathrm{CZ} on output 18, output 160, \mathrm{CZ} on output 18, check 184, \mathrm{CZ} on output 18, check 185, \mathrm{CZ} on output 18, check 186, \mathrm{CZ} on output 18, check 189, \mathrm{CZ} on output 19, output 20, \mathrm{CZ} on output 19, output 22, \mathrm{CZ} on output 19, output 108, \mathrm{CZ} on output 19, output 110, \mathrm{CZ} on output 19, output 112, \mathrm{CZ} on output 19, output 114, \mathrm{CZ} on output 19, output 177, \mathrm{CZ} on output 19, output 179, \mathrm{CZ} on output 19, output 181, \mathrm{CZ} on output 19, output 183, \mathrm{CZ} on output 19, check 188, \mathrm{CZ} on output 19, check 190, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 22, \mathrm{CZ} on output 20, output 39, \mathrm{CZ} on output 20, output 41, \mathrm{CZ} on output 20, output 43, \mathrm{CZ} on output 20, output 45, \mathrm{CZ} on output 20, check 187, \mathrm{CZ} on output 20, check 188, \mathrm{CZ} on output 20, check 189, \mathrm{CZ} on output 21, output 22, \mathrm{CZ} on output 21, check 187, \mathrm{CZ} on output 21, check 188, \mathrm{CZ} on output 21, check 190, \mathrm{CZ} on output 22, check 184, \mathrm{CZ} on output 22, check 189, \mathrm{CZ} on output 23, output 41, \mathrm{CZ} on output 23, output 43, \mathrm{CZ} on output 23, output 45, \mathrm{CZ} on output 23, output 62, \mathrm{CZ} on output 23, output 64, \mathrm{CZ} on output 23, output 85, \mathrm{CZ} on output 23, output 87, \mathrm{CZ} on output 23, check 191, \mathrm{CZ} on output 23, check 192, \mathrm{CZ} on output 39, output 40, \mathrm{CZ} on output 39, output 41, \mathrm{CZ} on output 39, output 43, \mathrm{CZ} on output 39, output 44, \mathrm{CZ} on output 39, output 45, \mathrm{CZ} on output 39, output 62, \mathrm{CZ} on output 39, output 64, \mathrm{CZ} on output 39, output 177, \mathrm{CZ} on output 39, output 179, \mathrm{CZ} on output 39, check 184, \mathrm{CZ} on output 39, check 192, \mathrm{CZ} on output 39, check 194, \mathrm{CZ} on output 39, check 195, \mathrm{CZ} on output 39, check 196, \mathrm{CZ} on output 40, output 44, \mathrm{CZ} on output 40, output 131, \mathrm{CZ} on output 40, output 133, \mathrm{CZ} on output 40, output 177, \mathrm{CZ} on output 40, output 179, \mathrm{CZ} on output 40, check 193, \mathrm{CZ} on output 40, check 194, \mathrm{CZ} on output 40, check 195, \mathrm{CZ} on output 41, output 43, \mathrm{CZ} on output 41, output 45, \mathrm{CZ} on output 41, output 154, \mathrm{CZ} on output 41, output 156, \mathrm{CZ} on output 41, check 184, \mathrm{CZ} on output 41, check 191, \mathrm{CZ} on output 41, check 192, \mathrm{CZ} on output 41, check 195, \mathrm{CZ} on output 42, output 43, \mathrm{CZ} on output 42, output 45, \mathrm{CZ} on output 42, output 108, \mathrm{CZ} on output 42, output 110, \mathrm{CZ} on output 42, output 177, \mathrm{CZ} on output 42, output 179, \mathrm{CZ} on output 42, check 194, \mathrm{CZ} on output 42, check 196, \mathrm{CZ} on output 43, output 44, \mathrm{CZ} on output 43, check 184, \mathrm{CZ} on output 43, check 193, \mathrm{CZ} on output 43, check 194, \mathrm{CZ} on output 43, check 195, \mathrm{CZ} on output 44, output 45, \mathrm{CZ} on output 44, check 193, \mathrm{CZ} on output 44, check 194, \mathrm{CZ} on output 44, check 196, \mathrm{CZ} on output 45, check 184, \mathrm{CZ} on output 45, check 195, \mathrm{CZ} on output 46, output 66, \mathrm{CZ} on output 46, output 68, \mathrm{CZ} on output 46, output 85, \mathrm{CZ} on output 46, output 87, \mathrm{CZ} on output 46, check 197, \mathrm{CZ} on output 62, output 63, \mathrm{CZ} on output 62, output 66, \mathrm{CZ} on output 62, output 67, \mathrm{CZ} on output 62, output 68, \mathrm{CZ} on output 62, output 177, \mathrm{CZ} on output 62, output 179, \mathrm{CZ} on output 62, check 185, \mathrm{CZ} on output 62, check 191, \mathrm{CZ} on output 62, check 197, \mathrm{CZ} on output 62, check 199, \mathrm{CZ} on output 62, check 200, \mathrm{CZ} on output 62, check 201, \mathrm{CZ} on output 63, output 67, \mathrm{CZ} on output 63, output 131, \mathrm{CZ} on output 63, output 133, \mathrm{CZ} on output 63, output 177, \mathrm{CZ} on output 63, output 179, \mathrm{CZ} on output 63, check 198, \mathrm{CZ} on output 63, check 199, \mathrm{CZ} on output 63, check 200, \mathrm{CZ} on output 64, output 66, \mathrm{CZ} on output 64, output 68, \mathrm{CZ} on output 64, output 154, \mathrm{CZ} on output 64, output 156, \mathrm{CZ} on output 64, check 185, \mathrm{CZ} on output 64, check 191, \mathrm{CZ} on output 64, check 197, \mathrm{CZ} on output 64, check 200, \mathrm{CZ} on output 65, output 66, \mathrm{CZ} on output 65, output 68, \mathrm{CZ} on output 65, output 108, \mathrm{CZ} on output 65, output 110, \mathrm{CZ} on output 65, output 177, \mathrm{CZ} on output 65, output 179, \mathrm{CZ} on output 65, check 199, \mathrm{CZ} on output 65, check 201, \mathrm{CZ} on output 66, output 67, \mathrm{CZ} on output 66, check 185, \mathrm{CZ} on output 66, check 198, \mathrm{CZ} on output 66, check 199, \mathrm{CZ} on output 66, check 200, \mathrm{CZ} on output 67, output 68, \mathrm{CZ} on output 67, check 198, \mathrm{CZ} on output 67, check 199, \mathrm{CZ} on output 67, check 201, \mathrm{CZ} on output 68, check 185, \mathrm{CZ} on output 68, check 200, \mathrm{CZ} on output 69, output 85, \mathrm{CZ} on output 69, output 87, \mathrm{CZ} on output 69, output 89, \mathrm{CZ} on output 69, output 91, \mathrm{CZ} on output 85, output 86, \mathrm{CZ} on output 85, output 89, \mathrm{CZ} on output 85, output 90, \mathrm{CZ} on output 85, output 91, \mathrm{CZ} on output 85, output 178, \mathrm{CZ} on output 85, output 180, \mathrm{CZ} on output 85, output 181, \mathrm{CZ} on output 85, output 182, \mathrm{CZ} on output 85, check 186, \mathrm{CZ} on output 85, check 192, \mathrm{CZ} on output 85, check 197, \mathrm{CZ} on output 85, check 203, \mathrm{CZ} on output 85, check 204, \mathrm{CZ} on output 85, check 205, \mathrm{CZ} on output 86, output 90, \mathrm{CZ} on output 86, output 132, \mathrm{CZ} on output 86, output 134, \mathrm{CZ} on output 86, output 135, \mathrm{CZ} on output 86, output 136, \mathrm{CZ} on output 86, output 178, \mathrm{CZ} on output 86, output 180, \mathrm{CZ} on output 86, output 181, \mathrm{CZ} on output 86, output 182, \mathrm{CZ} on output 86, check 202, \mathrm{CZ} on output 86, check 203, \mathrm{CZ} on output 86, check 204, \mathrm{CZ} on output 87, output 89, \mathrm{CZ} on output 87, output 91, \mathrm{CZ} on output 87, output 155, \mathrm{CZ} on output 87, output 157, \mathrm{CZ} on output 87, output 158, \mathrm{CZ} on output 87, output 159, \mathrm{CZ} on output 87, check 186, \mathrm{CZ} on output 87, check 192, \mathrm{CZ} on output 87, check 197, \mathrm{CZ} on output 87, check 204, \mathrm{CZ} on output 88, output 89, \mathrm{CZ} on output 88, output 91, \mathrm{CZ} on output 88, output 109, \mathrm{CZ} on output 88, output 111, \mathrm{CZ} on output 88, output 112, \mathrm{CZ} on output 88, output 113, \mathrm{CZ} on output 88, output 178, \mathrm{CZ} on output 88, output 180, \mathrm{CZ} on output 88, output 181, \mathrm{CZ} on output 88, output 182, \mathrm{CZ} on output 88, check 203, \mathrm{CZ} on output 88, check 205, \mathrm{CZ} on output 89, output 90, \mathrm{CZ} on output 89, check 186, \mathrm{CZ} on output 89, check 202, \mathrm{CZ} on output 89, check 203, \mathrm{CZ} on output 89, check 204, \mathrm{CZ} on output 90, output 91, \mathrm{CZ} on output 90, check 202, \mathrm{CZ} on output 90, check 203, \mathrm{CZ} on output 90, check 205, \mathrm{CZ} on output 91, check 186, \mathrm{CZ} on output 91, check 204, \mathrm{CZ} on output 92, output 108, \mathrm{CZ} on output 92, output 110, \mathrm{CZ} on output 92, output 112, \mathrm{CZ} on output 92, output 114, \mathrm{CZ} on output 108, output 109, \mathrm{CZ} on output 108, output 112, \mathrm{CZ} on output 108, output 113, \mathrm{CZ} on output 108, output 114, \mathrm{CZ} on output 108, output 177, \mathrm{CZ} on output 108, output 180, \mathrm{CZ} on output 108, output 181, \mathrm{CZ} on output 108, output 182, \mathrm{CZ} on output 108, check 187, \mathrm{CZ} on output 108, check 193, \mathrm{CZ} on output 108, check 198, \mathrm{CZ} on output 108, check 206, \mathrm{CZ} on output 108, check 207, \mathrm{CZ} on output 108, check 208, \mathrm{CZ} on output 109, output 111, \mathrm{CZ} on output 109, output 113, \mathrm{CZ} on output 109, output 131, \mathrm{CZ} on output 109, output 134, \mathrm{CZ} on output 109, output 135, \mathrm{CZ} on output 109, output 136, \mathrm{CZ} on output 109, output 177, \mathrm{CZ} on output 109, output 180, \mathrm{CZ} on output 109, output 181, \mathrm{CZ} on output 109, output 182, \mathrm{CZ} on output 109, check 202, \mathrm{CZ} on output 109, check 206, \mathrm{CZ} on output 109, check 207, \mathrm{CZ} on output 110, output 112, \mathrm{CZ} on output 110, output 114, \mathrm{CZ} on output 110, output 154, \mathrm{CZ} on output 110, output 157, \mathrm{CZ} on output 110, output 158, \mathrm{CZ} on output 110, output 159, \mathrm{CZ} on output 110, check 187, \mathrm{CZ} on output 110, check 193, \mathrm{CZ} on output 110, check 198, \mathrm{CZ} on output 110, check 207, \mathrm{CZ} on output 111, output 113, \mathrm{CZ} on output 111, output 114, \mathrm{CZ} on output 111, output 177, \mathrm{CZ} on output 111, output 180, \mathrm{CZ} on output 111, output 181, \mathrm{CZ} on output 111, output 182, \mathrm{CZ} on output 111, check 202, \mathrm{CZ} on output 111, check 206, \mathrm{CZ} on output 111, check 208, \mathrm{CZ} on output 112, output 113, \mathrm{CZ} on output 112, check 187, \mathrm{CZ} on output 112, check 202, \mathrm{CZ} on output 112, check 206, \mathrm{CZ} on output 112, check 207, \mathrm{CZ} on output 113, output 114, \mathrm{CZ} on output 113, check 202, \mathrm{CZ} on output 113, check 206, \mathrm{CZ} on output 113, check 208, \mathrm{CZ} on output 114, check 187, \mathrm{CZ} on output 114, check 207, \mathrm{CZ} on output 115, output 131, \mathrm{CZ} on output 115, output 133, \mathrm{CZ} on output 115, output 135, \mathrm{CZ} on output 115, output 137, \mathrm{CZ} on output 131, output 135, \mathrm{CZ} on output 131, output 136, \mathrm{CZ} on output 131, output 137, \mathrm{CZ} on output 131, output 177, \mathrm{CZ} on output 131, output 178, \mathrm{CZ} on output 131, output 181, \mathrm{CZ} on output 131, output 183, \mathrm{CZ} on output 131, check 188, \mathrm{CZ} on output 131, check 194, \mathrm{CZ} on output 131, check 199, \mathrm{CZ} on output 131, check 206, \mathrm{CZ} on output 131, check 209, \mathrm{CZ} on output 131, check 210, \mathrm{CZ} on output 132, output 135, \mathrm{CZ} on output 132, output 177, \mathrm{CZ} on output 132, output 178, \mathrm{CZ} on output 132, output 181, \mathrm{CZ} on output 132, output 183, \mathrm{CZ} on output 132, check 203, \mathrm{CZ} on output 132, check 209, \mathrm{CZ} on output 133, output 135, \mathrm{CZ} on output 133, output 137, \mathrm{CZ} on output 133, output 154, \mathrm{CZ} on output 133, output 155, \mathrm{CZ} on output 133, output 158, \mathrm{CZ} on output 133, output 160, \mathrm{CZ} on output 133, check 188, \mathrm{CZ} on output 133, check 194, \mathrm{CZ} on output 133, check 199, \mathrm{CZ} on output 133, check 209, \mathrm{CZ} on output 134, output 136, \mathrm{CZ} on output 134, output 137, \mathrm{CZ} on output 134, output 177, \mathrm{CZ} on output 134, output 178, \mathrm{CZ} on output 134, output 181, \mathrm{CZ} on output 134, output 183, \mathrm{CZ} on output 134, check 203, \mathrm{CZ} on output 134, check 206, \mathrm{CZ} on output 134, check 210, \mathrm{CZ} on output 135, output 136, \mathrm{CZ} on output 135, check 188, \mathrm{CZ} on output 135, check 203, \mathrm{CZ} on output 135, check 206, \mathrm{CZ} on output 135, check 209, \mathrm{CZ} on output 136, output 137, \mathrm{CZ} on output 136, check 203, \mathrm{CZ} on output 136, check 206, \mathrm{CZ} on output 136, check 210, \mathrm{CZ} on output 137, check 188, \mathrm{CZ} on output 137, check 209, \mathrm{CZ} on output 138, output 154, \mathrm{CZ} on output 138, output 156, \mathrm{CZ} on output 138, output 158, \mathrm{CZ} on output 138, output 160, \mathrm{CZ} on output 154, output 156, \mathrm{CZ} on output 154, output 158, \mathrm{CZ} on output 154, output 159, \mathrm{CZ} on output 154, output 160, \mathrm{CZ} on output 154, output 178, \mathrm{CZ} on output 154, output 182, \mathrm{CZ} on output 154, check 189, \mathrm{CZ} on output 154, check 195, \mathrm{CZ} on output 154, check 200, \mathrm{CZ} on output 154, check 207, \mathrm{CZ} on output 154, check 209, \mathrm{CZ} on output 154, check 211, \mathrm{CZ} on output 155, output 156, \mathrm{CZ} on output 155, output 158, \mathrm{CZ} on output 155, output 178, \mathrm{CZ} on output 155, output 182, \mathrm{CZ} on output 155, check 204, \mathrm{CZ} on output 155, check 209, \mathrm{CZ} on output 156, check 189, \mathrm{CZ} on output 156, check 195, \mathrm{CZ} on output 156, check 200, \mathrm{CZ} on output 157, output 159, \mathrm{CZ} on output 157, output 160, \mathrm{CZ} on output 157, output 178, \mathrm{CZ} on output 157, output 182, \mathrm{CZ} on output 157, check 204, \mathrm{CZ} on output 157, check 207, \mathrm{CZ} on output 157, check 211, \mathrm{CZ} on output 158, output 159, \mathrm{CZ} on output 158, check 189, \mathrm{CZ} on output 158, check 204, \mathrm{CZ} on output 158, check 207, \mathrm{CZ} on output 158, check 209, \mathrm{CZ} on output 159, output 160, \mathrm{CZ} on output 159, check 204, \mathrm{CZ} on output 159, check 207, \mathrm{CZ} on output 159, check 211, \mathrm{CZ} on output 160, check 189, \mathrm{CZ} on output 160, check 209, \mathrm{CZ} on output 161, output 177, \mathrm{CZ} on output 161, output 179, \mathrm{CZ} on output 161, output 181, \mathrm{CZ} on output 161, output 183, \mathrm{CZ} on output 177, output 179, \mathrm{CZ} on output 177, output 180, \mathrm{CZ} on output 177, output 181, \mathrm{CZ} on output 177, output 183, \mathrm{CZ} on output 177, check 190, \mathrm{CZ} on output 177, check 196, \mathrm{CZ} on output 177, check 201, \mathrm{CZ} on output 177, check 208, \mathrm{CZ} on output 177, check 210, \mathrm{CZ} on output 178, output 179, \mathrm{CZ} on output 178, output 181, \mathrm{CZ} on output 178, output 182, \mathrm{CZ} on output 178, check 205, \mathrm{CZ} on output 178, check 210, \mathrm{CZ} on output 178, check 211, \mathrm{CZ} on output 179, check 190, \mathrm{CZ} on output 179, check 196, \mathrm{CZ} on output 179, check 201, \mathrm{CZ} on output 180, output 183, \mathrm{CZ} on output 180, check 205, \mathrm{CZ} on output 180, check 208, \mathrm{CZ} on output 181, output 182, \mathrm{CZ} on output 181, check 190, \mathrm{CZ} on output 181, check 205, \mathrm{CZ} on output 181, check 208, \mathrm{CZ} on output 181, check 210, \mathrm{CZ} on output 182, output 183, \mathrm{CZ} on output 182, check 205, \mathrm{CZ} on output 182, check 208, \mathrm{CZ} on output 182, check 211, \mathrm{CZ} on output 183, check 190, \mathrm{CZ} on output 183, check 210

These Clifford gates cannot be avoided. No choice of \mathrm{T}, \mathrm{T}^3, \mathrm{T}^5 or \mathrm{T}^\dagger for each rotation removes them; the catalogue proves this by showing that the linear system over \mathbb{Z}_4 the powers would have to solve has no solution.

Rotations are numbered by matrix column, from 0. The correction comes from the columns by the weight expansion of Bravyi and Haah (2012). verify_catalog.py re-derives it, checks the corrected circuit's phase input by input against the gate, and on small circuits simulates it gate by gate.

Convert the output with CNOT and S

A CNOT circuit on the outputs, followed by S, Z and CZ gates, turns this factory's gate into other gates that prepare the same magic state. Type a target gate to check whether it is reachable. If it is, you get the circuit, checked on every basis state.

Or list every gate it reaches. The list is built in your browser and saved as a text file, one gate per line.

Python code that writes the same list

import json, urllib.request

NAMES = {1: "T", 2: "CS", 3: "CCZ"}


def equivalent_gates(k, terms, limit=1_000_000):
    """Every gate a CNOT circuit and S, Z, CZ gates reach from this one.

    A gate is its set of terms mod Clifford: {a} is T, {a,b} is CS and
    {a,b,c} is CCZ on those outputs. CNOT c->t sends x_t to
    x_c + x_t - 2 x_c x_t, so a term on t but not c adds the term with t
    replaced by c, and, below CCZ, the term with c added.
    """
    start = frozenset(frozenset(m) for m in terms)
    seen, queue = {start}, [start]
    for gate in queue:
        for c in range(k):
            for t in range(k):
                if c == t:
                    continue
                new = set(gate)
                for m in gate:
                    if t in m and c not in m:
                        new ^= {(m - {t}) | {c}}
                        if len(m) < 3:
                            new ^= {m | {c}}
                new = frozenset(new)
                if new not in seen:
                    seen.add(new)
                    queue.append(new)
                    if len(seen) > limit:
                        raise RuntimeError(f"more than {limit} equivalent gates")
    return seen


def name(gate, k):
    sep = "," if k > 10 else ""
    terms = sorted((sorted(m) for m in gate), key=lambda m: (len(m), m))
    return "·".join(NAMES[len(m)] + sep.join(map(str, m)) for m in terms) or "I"


url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/960.184.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-960.184.3.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.

Exactly 18,032 faults of weight 3 are undetectable and damaging, so A_{3}=18{,}032. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).

A damaging fault of weight 3 sits on columns [0,1,2].

A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.

Original source

S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535

Provenance

found by an AI search that glues catalogued small factories along a graph of paired-column contractions; exact distance verified from columns; a verified witness, not a maximum

Found by: AI search: graph gluing

Discovery: AI search

1 recorded source

[
 {
  "regime": "AI search: graph gluing",
  "file": "master_catalog/imports/2026-09-18_graph_gluing_d3/factories.json",
  "label": "graph gluing [[960,184,3]]",
  "N": 212,
  "d": 3,
  "d_is_exact": true,
  "origin": null,
  "provenance": "AI search: graph gluing -- eight [[127,23,3]] glued along K8 by 28 paired-column contraction(s) (independent ports); construction and witness in master_catalog/imports/2026-09-18_graph_gluing_d3/witnesses/graph_complete_n960_k184_d3.json",
  "notes": "Exact A3=18032 independently counted; details in master_catalog/imports/2026-09-18_graph_gluing_d3/README.md. General gluing has prior art; publication novelty is not asserted."
 }
]

Use it in code

Load this factory and re-derive every number from its circuit with the catalogue's own verifier.

# git clone https://github.com/shubhamj810/magic-state-factory-repo
# cd magic-state-factory-repo/master_catalog
import json, urllib.request
import verify_catalog as VC

url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/960.184.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]

facts, problems = VC.derive(columns, k, N)    # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N)  # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
      problems or "verified")

Raw record

Show the JSON this page is built from

Source: master_catalog.json, factories[1295].