[[825, 199, 3]] magic-state factory, T0·T1·T2·T3·T4·T5·T6·T7·T8·T9·T10·T11...

The circuit

The 237\times825 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.

output wires
check wires, measured and postselected

wire	0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \|
out 0 (199)	11111·11111·111·1111111111111111111·1·111111111111·1·1·111······························1···························1···1·······················1·····1·········1···1···1·······1··1·111························1·······1·············111······11·1·1·111·············111·······1·111··1····1···1···1·111·1·11111··1·1·111······························1···························1···1·······················1·····1·········1···1···1·······1··1·111························1·······1·············111······11·1·1·111·············111·······1·111··1····1···1···1·111·1·11111··1·1·111······························1···························1···1·······················1·····1·········1···1···1·······1··1·111························1·······1·············111······11·1·1·111·············111·······1·111··1····1···1···1·111·1·11111··1·1·11
out 1 (119)	11111·1111·1···1111····111··1··11····11111··11······1·1···1·····························1···························1···1·······················1·····1·········1···1···1·······1···1···1·······················1·······1·············1···········1·1·1···············1·········1·1·····1···1···1···1·1···1·1·······1·1···1·····························1···························1···1·······················1·····1·········1···1···1·······1···1···1·······················1·······1·············1···········1·1·1···············1·········1·1·····1···1···1···1·1···1·1·······1·1···1·····························1···························1···1·······················1·····1·········1···1···1·······1···1···1·······················1·······1·············1···········1·1·1···············1·········1·1·····1···1···1···1·1···1·1·······1·1··
out 2 (111)	1111·111111····111·1·11···1··1·1·1··1·111·1········1····1··1····························1···························1···1·······················1·······1·······1···1···1·······1··1····1·······················1·······1··············1·······11······1···············1········1··1···1····1···1···1··1···········1····1··1····························1···························1···1·······················1·······1·······1···1···1·······1··1····1·······················1·······1··············1·······11······1···············1········1··1···1····1···1···1··1···········1····1··1····························1···························1···1·······················1·······1·······1···1···1·······1··1····1·······················1·······1··············1·······11······1···············1········1··1···1····1···1···1··1···········1····1
out 3 (103)	1111·11111·1···111··1······1··11··1··1111··1········1···1···1···························1···························1···1·······················1·······1·······1···1···1·······1···1···1·······················1·······1···············1···············1···············1·······1···1···1···1···1···1···1···········1···1···1···························1···························1···1·······················1·······1·······1···1···1·······1···1···1·······················1·······1···············1···············1···············1·······1···1···1···1···1···1···1···········1···1···1···························1···························1···1·······················1·······1·······1···1···1·······1···1···1·······················1·······1···············1···············1···············1·······1···1···1···1···1···1···1···········1···1
out 4 (111)	1··11·1··1··11··1111111···1·1111···1·1···11···1·1····1··1····1··························1·······················································1·····1·········1···············1····11·························1·······1·············111······11······1··············111·······1·····1·1·············11·····1·1·····1··1····1··························1·······················································1·····1·········1···············1····11·························1·······1·············111······11······1··············111·······1·····1·1·············11·····1·1·····1··1····1··························1·······················································1·····1·········1···············1····11·························1·······1·············111······11······1··············111·······1·····1·1·············11·····1·1·····1··1
out 5 (79)	1··11·1··1······111········11··1···1·1···1·1···1·1····1·1·····1·························1·······················································1·····1·········1···············1·······························1·······1·············1·················1·············1·········1·····1·1·············1·1·····1·1·····1·1·····1·························1·······················································1·····1·········1···············1·······························1·······1·············1·················1·············1·········1·····1·1·············1·1·····1·1·····1·1·····1·························1·······················································1·····1·········1···············1·······························1·······1·············1·················1·············1·········1·····1·1·············1·1·····1·1·····1·1
out 6 (79)	1··1·11··1····1111·1·11···1··1·1··········11···········11······1························1·······················································1·······1·······1···············1······11·······················1·······1··············1·······11······1···············1········1······················11··············11······1························1·······················································1·······1·······1···············1······11·······················1·······1··············1·······11······1···············1········1······················11··············11······1························1·······················································1·······1·······1···············1······11·······················1·······1··············1·······11······1···············1········1······················11··············11
out 7 (47)	1··1·11··1······11··1······1··11································1·······················1·······················································1·······1·······1···············1·······························1·······1···············1···············1···············1·······1···············································1·······················1·······················································1·······1·······1···············1·······························1·······1···············1···············1···············1·······1···············································1·······················1·······················································1·······1·······1···············1·······························1·······1···············1···············1···············1·······1········································
out 8 (127)	111·11·1··1·1111··111··111··111·111·11···11·······111·1··········1······················1···························1···1·····························1·1···········1··············1·1111·············································111·········1·1·1···············111·········111··11·············11··········111·1··········1······················1···························1···1·····························1·1···········1··············1·1111·············································111·········1·1·1···············111·········111··11·············11··········111·1··········1······················1···························1···1·····························1·1···········1··············1·1111·············································111·········1·1·1···············111·········111··11·············11··········111·1··
out 9 (71)	111·11·1···1······1····111··1···1········1·1······1···1···········1·····················1···························1···1·····························1·1···········1···············1·················································1···········1·1·1···············1···········1···················1·1·········1···1···········1·····················1···························1···1·····························1·1···········1···············1·················································1···········1·1·1···············1···········1···················1·1·········1···1···········1·····················1···························1···1·····························1·1···········1···············1·················································1···········1·1·1···············1···········1···················1·1·········1···1··
out 10 (63)	111····1··1········1·······1·1···1··11····11·······1····1··········1····················1···························1···1···········································1··············1···················································1················1··············1···········1···11··············11··········1····1··········1····················1···························1···1···········································1··············1···················································1················1··············1···········1···11··············11··········1····1··········1····················1···························1···1···········································1··············1···················································1················1··············1···········1···11··············11··········1····1
out 11 (47)	111····1···1········1······1··1···1·················1···1···········1···················1···························1···1···········································1···············1···················································1···············1···············1···········1·······························1···1···········1···················1···························1···1···········································1···············1···················································1···············1···············1···········1·······························1···1···········1···················1···························1···1···········································1···············1···················································1···············1···············1···········1·······························1···1
out 12 (79)	1···11··1···11·1··111······1111····1·····11············11············1··················1·····························································1·1···············1············11·1·············································111···············1·············111·············1···············11···············11············1··················1·····························································1·1···············1············11·1·············································111···············1·············111·············1···············11···············11············1··················1·····························································1·1···············1············11·1·············································111···············1·············111·············1···············11···············11
out 13 (47)	1···11··1······1··1········11······1·····1·1··························1·················1·····························································1·1···············1···············1·············································1·················1·············1···············1···············1·1·····························1·················1·····························································1·1···············1···············1·············································1·················1·············1···············1···············1·1·····························1·················1·····························································1·1···············1···············1·············································1·················1·············1···············1···············1·1················
out 14 (47)	1·······1·····1····1·······1·1·······1····11···········11··············1················1···············································································1··············1···············································1················1··············1················1··············11··············11··············1················1···············································································1··············1···············································1················1··············1················1··············11··············11··············1················1···············································································1··············1···············································1················1··············1················1··············11··············11
out 15 (31)	1·······1······1····1······1··1······1··································1···············1···············································································1···············1···············································1···············1···············1···············1···············································1···············1···············································································1···············1···············································1···············1···············1···············1···············································1···············1···············································································1···············1···············································1···············1···············1···············1································
out 16 (127)	11111·····11111111···1111······11111·1······1·111··1111··················1··············1···························1···1·······················1·····1····························111111·······················1·······1······················11·1·1···························1·111·1·1·················1··111···1111··················1··············1···························1···1·······················1·····1····························111111·······················1·······1······················11·1·1···························1·111·1·1·················1··111···1111··················1··············1···························1···1·······················1·····1····························111111·······················1·······1······················11·1·1···························1·111·1·1·················1··111···1111··
out 17 (63)	11111···········11·····11······11··1·1······1····1························1·············1···························1···1·······················1·····1·························································1·······1·························1·1···························1·1···1·1·················1·····1·························1·············1···························1···1·······················1·····1·························································1·······1·························1·1···························1·1···1·1·················1·····1·························1·············1···························1···1·······················1·····1·························································1·······1·························1·1···························1·1···1·1·················1·····1········
out 18 (79)	1111·1····11····11···11········1·1···········1···1·11··11··················1············1···························1···1·······················1·······1··························11···························1·······1······················11·······························1··1························1···1··11··11··················1············1···························1···1·······················1·······1··························11···························1·······1······················11·······························1··1························1···1··11··11··················1············1···························1···1·······················1·······1··························11···························1·······1······················11·······························1··1························1···1··11··11
out 19 (47)	1111·1··········11·············1··1··········1···1··························1···········1···························1···1·······················1·······1·······················································1·······1·······················································1···1·······················1···1···························1···········1···························1···1·······················1·······1·······················································1·······1·······················································1···1·······················1···1···························1···········1···························1···1·······················1·······1·······················································1·······1·······················································1···1·······················1···1········
out 20 (79)	1··11·······11··11···11··1·1···1····1·········1·1····1111····················1··········1·······················································1·····1······························11·························1·······1······················11·····1·1·······················1······1·····················1·1·····1111····················1··········1·······················································1·····1······························11·························1·······1······················11·····1·1·······················1······1·····················1·1·····1111····················1··········1·······················································1·····1······························11·························1·······1······················11·····1·1·······················1······1·····················1·1·····1111
out 21 (47)	1··11···········11·······1·1···1·····1·········1·1····························1·········1·······················································1·····1·························································1·······1·····························1·1·······················1·······1·····················1·1·····························1·········1·······················································1·····1·························································1·······1·····························1·1·······················1·······1·····················1·1·····························1·········1·······················································1·····1·························································1·······1·····························1·1·······················1·······1·····················1·1········
out 22 (47)	1··1·1········1111···11········1····1··········································1········1·······················································1·······1······························11·······················1·······1······················11·······························1······1·······················································1········1·······················································1·······1······························11·······················1·······1······················11·······························1······1·······················································1········1·······················································1·······1······························11·······················1·······1······················11·······························1······1·································
out 23 (31)	1··1·1··········11·············1·····1··········································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1································
out 24 (95)	111·11····111111·······11·11····1111··············111··1·························1······1···························1···1·····························1·1··························111111·························································1·1··11·························111·1···························111··1·························1······1···························1···1·····························1·1··························111111·························································1·1··11·························111·1···························111··1·························1······1···························1···1·····························1·1··························111111·························································1·1··11·························111·1···························111··1·
out 25 (47)	111·11·················11·······1··1··············1·····1·························1·····1···························1···1·····························1·1·························································································1·1·····························1···1···························1·····1·························1·····1···························1···1·····························1·1·························································································1·1·····························1···1···························1·····1·························1·····1···························1···1·····························1·1·························································································1·1·····························1···1···························1·····1
out 26 (47)	111·······11··············11·····1···1·············1···1···························1····1···························1···1··························································11··································································11··························1····1··························1···1···························1····1···························1···1··························································11··································································11··························1····1··························1···1···························1····1···························1···1··························································11··································································11··························1····1··························1···1·
out 27 (31)	111·······························1··1··············1···1···························1···1···························1···1···························································································································································1···1···························1···1···························1···1···························1···1···························································································································································1···1···························1···1···························1···1···························1···1···························································································································································1···1···························1···1
out 28 (47)	1···11······11···········11·········11················1·1····························1··1·····························································1·1····························11·······························································11·······························11·····························1·1····························1··1·····························································1·1····························11·······························································11·······························11·····························1·1····························1··1·····························································1·1····························11·······························································11·······························11·····························1·1
out 29 (31)	1···11···················1·1··························1·1·····························1·1·····························································1·1·····························································································1·1·····························································1·1·····························1·1·····························································1·1·····························································································1·1·····························································1·1·····························1·1·····························································1·1·····························································································1·1·····························································1·1
out 30 (31)	1·············11··········11········11·················································11······························································································11······························································11······························11······························································11······························································································11······························································11······························11······························································11······························································································11······························································11······························11································
out 31 (111)	·1····111·1·1·1···1111·1111···········111···11111·1·11··1································1··························1···········································1···1···1··········1·1·1··············································111······1··1·1·11····································1···1···1·····1·1111··1·11··1································1··························1···········································1···1···1··········1·1·1··············································111······1··1·1·11····································1···1···1·····1·1111··1·11··1································1··························1···········································1···1···1··········1·1·1··············································111······1··1·1·11····································1···1···1·····1·1111··1·11··1
out 32 (95)	·1····111··1·1·1··1···1111·1··········111···11···11·1·1·1·································1·························1···········································1···1···1···········1·1·1·············································1·········1·1·1·1·1···································1···1···1·····1·1···1·1·1·1·1·································1·························1···········································1···1···1···········1·1·1·············································1·········1·1·1·1·1···································1···1···1·····1·1···1·1·1·1·1·································1·························1···········································1···1···1···········1·1·1·············································1·········1·1·1·1·1···································1···1···1·····1·1···1·1·1·1·1
out 33 (63)	·1····111·1········1·1····11··········111········1·····11··································1························1···········································1···1···1··········1···················································1·······1·······11···································1···1···1···········1······11··································1························1···········································1···1···1··········1···················································1·······1·······11···································1···1···1···········1······11··································1························1···········································1···1···1··········1···················································1·······1·······11···································1···1···1···········1······11
out 34 (47)	·1····111··1········1·1···············111········1··········································1·······················1···········································1···1···1···········1···················································1·······1···········································1···1···1···········1···········································1·······················1···········································1···1···1···········1···················································1·······1···········································1···1···1···········1···········································1·······················1···········································1···1···1···········1···················································1·······1···········································1···1···1···········1········
out 35 (63)	··1···1·····1·····1111····11···············1··1·11···11······································1··························1·······································1····················1················································111······1·······11···············································1····1·11····11······································1··························1·······································1····················1················································111······1·······11···············································1····1·11····11······································1··························1·······································1····················1················································111······1·······11···············································1····1·11····11··
out 36 (31)	··1···1······1····1···1····················1···1··············································1·························1·······································1·····················1···············································1·········1·······················································1·····1···············································1·························1·······································1·····················1···············································1·········1·······················································1·····1···············································1·························1·······································1·····················1···············································1·········1·······················································1·····1··········
out 37 (47)	··1···1·······1····1·1····11···············1·····1·····11······································1························1·······································1······················1···············································1·······1·······11···············································1·······1······11······································1························1·······································1······················1···············································1·······1·······11···············································1·······1······11······································1························1·······································1······················1···············································1·······1·······11···············································1·······1······11
out 38 (31)	··1···1········1····1·1····················1·····1··············································1·······················1·······································1·······················1···············································1·······1·······················································1·······1···············································1·······················1·······································1·······················1···············································1·······1·······················································1·······1···············································1·······················1·······································1·······················1···············································1·······1·······················································1·······1········
out 39 (63)	·1·····1··1·1·1···111··111·················1··········111········································1··················1···············································1··············1·1·1··············································111·········1·1·1·················································1·············111········································1··················1···············································1··············1·1·1··············································111·········1·1·1·················································1·············111········································1··················1···············································1··············1·1·1··············································111·········1·1·1·················································1·············111
out 40 (47)	·1·····1···1·1·1··1····111·················1··········1···········································1·················1···············································1···············1·1·1·············································1···········1·1·1·················································1·············1···········································1·················1···············································1···············1·1·1·············································1···········1·1·1·················································1·············1···········································1·················1···············································1···············1·1·1·············································1···········1·1·1·················································1·············1··
out 41 (31)	·1·····1··1········1·······1···············1···········1···········································1················1···············································1··············1···················································1················1···············································1··············1···········································1················1···············································1··············1···················································1················1···············································1··············1···········································1················1···············································1··············1···················································1················1···············································1··············1·
out 42 (31)	·1·····1···1········1······1···············1············1···········································1···············1···············································1···············1···················································1···············1···············································1···············1···········································1···············1···············································1···············1···················································1···············1···············································1···············1···········································1···············1···············································1···············1···················································1···············1···············································1···············1
out 43 (47)	··1·····1···1·····111······1···············1··········111············································1··················1···············································1············1················································111···············1···············································1·············111············································1··················1···············································1············1················································111···············1···············································1·············111············································1··················1···············································1············1················································111···············1···············································1·············111
out 44 (31)	··1·····1····1····1········1···············1··········1···············································1·················1···············································1·············1···············································1·················1···············································1·············1···············································1·················1···············································1·············1···············································1·················1···············································1·············1···············································1·················1···············································1·············1···············································1·················1···············································1·············1··
out 45 (31)	··1·····1·····1····1·······1···············1···········1···············································1················1···············································1··············1···············································1················1···············································1··············1···············································1················1···············································1··············1···············································1················1···············································1··············1···············································1················1···············································1··············1···············································1················1···············································1··············1·
out 46 (31)	··1·····1······1····1······1···············1············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1···············································1···············1
out 47 (79)	·1·······1111·11·····1·11··1················1·11111··1··1················································1··········1···························································1··111·11······················································1··1·1···1·················································1··1111·1··1··1················································1··········1···························································1··111·11······················································1··1·1···1·················································1··1111·1··1··1················································1··········1···························································1··111·11······················································1··1·1···1·················································1··1111·1··1··1
out 48 (47)	·1·······1···1········111··1················1·····1···1·1·················································1·········1···························································1·····1·························································1·1·1···1·················································1·······1···1·1·················································1·········1···························································1·····1·························································1·1·1···1·················································1·······1···1·1·················································1·········1···························································1·····1·························································1·1·1···1·················································1·······1···1·1
out 49 (47)	·1·······111···1·····1·····1·················1······1··11··················································1········1···························································1··11···1······················································1········1···················································1·······1··11··················································1········1···························································1··11···1······················································1········1···················································1·······1··11··················································1········1···························································1··11···1······················································1········1···················································1·······1··11
out 50 (31)	·1·······1·····1······1····1·················1······1·······················································1·······1···························································1·······1·······················································1·······1···················································1·······1·······················································1·······1···························································1·······1·······················································1·······1···················································1·······1·······················································1·······1···························································1·······1·······················································1·······1···················································1·······1····
out 51 (47)	··1······1··1········1···1····················1·11···11·1····················································1··········1·······················································1····1·························································1······1······················································1·11····11·1····················································1··········1·······················································1····1·························································1······1······················································1·11····11·1····················································1··········1·······················································1····1·························································1······1······················································1·11····11·1
out 52 (31)	··1······1···1········1··1·····················1········1·····················································1·········1·······················································1·····1·························································1·····1·······················································1·········1·····················································1·········1·······················································1·····1·························································1·····1·······················································1·········1·····················································1·········1·······················································1·····1·························································1·····1·······················································1·········1
out 53 (31)	··1······1····1······1·····1·····················1·····1·······················································1········1·······················································1······1·······················································1········1·······················································1······1·······················································1········1·······················································1······1·······················································1········1·······················································1······1·······················································1········1·······················································1······1·······················································1········1·······················································1······1·
out 54 (31)	··1······1·····1······1····1·····················1······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1·······················································1·······1
out 55 (47)	·1········111·1········11·11··························11·························································1··1······························································111·1··························································1·1··11·····························································11·························································1··1······························································111·1··························································1·1··11·····························································11·························································1··1······························································111·1··························································1·1··11·····························································11·
out 56 (31)	·1···········1·1·······11·····························1·1·························································1·1·································································1·1·························································1·1·································································1·1·························································1·1·································································1·1·························································1·1·································································1·1·························································1·1·································································1·1·························································1·1·································································1·1
out 57 (31)	·1········11··············11···························11··························································11······························································11··································································11······························································11··························································11······························································11··································································11······························································11··························································11······························································11··································································11······························································11
out 58 (31)	··1·········1··1·········11···························11·····························································1··1····························································1··1·····························································11······························································11·····························································1··1····························································1··1·····························································11······························································11·····························································1··1····························································1··1·····························································11······························································11·
out 59 (31)	··1··········1·1·········1·1··························1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1·····························································1·1
out 60 (31)	··1···········11··········11···························11······························································11······························································11······························································11······························································11······························································11······························································11······························································11······························································11······························································11······························································11······························································11······························································11
out 61 (135)	···1111111111111············111·111·11111···1111··11111··································································1······················1·····1·1·······1···1···1·······1··111111·············································································111·········111··11···1···1···1·····1·111···11111··································································1······················1·····1·1·······1···1···1·······1··111111·············································································111·········111··11···1···1···1·····1·111···11111··································································1······················1·····1·1·······1···1···1·······1··111111·············································································111·········111··11···1···1···1·····1·111···11111··
out 62 (63)	···1111111··················1···1·····111···11····1·······································································1·····················1·····1·1·······1···1···1·······1·····················································································1···········1·········1···1···1·····1·1·····1·······································································1·····················1·····1·1·······1···1···1·······1·····················································································1···········1·········1···1···1·····1·1·····1·······································································1·····················1·····1·1·······1···1···1·······1·····················································································1···········1·········1···1···1·····1·1·····1······
out 63 (79)	···1··111111·················1···1··11111·······11·1···11··································································1····················1···············1···1···1·······1··11··················································································1···········1···11···1···1···1··········11··1···11··································································1····················1···············1···1···1·······1··11··················································································1···········1···11···1···1···1··········11··1···11··································································1····················1···············1···1···1·······1··11··················································································1···········1···11···1···1···1··········11··1···11
out 64 (47)	···1··1111····················1···1···111···········1·······································································1···················1···············1···1···1·······1·······················································································1···········1·······1···1···1···············1·······································································1···················1···············1···1···1·······1·······················································································1···········1·······1···1···1···············1·······································································1···················1···············1···1···1·······1·······················································································1···········1·······1···1···1···············1····
out 65 (71)	···1111··1··11··············111····1·······1··1··1···1·11····································································1··················1·····1·1·······1···············1····11···············································································111·············1·················1····1··1····1·11····································································1··················1·····1·1·······1···············1····11···············································································111·············1·················1····1··1····1·11····································································1··················1·····1·1·······1···············1····11···············································································111·············1·················1····1··1····1·11
out 66 (47)	···1111··1··················1······1·······1···1·1····1·······································································1·················1·····1·1·······1···············1·····················································································1···············1·················1·····1·1·····1·······································································1·················1·····1·1·······1···············1·····················································································1···············1·················1·····1·1·····1·······································································1·················1·····1·1·······1···············1·····················································································1···············1·················1·····1·1·····1··
out 67 (47)	···1··1··1····11·············1·······1·····1····11······1······································································1················1···············1···············1······11··············································································1················1···············1······11·······1······································································1················1···············1···············1······11··············································································1················1···············1······11·······1······································································1················1···············1···············1······11··············································································1················1···············1······11·······1
out 68 (31)	···1··1··1····················1······1·····1············1·······································································1···············1···············1···············1·······················································································1···············1···············1···············1·······································································1···············1···············1···············1·······················································································1···············1···············1···············1·······································································1···············1···············1···············1·······················································································1···············1···············1···············1
out 69 (71)	····1··1··11111·············111·111·11·····1·······1·············································································1····················1·············1··············11111··············································································111·········111··11···············1··········1·············································································1····················1·············1··············11111··············································································111·········111··11···············1··········1·············································································1····················1·············1··············11111··············································································111·········111··11···············1··········1·····
out 70 (31)	····1··1·······1············1···1··········1········1·············································································1···················1·············1···················1·············································································1···········1·····················1···········1·············································································1···················1·············1···················1·············································································1···········1·····················1···········1·············································································1···················1·············1···················1·············································································1···········1·····················1···········1····
out 71 (47)	·····1·1··11···1·············1···1··11·····1·······1···············································································1····················1···········1··············11···1··············································································1···········1···11···············1··········1···············································································1····················1···········1··············11···1··············································································1···········1···11···············1··········1···············································································1····················1···········1··············11···1··············································································1···········1···11···············1··········1·····
out 72 (31)	·····1·1·······1··············1···1········1········1···············································································1···················1···········1···················1···············································································1···········1···················1···········1···············································································1···················1···········1···················1···············································································1···········1···················1···········1···············································································1···················1···········1···················1···············································································1···········1···················1···········1····
out 73 (47)	····1···1···11·1············111····1·······1···········1·············································································1················1·················1············11·1·············································································111·············1·················1··············1·············································································1················1·················1············11·1·············································································111·············1·················1··············1·············································································1················1·················1············11·1·············································································111·············1·················1··············1·
out 74 (31)	····1···1······1············1······1·······1············1·············································································1···············1·················1···············1·············································································1···············1·················1···············1·············································································1···············1·················1···············1·············································································1···············1·················1···············1·············································································1···············1·················1···············1·············································································1···············1·················1···············1
out 75 (31)	·····1··1·····1··············1·······1·····1···········1···············································································1················1···············1··············1···············································································1················1···············1··············1···············································································1················1···············1··············1···············································································1················1···············1··············1···············································································1················1···············1··············1···············································································1················1···············1··············1·
out 76 (31)	·····1··1······1··············1······1·····1············1···············································································1···············1···············1···············1···············································································1···············1···············1···············1···············································································1···············1···············1···············1···············································································1···············1···············1···············1···············································································1···············1···············1···············1···············································································1···············1···············1···············1
out 77 (79)	···111····1·111·················1111········1·11·111·11··················································································1······1·····1·1··························1·111··························································································111·1···················1··11·1·11·11··················································································1······1·····1·1··························1·111··························································································111·1···················1··11·1·11·11··················································································1······1·····1·1··························1·111··························································································111·1···················1··11·1·11·11··
out 78 (47)	···111·····1···1················1··1········1····11·1·····················································································1·····1·····1·1···························1···1·························································································1···1···················1·····1·1·1·····················································································1·····1·····1·1···························1···1·························································································1···1···················1·····1·1·1·····················································································1·····1·····1·1···························1···1·························································································1···1···················1·····1·1·1····
out 79 (47)	···1······1····1·················1···1·······1··1··11··11··················································································1····1··································1····1··························································································1····1···················1··1···11··11··················································································1····1··································1····1··························································································1····1···················1··1···11··11··················································································1····1··································1····1··························································································1····1···················1··1···11··11
out 80 (31)	···1·······1···1··················1··1·······1···1··························································································1···1···································1···1···························································································1···1···················1···1···························································································1···1···································1···1···························································································1···1···················1···1···························································································1···1···································1···1···························································································1···1···················1···1········
out 81 (47)	···111······11······················11········1··1···1·1·····················································································1··1·····1·1····························11································································································11····················1··1····1·1·····················································································1··1·····1·1····························11································································································11····················1··1····1·1·····················································································1··1·····1·1····························11································································································11····················1··1····1·1·
out 82 (31)	···111·········································1·1····1·1·····················································································1·1·····1·1·····················································································································································1·1·····1·1·····················································································1·1·····1·1·····················································································································································1·1·····1·1·····················································································1·1·····1·1·····················································································································································1·1·····1·1
out 83 (31)	···1··········11····················11··········11·····························································································11······································11······························································································11······················11······························································································11······································11······························································································11······················11······························································································11······································11······························································································11······················11········
out 84 (47)	····1·····1·111·················1111···············1····1························································································1····1····························1·111··························································································111·1····························1····1························································································1····1····························1·111··························································································111·1····························1····1························································································1····1····························1·111··························································································111·1····························1····1
out 85 (31)	····1······1···1················1··1················1···1·························································································1···1·····························1···1·························································································1···1·····························1···1·························································································1···1·····························1···1·························································································1···1·····························1···1·························································································1···1·····························1···1·························································································1···1·····························1···1
out 86 (31)	·····1····1····1·················1···1·············1····1··························································································1····1··························1····1··························································································1····1··························1····1··························································································1····1··························1····1··························································································1····1··························1····1··························································································1····1··························1····1··························································································1····1··························1····1
out 87 (31)	·····1·····1···1··················1··1··············1···1···························································································1···1···························1···1···························································································1···1···························1···1···························································································1···1···························1···1···························································································1···1···························1···1···························································································1···1···························1···1···························································································1···1···························1···1
out 88 (31)	····1·······11······················11·················11····························································································11······························11································································································11······························11····························································································11······························11································································································11······························11····························································································11······························11································································································11······························11
out 89 (31)	·····1········11····················11·················11······························································································11······························11······························································································11······························11······························································································11······························11······························································································11······························11······························································································11······························11······························································································11······························11
out 90 (87)	······111·111·1·······················1111111111·····1111································································································1······1···1···1··········111·1····································································································1···1···1·111·1·111······1111································································································1······1···1···1··········111·1····································································································1···1···1·111·1·111······1111································································································1······1···1···1··········111·1····································································································1···1···1·111·1·111······1111
out 91 (47)	······111····1·1······················1111··11············································································································1·····1···1···1·············1·1···································································································1···1···1·1···1·1·············································································································1·····1···1···1·············1·1···································································································1···1···1·1···1·1·············································································································1·····1···1···1·············1·1···································································································1···1···1·1···1·1············
out 92 (47)	······111·11··························111·1·····11·········································································································1····1···1···1··········11·······································································································1···1···1··1·······11··········································································································1····1···1···1··········11·······································································································1···1···1··1·······11··········································································································1····1···1···1··········11·······································································································1···1···1··1·······11········
out 93 (31)	······111·····························111··1················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1················
out 94 (47)	······1·····1··1·························11···1··1···1111····································································································1··1····················1··1·············································································································11·····1··1····1111····································································································1··1····················1··1·············································································································11·····1··1····1111····································································································1··1····················1··1·············································································································11·····1··1····1111
out 95 (31)	······1······1·1·························1·1···1·1············································································································1·1·····················1·1·············································································································1·1·····1·1·············································································································1·1·····················1·1·············································································································1·1·····1·1·············································································································1·1·····················1·1·············································································································1·1·····1·1········
out 96 (31)	······1·······11··························11····11·············································································································11······················11··············································································································11······11··············································································································11······················11··············································································································11······11··············································································································11······················11··············································································································11······11········
out 97 (47)	·······1··111·1··························11·······1·1··11········································································································1··1··············111·1··············································································································11··········1·1··11········································································································1··1··············111·1··············································································································11··········1·1··11········································································································1··1··············111·1··············································································································11··········1·1··11
out 98 (31)	·······1·····1·1·························1·1······1·1·············································································································1·1·················1·1·············································································································1·1·········1·1·············································································································1·1·················1·1·············································································································1·1·········1·1·············································································································1·1·················1·1·············································································································1·1·········1·1····
out 99 (31)	·······1··11······························11···········11··········································································································11··············11··················································································································11··············11··········································································································11··············11··················································································································11··············11··········································································································11··············11··················································································································11··············11
out 100 (31)	········1···1··1·························11···········11·············································································································1··1············1··1·············································································································11··············11·············································································································1··1············1··1·············································································································11··············11·············································································································1··1············1··1·············································································································11··············11·
out 101 (31)	········1····1·1·························1·1··········1·1·············································································································1·1·············1·1·············································································································1·1·············1·1·············································································································1·1·············1·1·············································································································1·1·············1·1·············································································································1·1·············1·1·············································································································1·1·············1·1
out 102 (31)	········1·····11··························11···········11··············································································································11··············11··············································································································11··············11··············································································································11··············11··············································································································11··············11··············································································································11··············11··············································································································11··············11
out 103 (47)	·········11·1·11····························1·11·1··11···················································································································1······1··1·1·11·················································································································1··11·1···11···················································································································1······1··1·1·11·················································································································1··11·1···11···················································································································1······1··1·1·11·················································································································1··11·1···11···
out 104 (31)	·········1·1·1······························1····1··1·1···················································································································1·····1···1·1···················································································································1·····1···1·1···················································································································1·····1···1·1···················································································································1·····1···1·1···················································································································1·····1···1·1···················································································································1·····1···1·1··
out 105 (31)	·········11····1·····························1··1···1··1···················································································································1····1··1····1···················································································································1··1····1··1···················································································································1····1··1····1···················································································································1··1····1··1···················································································································1····1··1····1···················································································································1··1····1··1·
out 106 (31)	·········1·1···1·····························1···1··1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1···················································································································1···1···1···1
out 107 (31)	·········1··1··1······························1··1···1··1····················································································································1··1····1··1····················································································································1··1····1··1····················································································································1··1····1··1····················································································································1··1····1··1····················································································································1··1····1··1····················································································································1··1····1··1
out 108 (31)	·········1···1·1·······························1·1····1·1·····················································································································1·1·····1·1·····················································································································1·1·····1·1·····················································································································1·1·····1·1·····················································································································1·1·····1·1·····················································································································1·1·····1·1·····················································································································1·1·····1·1
out 109 (31)	·········1····11································11·····11······················································································································11······11······················································································································11······11······················································································································11······11······················································································································11······11······················································································································11······11······················································································································11······11
out 110 (31)	··········1·1·1···································1·1·1·1························································································································1·1·1·1··························································································································1·1·1·1························································································································1·1·1·1··························································································································1·1·1·1························································································································1·1·1·1··························································································································1·1·1·1
out 111 (31)	···········1·1·1··································1·1·1·1·························································································································1·1·1·1·························································································································1·1·1·1·························································································································1·1·1·1·························································································································1·1·1·1·························································································································1·1·1·1·························································································································1·1·1·1
out 112 (111)	················1·111111·11·111·11111·1··11·11111·····1·1································································································································1······················1·····················111······11·1···11··············111·········111·11····1·········11··1·1111······1·1································································································································1······················1·····················111······11·1···11··············111·········111·11····1·········11··1·1111······1·1································································································································1······················1·····················111······11·1···11··············111·········111·11····1·········11··1·1111······1·1
out 113 (71)	················1·1····1·1·11···1··1·11··1·111···1····1·1·································································································································1·····················1·····················1···········1···1·1·············1···········1···1·1···1·········1·1·1·1···1·····1·1·································································································································1·····················1·····················1···········1···1·1·············1···········1···1·1···1·········1·1·1·1···1·····1·1·································································································································1·····················1·····················1···········1···1·1·············1···········1···1·1···1·········1·1·1·1···1·····1·1
out 114 (63)	················1··1·11·1·11·1···1··111···11·····1·········································································································································1····················1······················1·······11···1··11··············1···········1···11···1··········11·······1··········································································································································1····················1······················1·······11···1··11··············1···········1···11···1··········11·······1··········································································································································1····················1······················1·······11···1··11··············1···········1···11···1··········11·······1········
out 115 (31)	················1···1···1·····1···1···1··········1··········································································································································1···················1·······················1···········1···················1···········1·······1···················1···········································································································································1···················1·······················1···········1···················1···········1·······1···················1···········································································································································1···················1·······················1···········1···················1···········1·······1···················1········
out 116 (79)	················1·11111···1·111······1·1·11···1·11····1·1····································································································································1··················1·····················111······11······1··············111···············1·······1·····11·····1·11·····1·1····································································································································1··················1·····················111······11······1··············111···············1·······1·····11·····1·11·····1·1····································································································································1··················1·····················111······11······1··············111···············1·······1·····11·····1·11·····1·1
out 117 (47)	················1·1········11········1·1·1·1···1······1·1·····································································································································1·················1·····················1·················1·············1·················1·······1·····1·1·····1·······1·1·····································································································································1·················1·····················1·················1·············1·················1·······1·····1·1·····1·······1·1·····································································································································1·················1·····················1·················1·············1·················1·······1·····1·1·····1·······1·1
out 118 (47)	················1··1·11···1··1·······1·1··11·····1·············································································································································1················1······················1·······11······1···············1················1·······1······11·······1··············································································································································1················1······················1·······11······1···············1················1·······1······11·······1··············································································································································1················1······················1·······11······1···············1················1·······1······11·······1········
out 119 (31)	················1···1······1··1······1·1·········1··············································································································································1···············1·······················1···············1···············1···············1·······1···············1···············································································································································1···············1·······················1···············1···············1···············1·······1···············1···············································································································································1···············1·······················1···············1···············1···············1·······1···············1········
out 120 (95)	·················1111··1·1·1111·11111···111·······1·11·11········································································································································1······················1·············111·········1···1·1·············111·········111·11············1·11··········1·11·11········································································································································1······················1·············111·········1···1·1·············111·········111·11············1·11··········1·11·11········································································································································1······················1·············111·········1···1·1·············111·········111·11············1·11··········1·11·11
out 121 (63)	·················11····1·1·11···1··1·1··11·1······1·1·1···········································································································································1·····················1·············1···········1···1·1·············1···········1···1·1···········1·1·1·········1·1·1···········································································································································1·····················1·············1···········1···1·1·············1···········1···1·1···········1·1·1·········1·1·1···········································································································································1·····················1·············1···········1···1·1·············1···········1···1·1···········1·1·1·········1·1·1··
out 122 (47)	·················1·1····1····1···1··11··1·11············1··········································································································································1····················1··············1············1··················1···········1···11···········1··11···············1··········································································································································1····················1··············1············1··················1···········1···11···········1··11···············1··········································································································································1····················1··············1············1··················1···········1···11···········1··11···············1
out 123 (31)	·················1··1···1·····1···1·····1···············1···········································································································································1···················1···············1···········1···················1···········1···············1···················1···········································································································································1···················1···············1···········1···················1···········1···············1···················1···········································································································································1···················1···············1···········1···················1···········1···············1···················1
out 124 (63)	·················1111······1111······1···111·········111·············································································································································1··················1·············111···············1·············111···············1·············111············111·············································································································································1··················1·············111···············1·············111···············1·············111············111·············································································································································1··················1·············111···············1·············111···············1·············111············111·
out 125 (31)	·················11········11········1···1··············1·············································································································································1·················1·············1·················1·············1·················1·············1·················1·············································································································································1·················1·············1·················1·············1·················1·············1·················1·············································································································································1·················1·············1·················1·············1·················1·············1·················1
out 126 (31)	·················1·1·······1·1·······1····1·············1··············································································································································1················1··············1················1··············1················1··············1················1··············································································································································1················1··············1················1··············1················1··············1················1··············································································································································1················1··············1················1··············1················1··············1················1
out 127 (31)	·················1··1······1··1······1·····1············1···············································································································································1···············1···············1···············1···············1···············1···············1···············1···············································································································································1···············1···············1···············1···············1···············1···············1···············1···············································································································································1···············1···············1···············1···············1···············1···············1···············1
out 128 (63)	················1····111···1····111··1······1·111······11················································································································································1······1······························11·1·····1·························111···1·················1··111·······11················································································································································1······1······························11·1·····1·························111···1·················1··111·······11················································································································································1······1······························11·1·····1·························111···1·················1··111·······11
out 129 (31)	················1······1···1····1····1······1····1························································································································································1·····1·································1·····1·························1·····1·················1·····1·························································································································································1·····1·································1·····1·························1·····1·················1·····1·························································································································································1·····1·································1·····1·························1·····1·················1·····1········
out 130 (47)	················1····11·1··1·····1···1·······1···1·····11··················································································································································1····1······························11···1···1··························1····1···················1···1······11··················································································································································1····1······························11···1···1··························1····1···················1···1······11··················································································································································1····1······························11···1···1··························1····1···················1···1······11
out 131 (31)	················1·······1··1······1··1·······1···1··························································································································································1···1···································1···1···························1···1···················1···1···························································································································································1···1···································1···1···························1···1···················1···1···························································································································································1···1···································1···1···························1···1···················1···1········
out 132 (47)	················1····11··1·1·······11·········1·1······11····················································································································································1··1······························11·····1·1·····························11·····················1·1·······11····················································································································································1··1······························11·····1·1·····························11·····················1·1·······11····················································································································································1··1······························11·····1·1·····························11·····················1·1·······11
out 133 (31)	················1········1·1·······1·1·········1·1····························································································································································1·1·····································1·1·····························1·1·····················1·1·····························································································································································1·1·····································1·1·····························1·1·····················1·1·····························································································································································1·1·····································1·1·····························1·1·····················1·1········
out 134 (31)	················1····11·············11·················11······················································································································································11······························11······································11······························11······················································································································································11······························11······································11······························11······················································································································································11······························11······································11······························11
out 135 (47)	·················1·····1··1·····111··1············1··11·1························································································································································1······1·························1····1··························111···1·························1··11·1························································································································································1······1·························1····1··························111···1·························1··11·1························································································································································1······1·························1····1··························111···1·························1··11·1
out 136 (31)	·················1·····1···1····1····1············1·····1·························································································································································1·····1·························1·····1·························1·····1·························1·····1·························································································································································1·····1·························1·····1·························1·····1·························1·····1·························································································································································1·····1·························1·····1·························1·····1·························1·····1
out 137 (31)	·················1······1·1······1···1··············1··1···························································································································································1····1···························1··1···························1····1···························1··1···························································································································································1····1···························1··1···························1····1···························1··1···························································································································································1····1···························1··1···························1····1···························1··1·
out 138 (31)	·················1······1··1······1··1··············1···1···························································································································································1···1···························1···1···························1···1···························1···1···························································································································································1···1···························1···1···························1···1···························1···1···························································································································································1···1···························1···1···························1···1···························1···1
out 139 (31)	·················1·······11········11················1··1····························································································································································1··1·····························11······························11·····························1··1····························································································································································1··1·····························11······························11·····························1··1····························································································································································1··1·····························11······························11·····························1··1
out 140 (31)	·················1·······1·1·······1·1················1·1·····························································································································································1·1·····························1·1·····························1·1·····························1·1·····························································································································································1·1·····························1·1·····························1·1·····························1·1·····························································································································································1·1·····························1·1·····························1·1·····························1·1
out 141 (31)	·················1········11········11·················11······························································································································································11······························11······························11······························11······························································································································································11······························11······························11······························11······························································································································································11······························11······························11······························11
out 142 (79)	··················1111·1·11···········1····111111·111··11································································································································································1············111······1··1···11····································1···········1·1·1111··111··11································································································································································1············111······1··1···11····································1···········1·1·1111··111··11································································································································································1············111······1··1···11····································1···········1·1·1111··111··11
out 143 (47)	··················1···11·1·1··········1····111···11·······································································································································································1···········1·········1·1···1·1···································1···········1·1·1···1·1·······································································································································································1···········1·········1·1···1·1···································1···········1·1·1···1·1·······································································································································································1···········1·········1·1···1·1···································1···········1·1·1···1·1······
out 144 (47)	···················1·1··1·11··········1····1·····1·1···11··································································································································································1···········1·······1····1··11···································1···········1·······1··1···11··································································································································································1···········1·······1····1··11···································1···········1·······1··1···11··································································································································································1···········1·······1····1··11···································1···········1·······1··1···11
out 145 (31)	····················1·1·1·············1····1·····1··1·······································································································································································1···········1·······1···1·······································1···········1·······1···1·······································································································································································1···········1·······1···1·······································1···········1·······1···1·······································································································································································1···········1·······1···1·······································1···········1·······1···1····
out 146 (47)	··················1111····1············1···1··1·11····1······································································································································································1········111······1·······1········································1·······1····1·11·····1······································································································································································1········111······1·······1········································1·······1····1·11·····1······································································································································································1········111······1·······1········································1·······1····1·11·····1··
out 147 (31)	··················1···1····1···········1···1···1······1·······································································································································································1·······1·········1·······1·······································1·······1·····1·······1·······································································································································································1·······1·········1·······1·······································1·······1·····1·······1·······································································································································································1·······1·········1·······1·······································1·······1·····1·······1··
out 148 (31)	···················1·1····1············1···1·····1······1······································································································································································1·······1·······1·······1········································1·······1·······1·······1······································································································································································1·······1·······1·······1········································1·······1·······1·······1······································································································································································1·······1·······1·······1········································1·······1·······1·······1
out 149 (31)	····················1·1····1···········1···1·····1······1·······································································································································································1·······1·······1·······1·······································1·······1·······1·······1·······································································································································································1·······1·······1·······1·······································1·······1·······1·······1·······································································································································································1·······1·······1·······1·······································1·······1·······1·······1
out 150 (47)	··················111··1·1··············1··1·······1·11·1········································································································································································1····111·········1···1·············································1···1··········1·11·1········································································································································································1····111·········1···1·············································1···1··········1·11·1········································································································································································1····111·········1···1·············································1···1··········1·11·1
out 151 (31)	··················1····1·1··············1··1········1···1·········································································································································································1···1···········1···1·············································1···1···········1···1·········································································································································································1···1···········1···1·············································1···1···········1···1·········································································································································································1···1···········1···1·············································1···1···········1···1
out 152 (31)	···················1····1··1············1··1·······1···1···········································································································································································1···1············1···1···········································1···1··········1···1···········································································································································································1···1············1···1···········································1···1··········1···1···········································································································································································1···1············1···1···········································1···1··········1···1·
out 153 (31)	····················1···1··1············1··1········1···1···········································································································································································1···1···········1···1···········································1···1···········1···1···········································································································································································1···1···········1···1···········································1···1···········1···1···········································································································································································1···1···········1···1···········································1···1···········1···1
out 154 (31)	··················111································1111············································································································································································1111············································································1111············································································································································································1111············································································1111············································································································································································1111············································································1111
out 155 (47)	·····················1·1···1················1·111·111··1·················································································································································································1·····1··1·····1·················································1··111··111··1·················································································································································································1·····1··1·····1·················································1··111··111··1·················································································································································································1·····1··1·····1·················································1··111··111··1·
out 156 (31)	······················11···1················1····11·····1·················································································································································································1·····1·1·····1·················································1·····1·1·····1·················································································································································································1·····1·1·····1·················································1·····1·1·····1·················································································································································································1·····1·1·····1·················································1·····1·1·····1
out 157 (31)	·····················1··1··1·················1···1·1···1···················································································································································································1···1····1···1···················································1···1··1···1···················································································································································································1···1····1···1···················································1···1··1···1···················································································································································································1···1····1···1···················································1···1··1···1·
out 158 (31)	······················1·1··1·················1···1··1···1···················································································································································································1···1···1···1···················································1···1···1···1···················································································································································································1···1···1···1···················································1···1···1···1···················································································································································································1···1···1···1···················································1···1···1···1
out 159 (31)	·····················1···1·1··················1·1·····1·1····················································································································································································1·1······1·1····················································1·1······1·1····················································································································································································1·1······1·1····················································1·1······1·1····················································································································································································1·1······1·1····················································1·1······1·1
out 160 (31)	······················1··1·1···················1·1····1·1·····················································································································································································1·1·····1·1·····················································1·1·····1·1·····················································································································································································1·1·····1·1·····················································1·1·····1·1·····················································································································································································1·1·····1·1·····················································1·1·····1·1
out 161 (31)	·······················1··11·······················1111··························································································································································································11····11··························································1111··························································································································································································11····11··························································1111··························································································································································································11····11··························································1111··
out 162 (31)	························1·11·······················11··11··························································································································································································11··11··························································11··11··························································································································································································11··11··························································11··11··························································································································································································11··11··························································11··11
out 163 (31)	·························111·························1111····························································································································································································1111····························································1111····························································································································································································1111····························································1111····························································································································································································1111····························································1111
out 164 (79)	····························111111111·1····11111·11····11································································································································································································1············111·······1·111·11····1···········1·1·111·1·1····11································································································································································································1············111·······1·111·11····1···········1·1·111·1·1····11································································································································································································1············111·······1·111·11····1···········1·1·111·1·1····11
out 165 (47)	····························1··11··1·11····111···11·······································································································································································································1···········1·········1·1···1·1···1···········1·1·1···1·1·······································································································································································································1···········1·········1·1···1·1···1···········1·1·1···1·1·······································································································································································································1···········1·········1·1···1·1···1···········1·1·1···1·1······
out 166 (47)	·····························1·1·1··111····1····1···1··11··································································································································································································1···········1········1··1···11···1···········1······1····1··11··································································································································································································1···········1········1··1···11···1···········1······1····1··11··································································································································································································1···········1········1··1···11···1···········1······1····1··11
out 167 (31)	······························11··1···1····1·····1··1·······································································································································································································1···········1·······1···1·······1···········1·······1···1·······································································································································································································1···········1·······1···1·······1···········1·······1···1·······································································································································································································1···········1·······1···1·······1···········1·······1···1····
out 168 (47)	····························1111·····1·1···1··1·······111····································································································································································································1········111·······1·······1·······1·······1····1········111····································································································································································································1········111·······1·······1·······1·······1····1········111····································································································································································································1········111·······1·······1·······1·······1····1········111
out 169 (31)	····························1··1·····1·1···1···1······1·······································································································································································································1·······1·········1·······1·······1·······1·····1·······1·······································································································································································································1·······1·········1·······1·······1·······1·····1·······1·······································································································································································································1·······1·········1·······1·······1·······1·····1·······1··
out 170 (31)	·····························1·1·····1·1···1····1······1·······································································································································································································1·······1········1·······1·······1·······1······1·······1·······································································································································································································1·······1········1·······1·······1·······1······1·······1·······································································································································································································1·······1········1·······1·······1·······1······1·······1·
out 171 (31)	······························11·····1·1···1·····1······1·······································································································································································································1·······1·······1·······1·······1·······1·······1·······1·······································································································································································································1·······1·······1·······1·······1·······1·······1·······1·······································································································································································································1·······1·······1·······1·······1·······1·······1·······1
out 172 (63)	····························111·111111··1··1········1111·········································································································································································································1····111·········111·111···········1···1···········1111·········································································································································································································1····111·········111·111···········1···1···········1111·········································································································································································································1····111·········111·111···········1···1···········1111·
out 173 (31)	····························1···1··1····1··1········1···1·········································································································································································································1···1···········1···1·············1···1···········1···1·········································································································································································································1···1···········1···1·············1···1···········1···1·········································································································································································································1···1···········1···1·············1···1···········1···1
out 174 (31)	·····························1···1··1···1··1········1···1··········································································································································································································1···1···········1···1············1···1···········1···1··········································································································································································································1···1···········1···1············1···1···········1···1··········································································································································································································1···1···········1···1············1···1···········1···1
out 175 (31)	······························1···1··1··1··1········1···1···········································································································································································································1···1···········1···1···········1···1···········1···1···········································································································································································································1···1···········1···1···········1···1···········1···1···········································································································································································································1···1···········1···1···········1···1···········1···1
out 176 (31)	····························111······················1111············································································································································································································1111············································1111············································································································································································································1111············································1111············································································································································································································1111············································1111
out 177 (47)	·······························1111··1······1·11·11····1·················································································································································································································1······1·111···1·················1··11·1·1····1·················································································································································································································1······1·111···1·················1··11·1·1····1·················································································································································································································1······1·111···1·················1··11·1·1····1·
out 178 (31)	·······························11····1······1····11·····1·················································································································································································································1·····1·1·····1·················1·····1·1·····1·················································································································································································································1·····1·1·····1·················1·····1·1·····1·················································································································································································································1·····1·1·····1·················1·····1·1·····1
out 179 (31)	·······························1·1···1·······1··1···1··1···················································································································································································································1····1··1····1···················1··1····1··1···················································································································································································································1····1··1····1···················1··1····1··1···················································································································································································································1····1··1····1···················1··1····1··1·
out 180 (31)	·······························1··1··1·······1···1··1···1···················································································································································································································1···1···1···1···················1···1···1···1···················································································································································································································1···1···1···1···················1···1···1···1···················································································································································································································1···1···1···1···················1···1···1···1
out 181 (31)	·······························1···11·········1··1····11·····················································································································································································································1··1·····11·····················1··1·····11·····················································································································································································································1··1·····11·····················1··1·····11·····················································································································································································································1··1·····11·····················1··1·····11·
out 182 (31)	·······························1···1·1·········1·1····1·1·····················································································································································································································1·1·····1·1·····················1·1·····1·1·····················································································································································································································1·1·····1·1·····················1·1·····1·1·····················································································································································································································1·1·····1·1·····················1·1·····1·1
out 183 (31)	·······························1····11··········11·····11······················································································································································································································11······11······················11······11······················································································································································································································11······11······················11······11······················································································································································································································11······11······················11······11
out 184 (31)	································111··················1111························································································································································································································1111································1111························································································································································································································1111································1111························································································································································································································1111································1111
out 185 (31)	···································111···············1111····························································································································································································································1111····························1111····························································································································································································································1111····························1111····························································································································································································································1111····························1111
out 186 (47)	······································1··11·1111···11·1·1································································································································································································································1··1·········11··1·111····11·1·1································································································································································································································1··1·········11··1·111····11·1·1································································································································································································································1··1·········11··1·111····11·1·1
out 187 (31)	······································1··1·111········1·1·································································································································································································································1·1·········1·1·1·1·········1·1·································································································································································································································1·1·········1·1·1·1·········1·1·································································································································································································································1·1·········1·1·1·1·········1·1
out 188 (31)	······································1···11····11·11······································································································································································································································11··········11······11··11······································································································································································································································11··········11······11··11······································································································································································································································11··········11······11··11····
out 189 (31)	·······································1·11···1··1····11·····································································································································································································································1··1·····11·····1··1·····11·····································································································································································································································1··1·····11·····1··1·····11·····································································································································································································································1··1·····11·····1··1·····11·
out 190 (31)	·······································1·1·1···1·1····1·1·····································································································································································································································1·1·····1·1·····1·1·····1·1·····································································································································································································································1·1·····1·1·····1·1·····1·1·····································································································································································································································1·1·····1·1·····1·1·····1·1
out 191 (31)	·······································1··11····11·····11······································································································································································································································11······11······11······11······································································································································································································································11······11······11······11······································································································································································································································11······11······11······11
out 192 (31)	········································111·······11·1··1········································································································································································································································1··1·11··········11·1··1········································································································································································································································1··1·11··········11·1··1········································································································································································································································1··1·11··········11·1··1
out 193 (31)	········································11·1······1·1·1·1·········································································································································································································································1·1·1·1·········1·1·1·1·········································································································································································································································1·1·1·1·········1·1·1·1·········································································································································································································································1·1·1·1·········1·1·1·1
out 194 (31)	········································1·11·······11··11··········································································································································································································································11··11··········11··11··········································································································································································································································11··11··········11··11··········································································································································································································································11··11··········11··11
out 195 (31)	·········································111·········1111············································································································································································································································1111············1111············································································································································································································································1111············1111············································································································································································································································1111············1111
out 196 (31)	············································1·11···11··11················································································································································································································································11··11····11··11················································································································································································································································11··11····11··11················································································································································································································································11··11····11··11
out 197 (31)	·············································1··11·11··11··················································································································································································································································11··11··11··11··················································································································································································································································11··11··11··11··················································································································································································································································11··11··11··11
out 198 (31)	··················································1111111························································································································································································································································11111111························································································································································································································································11111111························································································································································································································································11111111
check 199 (512)	·························································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 200 (32)	··········11··11···································11··11··························································································································11··11··························································································································11··11··························································································································11··11··························································································································11··11··························································································································11··11··························································································································11··11
check 201 (32)	············1111·····································1111····························································································································1111····························································································································1111····························································································································1111····························································································································1111····························································································································1111····························································································································1111
check 202 (256)	·····························································································································································································································································································································1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111
check 203 (32)	················11····1····1···1·····1···········1······1·······················································································································································1·······1·······················1·······1·······················1·······1·······················1·······1·······················································································································································1·······1·······················1·······1·······················1·······1·······················1·······1·······················································································································································1·······1·······················1·······1·······················1·······1·······················1·······1
check 204 (256)	·································································11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········································································································································································································································································11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111
check 205 (256)	·········································································································································································································································································································································1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111
check 206 (256)	·········································································1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················································································································································································································································································1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111
check 207 (256)	···························································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··································································································································································································································································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11
check 208 (256)	·························································································································································································································································································································································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111
check 209 (32)	··················1·1····1·1·············1·1··········1·1·············································································································································································1·1·············1·1·············································1·1·············1·1·············································································································································································1·1·············1·1·············································1·1·············1·1·············································································································································································1·1·············1·1·············································1·1·············1·1
check 210 (32)	···················11·····11··············11···········11··············································································································································································11··············11··············································11··············11··············································································································································································11··············11··············································11··············11··············································································································································································11··············11··············································11··············11
check 211 (512)	·························································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 212 (256)	·························································································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································································································································································································································································································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111
check 213 (32)	·····················11···11····················11·····11······················································································································································································11······11······················································11······11······················································································································································································11······11······················································11······11······················································································································································································11······11······················································11······11
check 214 (32)	·······················111·1······················1·1·1·1·························································································································································································1·1·1·1·························································1·1·1·1·························································································································································································1·1·1·1·························································1·1·1·1·························································································································································································1·1·1·1·························································1·1·1·1
check 215 (256)	··························································································································································································································································································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1
check 216 (256)	·································································································································································································································································································································11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111
check 217 (256)	·····························································1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····································································································································································································································································1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111
check 218 (32)	·11········1···1········1··1························1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1···························································1···1
check 219 (32)	····························1·1····1·1···1·1··········1·1·············································································································································································································1·1·············1·1·············1·1·············1·1·············································································································································································································1·1·············1·1·············1·1·············1·1·············································································································································································································1·1·············1·1·············1·1·············1·1
check 220 (32)	·····························11·····11····11···········11··············································································································································································································11··············11··············11··············11··············································································································································································································11··············11··············11··············11··············································································································································································································11··············11··············11··············11
check 221 (32)	······1·11·····1·······················1···1·····1······1·······································································································1·······1·······1·······1·······································································································1·······1·······1·······1·······································································································1·······1·······1·······1·······································································································1·······1·······1·······1·······································································································1·······1·······1·······1·······································································································1·······1·······1·······1
check 222 (256)	·························································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 223 (256)	·························································································································································································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 224 (32)	································1·11·1············1·1·1·1·························································································································································································································1·1·1·1·························1·1·1·1·························································································································································································································1·1·1·1·························1·1·1·1·························································································································································································································1·1·1·1·························1·1·1·1
check 225 (32)	·································11·11·············11··11··························································································································································································································11··11··························11··11··························································································································································································································11··11··························11··11··························································································································································································································11··11··························11··11
check 226 (256)	··························································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·································································································································································································································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1
check 227 (32)	······································111··1·1···1··1···1···································································································································································································································1···1···1···1···1···1···1···1···································································································································································································································1···1···1···1···1···1···1···1···································································································································································································································1···1···1···1···1···1···1···1
check 228 (32)	····11·······1·1···················1·1················1·1·····························································································1·1·····························1·1·····························································································1·1·····························1·1·····························································································1·1·····························1·1·····························································································1·1·····························1·1·····························································································1·1·····························1·1·····························································································1·1·····························1·1
check 229 (256)	···························································································································································································································································································································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11
check 230 (32)	·······11··1···1························1··1········1···1···········································································································1···1···········1···1···········································································································1···1···········1···1···········································································································1···1···········1···1···········································································································1···1···········1···1···········································································································1···1···········1···1···········································································································1···1···········1···1
check 231 (32)	1·1··1·········1·1·········1·········1··················1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1·······························1
check 232 (256)	·························································································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111
check 233 (32)	············································11·1·11·1·1·1·················································································································································································································································1·1·1·1·1·1·1·1·················································································································································································································································1·1·1·1·1·1·1·1·················································································································································································································································1·1·1·1·1·1·1·1
check 234 (256)	·························································································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111
check 235 (32)	··············································1111···1111····················································································································································································································································1111····1111····················································································································································································································································1111····1111····················································································································································································································································1111····1111
check 236 (32)	···1·1···1·····1···············1·····1···········1······1·······················································································1·······1·······················1·······1·······················································································1·······1·······················1·······1·······················································································1·······1·······················1·······1·······················································································1·······1·······················1·······1·······················································································1·······1·······················1·······1·······················································································1·······1·······················1·······1

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

Figures of merit

inputs n825Noisy T states per run.

outputs k199

distance d3Exact, proved and witnessed here.

error coefficient A_{3}224Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.

wires N237

checks r38

V_{\mathrm{ex}}199T states per run. CCZ counts as two.

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.2944Overhead per extractable T state. Lower is better.

\gamma = \log(n/k)/\log d1.2944Overhead per output qubit.

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

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

phase-polynomial degreenot computedMinimised over changes of output basis.

effective width199Rank of the output rows modulo the check rows.

Output gate

199 T0 CS0 CCZon 199 output wires

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

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

All 199 correction gates

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

Or no Clifford gate at all: run every rotation as \mathrm{T}^\dagger. 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.

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/825.199.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-825.199.3.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

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

Exactly 224 faults of weight 3 are undetectable and damaging, so A_{3}=224. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).

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

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

Original source

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

Provenance

built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows

Found by: AI search (gamma frontier): from Wills parent codes

Discovery: AI search

1 recorded source

[
 {
  "regime": "AI search (gamma frontier): from Wills parent codes",
  "file": "gamma_frontier_release/protocols/weighted_sources_825_199_3.json",
  "label": "weighted_sources_825_199_3",
  "N": 237,
  "d": 3,
  "d_is_exact": true,
  "origin": "Triorthogonal; matrix verified",
  "provenance": "gamma frontier release record weighted_sources_825_199_3 (source catalogue id weighted_sources_825_199_3); construction: Triorthogonal; matrix verified; matrix 0cdb74cb73d439b9...; the release states d=3 (exact), gamma=1.2944316901226631 (exact)",
  "notes": "matrix gamma_frontier_release/matrices/0cdb74cb73d439b931f41d52788e1a6a2951032db8fc08bfa3f461f7cf0ea60d.matrix"
 }
]

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/825.199.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]

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

Raw record

Show the JSON this page is built from

Source: master_catalog.json, factories[1240].