[[777, 1, 6]] magic-state factory, T0 · Magic State Factory Catalog

The circuit

The 199\times777 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 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| '
out 0 (777)	111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 1 (52)	1·1····11··1111·1111·····1·11111··1·1····111···11·1··················································1·1····11··1111·1111·····1·11111··1·1····111···11·1·················································································································································································································································································································································································································································································································································································································································
check 2 (52)	···11··1··11·11···11·1···11··111·111·11··1·1·1·1···11···················································11··1··11·11···11·1···11··111·111·11··1·1·1·1···11···············································································································································································································································································································································································································································································································································································································································
check 3 (52)	·1···1·1·11···1··1·1·11··1111·11·1·11··1·1···111·1···1················································1···1·1·11···1··1·1·11··1111·11·1·11··1·1···111·1···1··············································································································································································································································································································································································································································································································································································································································
check 4 (52)	11·1··11111·····1·1···11·1··11·1···1····111·1·1·11·1··1··············································11·1··11111·····1·1···11·1··11·1···1····111·1·1·11·1··1·············································································································································································································································································································································································································································································································································································································································
check 5 (48)	1······11··1·111111·11·11·11···1·1····1··11·1··1·······1·············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1············································································································································································································································································································································································································································································································································································································································
check 6 (48)	·1······11··1·111111·11·11·11···1·1····1··11·1··1·······1·············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···········································································································································································································································································································································································································································································································································································································································
check 7 (48)	··1······11··1·111111·11·11·11···1·1····1··11·1··1·······1·············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1··········································································································································································································································································································································································································································································································································································································································
check 8 (44)	1·11···11·1·11······11·1111·1··1··········1111··1·········1··········································1·11···11·1·11······11·1111·1··1··········1111··1·········1·········································································································································································································································································································································································································································································································································································································································
check 9 (48)	····1······11··1·111111·11·11·11···1·1····1··11·1··1·······1·············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1········································································································································································································································································································································································································································································································································································································································
check 10 (52)	···111·1··111·1·1···1·11····1·1·111111···1···11··1·1········1···········································111·1··111·1·1···1·11····1·1·111111···1···11··1·1········1·······································································································································································································································································································································································································································································································································································································································
check 11 (64)	111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1·······································111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1······································································································································································································································································································································································································································································································································································································································
check 12 (52)	11·1··1·111···111···11··1··1·11··111··1··11·111···············1······································11·1··1·111···111···11··1··1·11··111··1··11·111···············1·····································································································································································································································································································································································································································································································································································································································
check 13 (64)	··111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1·······································111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1····································································································································································································································································································································································································································································································································································································································
check 14 (48)	1·1··1···111·1111··11·11····1·1·····1···1·1···11·1·1············1····································1·1··1···111·1111··11·11····1·1·····1···1·1···11·1·1············1···································································································································································································································································································································································································································································································································································································································
check 15 (56)	111·1·1·1··1··11····1··11·1111·1·1·11·1··111·1·1···1·············1···································111·1·1·1··1··11····1··11·1111·1·1·11·1··111·1·1···1·············1··································································································································································································································································································································································································································································································································································································································
check 16 (68)	·11·11···11111111·11····1·111··111·11·11·11·11111··1··············1···································11·11···11111111·11····1·111··111·11·11·11·11111··1··············1·································································································································································································································································································································································································································································································································································································································
check 17 (52)	·111111111···11·1··1·1·····1·1······111111·11·1····················1··································111111111···11·1··1·1·····1·1······111111·11·1····················1································································································································································································································································································································································································································································································································································································································
check 18 (56)	·11·1111··1·11····11··1···1··1·11··1··1111·1·1·111·1················1·································11·1111··1·11····11··1···1··1·11··1··1111·1·1·111·1················1·······························································································································································································································································································································································································································································································································································································································
check 19 (64)	1···1111··11111·11·111·1··1·1·1·1··1·11111··111··1·1·················1·······························1···1111··11111·11·111·1··1·1·1·1··1·11111··111··1·1·················1······························································································································································································································································································································································································································································································································································································································
check 20 (64)	11111111··11·1111·1·1·1·1·1·11·1···1·1·111····111··1··················1······························11111111··11·1111·1·1·1·1·1·11·1···1·1·111····111··1··················1·····························································································································································································································································································································································································································································································································································································································
check 21 (60)	·11··11·1·1·11·1111····1··11···1111111··1·11·1··11·1···················1······························11··11·1·1·11·1111····1··11···1111111··1·11·1··11·1···················1····························································································································································································································································································································································································································································································································································································································
check 22 (48)	11·11·11··11···1·1··11··1···1111··11·1···1···11·························1····························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1···························································································································································································································································································································································································································································································································································································································
check 23 (48)	·11·11·11··11···1·1··11··1···1111··11·1···1···11·························1····························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1··························································································································································································································································································································································································································································································································································································································
check 24 (48)	··11·11·11··11···1·1··11··1···1111··11·1···1···11·························1····························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1·························································································································································································································································································································································································································································································································································································································
check 25 (48)	···11·11·11··11···1·1··11··1···1111··11·1···1···11·························1····························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1························································································································································································································································································································································································································································································································································································································
check 26 (60)	1·1·11····1·11·1111··1··1··1·11111·11·11··11·1·111··························1························1·1·11····1·11·1111··1··1··1·11111·11·11··11·1·111··························1·······················································································································································································································································································································································································································································································································································································································
check 27 (60)	1·1··111·1···111·1111·1···111·11·1·1···111·1··111··1·························1·······················1·1··111·1···111·1111·1···111·11·1·1···111·1··111··1·························1······················································································································································································································································································································································································································································································································································································································
check 28 (44)	···11·1··1·11·1·1111···1·1·1·1·1·1··1·1·1····1································1·························11·1··1·11·1·1111···1·1·1·1·1·1··1·1·1····1································1·····················································································································································································································································································································································································································································································································································································································
check 29 (48)	·1·111·1111···1·········1····1·1··11···1·1111·1·11·1···························1······················1·111·1111···1·········1····1·1··11···1·1111·1·11·1···························1····················································································································································································································································································································································································································································································································································································································
check 30 (56)	1··1·11··1·11··111···1···1111·1·11···11·1··11··111·1····························1····················1··1·11··1·11··111···1···1111·1·11···11·1··11··111·1····························1···················································································································································································································································································································································································································································································································································································································
check 31 (48)	1111··111····1····1··11······1·1··1111·1·11·1····1·1·····························1···················1111··111····1····1··11······1·1··1111·1·11·1····1·1·····························1··················································································································································································································································································································································································································································································································································································································
check 32 (48)	11·····1·11·1·1·11·1·111··111·1·11······1··1····1··1······························1··················11·····1·11·1·1·11·1·111··111·1·11······1··1····1··1······························1·················································································································································································································································································································································································································································································································································································································
check 33 (60)	·1111··11·····11·1·1111111111·1····1·11····111·1·1·1·······························1··················1111··11·····11·1·1111111111·1····1·11····111·1·1·1·······························1················································································································································································································································································································································································································································································································································································································
check 34 (48)	11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1················11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1···············································································································································································································································································································································································································································································································································································································
check 35 (60)	11··1·1111··11·111111··11·1·1·1··1··1···11111···11···································1···············11··1·1111··11·111111··11·1·1·1··1··1···11111···11···································1··············································································································································································································································································································································································································································································································································································································
check 36 (52)	1··1·1··1·11·111·111·1··1·1··1·11··11·····11·1·1···1··································1··············1··1·1··1·11·111·111·1··1·1··1·11··11·····11·1·1···1··································1·············································································································································································································································································································································································································································································································································································································
check 37 (52)	······111·1···1·1111·11····11·1···1·111··111·111·1·····································1···················111·1···1·1111·11····11·1···1·111··111·111·1·····································1············································································································································································································································································································································································································································································································································································································
check 38 (60)	1111····1·······1111··11·11111·11·1·1·11·111··1·11·1····································1············1111····1·······1111··11·11111·11·1·1·11·111··1·11·1····································1···········································································································································································································································································································································································································································································································································································································
check 39 (48)	1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1···········1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1··········································································································································································································································································································································································································································································································································································································
check 40 (48)	·1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1···········1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·········································································································································································································································································································································································································································································································································································································
check 41 (48)	··1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1···········1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1········································································································································································································································································································································································································································································································································································································
check 42 (44)	1·11··111··11·1·····1···111·1·1·····1·111····1·1············································1········1·11··111··11·1·····1···111·1·1·····1·111····1·1············································1·······································································································································································································································································································································································································································································································································································································
check 43 (48)	····1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1···········1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1······································································································································································································································································································································································································································································································································································································
check 44 (56)	1·1111····1·1··111111·1····1·1·1···1·11·11·11··11··1··········································1······1·1111····1·1··111111·1····1·1·1···1·11·11·11··11··1··········································1·····································································································································································································································································································································································································································································································································································································
check 45 (60)	·1···111··1···1·11··1··1·11·11·1111111·1··111··111·1···········································1······1···111··1···1·11··1··1·11·11·1111111·1··111··111·1···········································1····································································································································································································································································································································································································································································································································································································
check 46 (48)	11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1····11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1···································································································································································································································································································································································································································································································································································································
check 47 (48)	·11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1····11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1··································································································································································································································································································································································································································································································································································································
check 48 (52)	1··1··11·11···11·1···11··111·111·11··1·1·1·1···11·················································1··1··1··11·11···11·1···11··111·111·11··1·1·1·1···11·················································1·································································································································································································································································································································································································································································································································································································
check 49 (48)	···11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1····11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1································································································································································································································································································································································································································································································································································································
check 50 (52)	···1·1·11···1··1·1·11··1111·11·1·11··1·1···111·1···1················································1···1·1·11···1··1·1·11··1111·11·1·11··1·1···111·1···1················································1·······························································································································································································································································································································································································································································································································································································
check 51 (40)	··········································································································································································································1··11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11·······································································································································································································································································································································································································································································
check 52 (48)	··········································································································································································································11·1·111···1··11···1··1111··1·1·11·11111·1·····································11·1·111···1··11···1··1111··1·1·11·11111·1······································································································································································································································································································································································································································································
check 53 (48)	··········································································································································································································1111···11··1·1···11·1·11·11·1··111111·1···1····································1111···11··1·1···11·1·11·11·1··111111·1···1·····································································································································································································································································································································································································································································
check 54 (48)	···········································································································································································································1111···11··1·1···11·1·11·11·1··111111·1···1····································1111···11··1·1···11·1·11·11·1··111111·1···1····································································································································································································································································································································································································································································
check 55 (48)	··········································································································································································································1·1··11··1111···11111····1·1·11·111·1·11····1··································1·1··11··1111···11111····1·1·11·111·1·11····1···································································································································································································································································································································································································································································
check 56 (40)	··········································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1··································································································································································································································································································································································································································································
check 57 (40)	···········································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·································································································································································································································································································································································································································································
check 58 (40)	············································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1································································································································································································································································································································································································································································
check 59 (40)	·············································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·······························································································································································································································································································································································································································································
check 60 (40)	··············································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1······························································································································································································································································································································································································································································
check 61 (40)	···············································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·····························································································································································································································································································································································································································································
check 62 (40)	··········································································································································································································1··11··1··111··1·11··1··1111·11·····1·1············1···························1··11··1··111··1·11··1··1111·11·····1·1············1····························································································································································································································································································································································································································································
check 63 (40)	···········································································································································································································1··11··1··111··1·11··1··1111·11·····1·1············1···························1··11··1··111··1·11··1··1111·11·····1·1············1···························································································································································································································································································································································································································································
check 64 (48)	··········································································································································································································1·1111···1·1··111·111·111·11···1···1·111·············1·························1·1111···1·1··111·111·111·11···1···1·111·············1··························································································································································································································································································································································································································································
check 65 (40)	··········································································································································································································11···1····11·1····111111·1·1·1·····1111···············1························11···1····11·1····111111·1·1·1·····1111···············1·························································································································································································································································································································································································································································
check 66 (40)	···········································································································································································································11···1····11·1····111111·1·1·1·····1111···············1························11···1····11·1····111111·1·1·1·····1111···············1························································································································································································································································································································································································································································
check 67 (40)	··········································································································································································································1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················1·1·1·11···1····111·11·1·1·11··11··1··1·················1·······················································································································································································································································································································································································································································
check 68 (40)	···········································································································································································································1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················································································································································································································································································································································································································································
check 69 (48)	··········································································································································································································1·11····11·11··111·11··111·11·1·1111···1··················1····················1·11····11·11··111·11··111·11·1·1111···1··················1·····················································································································································································································································································································································································································································
check 70 (40)	··········································································································································································································11····1··111···1····111··11····1111·11·1···················1···················11····1··111···1····111··11····1111·11·1···················1····················································································································································································································································································································································································································································
check 71 (48)	··········································································································································································································11111·11··1··1·1·11··1·11·1111···11···11····················1··················11111·11··1··1·1·11··1·11·1111···11···11····················1···················································································································································································································································································································································································································································
check 72 (40)	··········································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1··················································································································································································································································································································································································································································
check 73 (40)	···········································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················································································································································································································································································································································································································································
check 74 (40)	············································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1················································································································································································································································································································································································································································
check 75 (32)	··········································································································································································································1····11·111·11······1···1····11·11·····1························1··············1····11·111·11······1···1····11·11·····1························1···············································································································································································································································································································································································································································
check 76 (56)	··········································································································································································································11·11··1·11·1·11111··11·11··11111111·1·1·························1·············11·11··1·11·1·11111··11·11··11111111·1·1·························1··············································································································································································································································································································································································································································
check 77 (48)	··········································································································································································································1111·11·1·1·1······1···1111·1·11·11·1111··························1············1111·11·1·1·1······1···1111·1·11·11·1111··························1·············································································································································································································································································································································································································································
check 78 (40)	··········································································································································································································111····1·1··1··1111·1·1··1111··1··1···1····························1···········111····1·1··1··1111·1·1··1111··1··1···1····························1············································································································································································································································································································································································································································
check 79 (40)	···········································································································································································································111····1·1··1··1111·1·1··1111··1··1···1····························1···········111····1·1··1··1111·1·1··1111··1··1···1····························1···········································································································································································································································································································································································································································
check 80 (40)	··········································································································································································································1·1···1··1··11111··11······1··1·11·111·1·····························1·········1·1···1··1··11111··11······1··1·11·111·1·····························1··········································································································································································································································································································································································································································
check 81 (48)	··········································································································································································································11··1·11··111·1···1·111·1····1·111111·11······························1········11··1·11··111·1···1·111·1····1·111111·11······························1·········································································································································································································································································································································································································································
check 82 (48)	··········································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1········································································································································································································································································································································································································································
check 83 (48)	···········································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1·······································································································································································································································································································································································································································
check 84 (48)	············································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1······································································································································································································································································································································································································································
check 85 (48)	·············································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1·····································································································································································································································································································································································································································
check 86 (48)	··········································································································································································································1··1·1·1111··1·1111·11·111·1·····111··11···································1···1··1·1·1111··1·1111·11·111·1·····111··11···································1····································································································································································································································································································································································································································
check 87 (40)	··········································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1···································································································································································································································································································································································································································
check 88 (40)	···········································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1··································································································································································································································································································································································································································
check 89 (40)	············································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1·································································································································································································································································································································································································································
check 90 (32)	··········································································································································································································································································································································································1·····1··111·1·1·1···11111··1··1·1···································1·····1··111·1·1·1···11111··1··1·1························································································································································································································································································································
check 91 (32)	···········································································································································································································································································································································································1·····1··111·1·1·1···11111··1··1·1···································1·····1··111·1·1·1···11111··1··1·1·······················································································································································································································································································································
check 92 (32)	··········································································································································································································································································································································································1·1···1·111·1······1·11···111·11···1·································1·1···1·111·1······1·11···111·11···1······················································································································································································································································································································
check 93 (32)	···········································································································································································································································································································································································1·1···1·111·1······1·11···111·11···1·································1·1···1·111·1······1·11···111·11···1·····················································································································································································································································································································
check 94 (40)	········································································································································································································································································································································································1·1·1·1·1·11··1111·1···11··1···1111····1·····························1·1·1·1·1·11··1111·1···11··1···1111····1····················································································································································································································································································································
check 95 (40)	·········································································································································································································································································································································································111·1·111···1··1·111··1··111·1·1·1·····1·····························111·1·111···1··1·111··1··111·1·1·1·····1···················································································································································································································································································································
check 96 (40)	···········································································································································································································································································································································································11·1··1111111····11·1·11·1111·········1······························11·1··1111111····11·1·11·1111·········1··················································································································································································································································································································
check 97 (40)	············································································································································································································································································································································································11·1··1111111····11·1·11·1111·········1······························11·1··1111111····11·1·11·1111·········1·················································································································································································································································································································
check 98 (40)	········································································································································································································································································································································································1····11·1··1111111····1··1·11·1111·········1·························1····11·1··1111111····1··1·11·1111·········1················································································································································································································································································································
check 99 (40)	········································································································································································································································································································································································11····11·1··1111111·······1·11·1111·········1························11····11·1··1111111·······1·11·1111·········1···············································································································································································································································································································
check 100 (32)	·········································································································································································································································································································································································1·····1··111·1·1·1····1111··1··1·1··········1························1·····1··111·1·1·1····1111··1··1·1··········1··············································································································································································································································································································
check 101 (28)	·········································································································································································································································································································································································1·1·1···11··1·1·1·11··1······1·1·············1·······················1·1·1···11··1·1·1·11··1······1·1·············1·············································································································································································································································································································
check 102 (28)	··········································································································································································································································································································································································1·1·1···11··1·1·1·11··1······1·1·············1·······················1·1·1···11··1·1·1·11··1······1·1·············1············································································································································································································································································································
check 103 (28)	···········································································································································································································································································································································································1·1·1···11··1·1·1·11··1······1·1·············1·······················1·1·1···11··1·1·1·11··1······1·1·············1···········································································································································································································································································································
check 104 (36)	········································································································································································································································································································································································1·1·1·1····1···111111·1111·1··1··················1···················1·1·1·1····1···111111·1111·1··1··················1··········································································································································································································································································································
check 105 (36)	········································································································································································································································································································································································11·1·1·1····1···111111··111·1··1··················1··················11·1·1·1····1···111111··111·1··1··················1·········································································································································································································································································································
check 106 (36)	·········································································································································································································································································································································································11·1·1·1····1···111111··111·1··1··················1··················11·1·1·1····1···111111··111·1··1··················1········································································································································································································································································································
check 107 (36)	········································································································································································································································································································································································1·11·1·1·1····1···11111···111·1··1··················1················1·11·1·1·1····1···11111···111·1··1··················1·······································································································································································································································································································
check 108 (36)	········································································································································································································································································································································································11·11·1·1·1····1···1111····111·1··1··················1···············11·11·1·1·1····1···1111····111·1··1··················1······································································································································································································································································································
check 109 (52)	········································································································································································································································································································································································11··11·111··11·111·11111111111··11····················1··············11··11·111··11·111·11111111111··11····················1·····································································································································································································································································································
check 110 (52)	········································································································································································································································································································································································111··11·111··11·111·111·1111111··11····················1·············111··11·111··11·111·111·1111111··11····················1····································································································································································································································································································
check 111 (44)	········································································································································································································································································································································································11·1··11111·111···1··1111···11·1·11·····················1············11·1··11111·111···1··1111···11·1·11·····················1···································································································································································································································································································
check 112 (36)	········································································································································································································································································································································································11··1··1·11·1·1··1····11··11·1··111······················1···········11··1··1·11·1·1··1····11··11·1··111······················1··································································································································································································································································································
check 113 (28)	········································································································································································································································································································································································11···1····1·1····111···1·11·1·····1·······················1··········11···1····1·1····111···1·11·1·····1·······················1·································································································································································································································································································
check 114 (28)	·········································································································································································································································································································································································1····1·1···1··1·11·1··1·1···11··1·························1··········1····1·1···1··1·11·1··1·1···11··1·························1································································································································································································································································································
check 115 (28)	··········································································································································································································································································································································································1····1·1···1··1·11·1··1·1···11··1·························1··········1····1·1···1··1·11·1··1·1···11··1·························1·······························································································································································································································································································
check 116 (36)	··········································································································································································································································································································································································11······111111····1·111·1···1111···························1·········11······111111····1·111·1···1111···························1······························································································································································································································································································
check 117 (36)	········································································································································································································································································································································································1··11······111111····1··11·1···1111···························1······1··11······111111····1··11·1···1111···························1·····························································································································································································································································································
check 118 (36)	·········································································································································································································································································································································································11·11··1··1··1·1··1··111··11·1·1·1····························1······11·11··1··1··1·1··1··111··11·1·1·1····························1····························································································································································································································································································
check 119 (36)	········································································································································································································································································································································································1··1·11·11·1·1·····11··1··111111································1····1··1·11·11·1·1·····11··1··111111································1···························································································································································································································································································
check 120 (36)	·········································································································································································································································································································································································1··1·11·11·1·1·····11··1··111111································1····1··1·11·11·1·1·····11··1··111111································1··························································································································································································································································································
check 121 (36)	··········································································································································································································································································································································································1··1·11·11·1·1·····11··1··111111································1····1··1·11·11·1·1·····11··1··111111································1·························································································································································································································································································
check 122 (36)	········································································································································································································································································································································································1··1··1·11·11·1·1·····1···1··111111································1·1··1··1·11·11·1·1·····1···1··111111································1························································································································································································································································································
check 123 (36)	········································································································································································································································································································································································111·1··11111·······1···1111····11·1·································1111·1··11111·······1···1111····11·1·································1·······················································································································································································································································································
check 124 (24)	··················································································································································································································································································································································································································································································································1···11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11···············································································································································································································
check 125 (32)	··················································································································································································································································································································································································································································································································11··1·1·1·11·1·11·1111·1·1·····················11··1·1·1·11·1·11·1111·1·1··············································································································································································································
check 126 (32)	··················································································································································································································································································································································································································································································································111·1··11·····111111·111··1····················111·1··11·····111111·111··1·············································································································································································································
check 127 (24)	··················································································································································································································································································································································································································································································································11111······11···11·1··1····1···················11111······11···11·1··1····1············································································································································································································
check 128 (24)	···················································································································································································································································································································································································································································································································11111······11···11·1··1····1···················11111······11···11·1··1····1···········································································································································································································
check 129 (32)	··················································································································································································································································································································································································································································································································1·11··1·11·11111···111·1·····1·················1·11··1·11·11111···111·1·····1··········································································································································································································
check 130 (32)	··················································································································································································································································································································································································································································································································11·1·1·11·11·11·1·1··111······1················11·1·1·11·11·11·1·1··111······1·········································································································································································································
check 131 (24)	··················································································································································································································································································································································································································································································································111··11·······1··1111·1········1···············111··11·······1··1111·1········1········································································································································································································
check 132 (24)	···················································································································································································································································································································································································································································································································111··11·······1··1111·1········1···············111··11·······1··1111·1········1·······································································································································································································
check 133 (32)	··················································································································································································································································································································································································································································································································1·11·1·1·1·11··11·11·111·········1·············1·11·1·1·1·11··11·11·111·········1······································································································································································································
check 134 (32)	··················································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1············11·1·11··111·1·11111··1···········1·····································································································································································································
check 135 (32)	···················································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1············11·1·11··111·1·11111··1···········1····································································································································································································
check 136 (24)	··················································································································································································································································································································································································································································································································1·111··1·1···1···1·1·1·1············1··········1·111··1·1···1···1·1·1·1············1···································································································································································································
check 137 (24)	··················································································································································································································································································································································································································································································································11·1·····1111·11······11·············1·········11·1·····1111·11······11·············1··································································································································································································
check 138 (24)	··················································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1·································································································································································································
check 139 (24)	···················································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1································································································································································································
check 140 (24)	····················································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1·······························································································································································································
check 141 (24)	·····················································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1······························································································································································································
check 142 (24)	··················································································································································································································································································································································································································································································································1·····1·1··1·111·11···11··················1····1·····1·1··1·111·11···11··················1·····························································································································································································
check 143 (24)	··················································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1····························································································································································································
check 144 (24)	···················································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1···························································································································································································
check 145 (24)	····················································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1··························································································································································································
check 146 (24)	·····················································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1·························································································································································································
check 147 (28)	················································································································································································································································································································································································································································································································································································································111·111·11·111···11···1······················111·111·11·111···11···1·····················································································································
check 148 (24)	················································································································································································································································································································································································································································································································································································································1···11··11·11··1··1·1··11····················1···11··11·11··1··1·1··11···················································································································
check 149 (32)	················································································································································································································································································································································································································································································································································································································11··1·1·1·11·1·11·1111·1·1···················11··1·1·1·11·1·11·1111·1·1··················································································································
check 150 (28)	·····················································································································································································································································································································································································································································································································································································································111·1·111111··1·1·1··1·······················111·1·111111··1·1·1··1·················································································································
check 151 (20)	···················································································································································································································································································································································································································································································································································································································1·11·11···1··1·11·······1····················1·11·11···1··1·11·······1················································································································
check 152 (24)	·················································································································································································································································································································································································································································································································································································································11111······11···11·1··1····1·················11111······11···11·1··1····1···············································································································
check 153 (32)	················································································································································································································································································································································································································································································································································································································1·11··1·11·11111···111·1·····1···············1·11··1·11·11111···111·1·····1··············································································································
check 154 (28)	··················································································································································································································································································································································································································································································································································································································111·11·11·1·1·11···1·1······1················111·11·11·1·1·11···1·1······1·············································································································
check 155 (20)	····················································································································································································································································································································································································································································································································································································································1···11·1111····11··········1·················1···11·1111····11··········1············································································································
check 156 (24)	·················································································································································································································································································································································································································································································································································································································111··11·······1··1111·1········1·············111··11·······1··1111·1········1···········································································································
check 157 (28)	·················································································································································································································································································································································································································································································································································································································1·11·111····1·111·1·1·1·········1············1·11·111····1·111·1·1·1·········1··········································································································
check 158 (20)	··················································································································································································································································································································································································································································································································································································································111···1·1·1··11··1··············1············111···1·1·1··11··1··············1·········································································································
check 159 (32)	·················································································································································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1··········11·1·11··111·1·11111··1···········1········································································································
check 160 (24)	················································································································································································································································································································································································································································································································································································································1·111··1·1···1···1·1·1·1············1········1·111··1·1···1···1·1·1·1············1·······································································································
check 161 (28)	··················································································································································································································································································································································································································································································································································································································11111·1·1··111·11····1·············1·········11111·1·1··111·11····1·············1······································································································
check 162 (24)	················································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1······111··1··111··1··1·1·1·················1·····································································································
check 163 (24)	·················································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1······111··1··111··1··1·1·1·················1····································································································
check 164 (28)	················································································································································································································································································································································································································································································································································································································11·1·111111··1·1·1··1···················1····11·1·111111··1·1·1··1···················1···································································································
check 165 (24)	···················································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1······111··1··111··1··1·1·1·················1··································································································
check 166 (20)	·················································································································································································································································································································································································································································································································································································································11·11···1··1·11·······1··················1···11·11···1··1·11·······1··················1·································································································
check 167 (24)	················································································································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1·11··11·11··1··1·1··11······················1································································································
check 168 (24)	·················································································································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1·11··11·11··1··1·1··11······················1·······························································································
check 169 (16)	··········································································································································································································································································································································································································································································································································································································································································································1·1··1··11111··········1·1··1··11111···························································
check 170 (16)	··········································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1··························································
check 171 (16)	···········································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1·························································
check 172 (16)	············································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1························································
check 173 (16)	·············································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1·······················································
check 174 (16)	··········································································································································································································································································································································································································································································································································································································································································································1·1·1·111··1·····1·····1·1·1·111··1·····1······················································
check 175 (16)	··········································································································································································································································································································································································································································································································································································································································································································1111···1··11······1····1111···1··11······1·····················································
check 176 (16)	··········································································································································································································································································································································································································································································································································································································································································································11·111···11········1···11·111···11········1····················································
check 177 (16)	···········································································································································································································································································································································································································································································································································································································································································································11·111···11········1···11·111···11········1···················································
check 178 (16)	··········································································································································································································································································································································································································································································································································································································································································································1··1··11111··········1·1··1··11111··········1··················································
check 179 (16)	···········································································································································································································································································································································································································································································································································································································································································································1··1··11111··········1·1··1··11111··········1·················································
check 180 (8)	·························································································································································································································································································································································································································································································································································································································································································································································11····11·········11····11·······················
check 181 (8)	························································································································································································································································································································································································································································································································································································································································································································································1···1········1··11···1········1··1···············
check 182 (8)	····························································································································································································································································································································································································································································································································································································································································································································································1····11··1·······1····11··1··················
check 183 (8)	······························································································································································································································································································································································································································································································································································································································································································································································111·····1········111·····1·················
check 184 (8)	····························································································································································································································································································································································································································································································································································································································································································································································1····1·····11····1····1·····11···············
check 185 (8)	···························································································································································································································································································································································································································································································································································································································································································································································1·1·····11·······1·1·····11···················
check 186 (8)	·························································································································································································································································································································································································································································································································································································································································································································································11··1······1·····11··1······1···················
check 187 (16)	························································································································································································································································································································································································································································································································································································································································································································································11·1··11····1··1111·1··11····1··11···············
check 188 (8)	··························································································································································································································································································································································································································································································································································································································································································································································································1·111··1·111···
check 189 (8)	··························································································································································································································································································································································································································································································································································································································································································································································································111··1·111··1··
check 190 (8)	···························································································································································································································································································································································································································································································································································································································································································································································································111··1·111··1·
check 191 (8)	·································································································································································································································································································································································································································································································································································································································································································································································································11111111
check 192 (32)	·········································································································································································································································································································································································································································································································································································································································································································································································11111111111111111111111111111111
check 193 (72)	·································································································································································································································································································································································································································································································································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111
check 194 (140)	·····························································································································································································································································································································································································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 195 (232)	·································································································································································································································································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 196 (348)	·············································································································································································································································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 197 (496)	·························································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 198 (676)	·····································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

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 n777Noisy T states per run.

outputs k1

distance d≥ 6A lower bound proved here. Its source certifies d\ge 17, and a fault of weight 17 is shown below, so d=17.

error coefficient A_{6}not definedUndefined while the distance is only a lower bound.

wires N199

checks r198

V_{\mathrm{ex}}1T states per run. CCZ counts as two.

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d3.7145Overhead per extractable T state. Lower is better. At the certified d=17: 2.3491.

\gamma = \log(n/k)/\log d3.7145Overhead per output qubit. At the certified d=17: 2.3491.

\gamma_T = \log(n/T)/\log d3.7145Overhead per unit of T-count. At the certified d=17: 2.3491.

T-count1Minimal T-count of the output gate.

phase-polynomial degree1Minimised over changes of output basis.

effective width1Rank of the output rows modulo the check rows.

Output gate

1 T0 CS0 CCZon 1 output wire

As gates: \mathrm{T}_{0}

As monomials: 0 (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 58 single-wire gates and 55 \mathrm{CZ} gates: \mathrm{Z} on check 1, \mathrm{Z} on check 2, \mathrm{Z} on check 3, \mathrm{Z} on check 4, \mathrm{Z} on check 8, \mathrm{Z} on check 10, \mathrm{Z} on check 12, \mathrm{Z} on check 16, \mathrm{Z} on check 17, \mathrm{Z} on check 21, \mathrm{Z} on check 26, \mathrm{Z} on check 27, \mathrm{Z} on check 28, \mathrm{Z} on check 33, \mathrm{Z} on check 35, \mathrm{Z} on check 36, \mathrm{Z} on check 37, \mathrm{Z} on check 38, \mathrm{Z} on check 42, \mathrm{Z} on check 45, \mathrm{Z} on check 48, \mathrm{Z} on check 50, \mathrm{Z} on check 101, \mathrm{Z} on check 102 and 89 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

All 113 correction gates

\mathrm{Z} on check 1, \mathrm{Z} on check 2, \mathrm{Z} on check 3, \mathrm{Z} on check 4, \mathrm{Z} on check 8, \mathrm{Z} on check 10, \mathrm{Z} on check 12, \mathrm{Z} on check 16, \mathrm{Z} on check 17, \mathrm{Z} on check 21, \mathrm{Z} on check 26, \mathrm{Z} on check 27, \mathrm{Z} on check 28, \mathrm{Z} on check 33, \mathrm{Z} on check 35, \mathrm{Z} on check 36, \mathrm{Z} on check 37, \mathrm{Z} on check 38, \mathrm{Z} on check 42, \mathrm{Z} on check 45, \mathrm{Z} on check 48, \mathrm{Z} on check 50, \mathrm{Z} on check 101, \mathrm{Z} on check 102, \mathrm{Z} on check 103, \mathrm{Z} on check 104, \mathrm{Z} on check 105, \mathrm{Z} on check 106, \mathrm{Z} on check 107, \mathrm{Z} on check 108, \mathrm{Z} on check 109, \mathrm{Z} on check 110, \mathrm{Z} on check 111, \mathrm{Z} on check 112, \mathrm{Z} on check 113, \mathrm{Z} on check 114, \mathrm{Z} on check 115, \mathrm{Z} on check 116, \mathrm{Z} on check 117, \mathrm{Z} on check 118, \mathrm{Z} on check 119, \mathrm{Z} on check 120, \mathrm{Z} on check 121, \mathrm{Z} on check 122, \mathrm{Z} on check 123, \mathrm{Z} on check 147, \mathrm{Z} on check 150, \mathrm{Z} on check 151, \mathrm{Z} on check 154, \mathrm{Z} on check 155, \mathrm{Z} on check 157, \mathrm{Z} on check 158, \mathrm{Z} on check 161, \mathrm{Z} on check 164, \mathrm{Z} on check 166, \mathrm{Z} on check 194, \mathrm{Z} on check 196, \mathrm{Z} on check 198, \mathrm{CZ} on check 1, check 198, \mathrm{CZ} on check 2, check 198, \mathrm{CZ} on check 3, check 198, \mathrm{CZ} on check 4, check 198, \mathrm{CZ} on check 8, check 198, \mathrm{CZ} on check 10, check 198, \mathrm{CZ} on check 12, check 198, \mathrm{CZ} on check 16, check 198, \mathrm{CZ} on check 17, check 198, \mathrm{CZ} on check 21, check 198, \mathrm{CZ} on check 26, check 198, \mathrm{CZ} on check 27, check 198, \mathrm{CZ} on check 28, check 198, \mathrm{CZ} on check 33, check 198, \mathrm{CZ} on check 35, check 198, \mathrm{CZ} on check 36, check 198, \mathrm{CZ} on check 37, check 198, \mathrm{CZ} on check 38, check 198, \mathrm{CZ} on check 42, check 198, \mathrm{CZ} on check 45, check 198, \mathrm{CZ} on check 48, check 198, \mathrm{CZ} on check 50, check 198, \mathrm{CZ} on check 101, check 196, \mathrm{CZ} on check 102, check 196, \mathrm{CZ} on check 103, check 196, \mathrm{CZ} on check 104, check 196, \mathrm{CZ} on check 105, check 196, \mathrm{CZ} on check 106, check 196, \mathrm{CZ} on check 107, check 196, \mathrm{CZ} on check 108, check 196, \mathrm{CZ} on check 109, check 196, \mathrm{CZ} on check 110, check 196, \mathrm{CZ} on check 111, check 196, \mathrm{CZ} on check 112, check 196, \mathrm{CZ} on check 113, check 196, \mathrm{CZ} on check 114, check 196, \mathrm{CZ} on check 115, check 196, \mathrm{CZ} on check 116, check 196, \mathrm{CZ} on check 117, check 196, \mathrm{CZ} on check 118, check 196, \mathrm{CZ} on check 119, check 196, \mathrm{CZ} on check 120, check 196, \mathrm{CZ} on check 121, check 196, \mathrm{CZ} on check 122, check 196, \mathrm{CZ} on check 123, check 196, \mathrm{CZ} on check 147, check 194, \mathrm{CZ} on check 150, check 194, \mathrm{CZ} on check 151, check 194, \mathrm{CZ} on check 154, check 194, \mathrm{CZ} on check 155, check 194, \mathrm{CZ} on check 157, check 194, \mathrm{CZ} on check 158, check 194, \mathrm{CZ} on check 161, check 194, \mathrm{CZ} on check 164, check 194, \mathrm{CZ} on check 166, check 194

Or no Clifford gate at all: run \mathrm{T}^3 on rotations 0, 3, 6, 7, 8, 9, 10, 11, 14, 16, 19, 20, 24, 27, 31, 32, 33, 37, 40, 41, 43, 44, 46, 47 and 140 more (listed below), and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.

All 164 rotations at T³

0, 3, 6, 7, 8, 9, 10, 11, 14, 16, 19, 20, 24, 27, 31, 32, 33, 37, 40, 41, 43, 44, 46, 47, 48, 51, 101, 104, 107, 108, 109, 110, 111, 112, 115, 117, 120, 121, 125, 128, 132, 133, 134, 138, 141, 142, 144, 145, 147, 148, 149, 152, 362, 363, 364, 365, 366, 367, 371, 373, 374, 377, 378, 383, 385, 387, 388, 389, 393, 394, 431, 432, 433, 434, 435, 436, 440, 442, 443, 446, 447, 452, 454, 456, 457, 458, 462, 463, 593, 596, 597, 603, 604, 605, 606, 607, 608, 610, 611, 612, 615, 636, 637, 639, 640, 643, 644, 645, 646, 647, 654, 658, 659, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 682, 686, 687, 688, 690, 692, 704, 705, 709, 710, 711, 713, 715, 727, 729, 730, 732, 738, 744, 745, 748, 750, 751, 752, 753, 754, 756, 757, 758, 759, 760

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/777.1.6.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-777.1.6.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

6\le d\le 17. No fault of weight below 6 is both undetectable and damaging. None of weight 6 has been found, and one of weight 17 is, so the distance lies between the two.

A damaging fault of weight 17 sits on columns [0,101,202,281,360,429,498,545,592,637,682,705,728,745,762,769,776].

Its source certifies d\ge 17, as a lower bound. That certificate is not re-checked here, but rankings on this site may use it. With the damaging fault of weight 17 above, it makes the distance exactly d=17. Source: Jain and Albert (arXiv:2408.12752), Table I: [[101,1,17]] code of the self-dual [102,51,18] code sub(XQ103) doubled onto [[575,1,15]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 17, with d_sd at least the classical distance less one (their Lemma 2.4); the [[69,1,13]] input's distance is proved here by enumerating every word of SD70 through the punctured coordinate.

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 and V. V. Albert, "Transversal Clifford and T-gate codes of short length and high distance," IEEE J. Sel. Areas Inf. Theory 6, 127-137 (2025); arXiv:2408.12752. doi.org/10.1109/JSAIT.2025.3570832

Provenance

a code of the triorthogonal family of Jain and Albert (arXiv:2408.12752, Table I; transversal_t_codes/), self-dual CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction; a verified witness, not a maximum

Found by: Jain-Albert doubling: triorthogonal family

Discovery: pre-existing

1 recorded source

[
 {
  "regime": "Jain-Albert doubling: triorthogonal family",
  "file": "transversal_t_codes/factories.json",
  "label": "JA-777",
  "N": 199,
  "d": 6,
  "d_is_exact": false,
  "origin": "S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance\", IEEE J. Sel. Areas Inf. Theory 6, 127 (2025), arXiv:2408.12752",
  "provenance": "[[101,1,17]] code of the self-dual [102,51,18] code sub(XQ103) doubled onto [[575,1,15]] (Table I)",
  "notes": "its [[69,1,13]] input is the self-dual [70,35,12] code found by transversal_t_codes/search_sd70.py, whose words through the punctured coordinate all weigh at least 14, in place of the paper's [70,35,14] code, which is only formally self-dual"
 }
]

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/777.1.6.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[1228].

[\![777,\,1,\,6]\!] factory