[[805, 1, 6]] magic-state factory, T0 · Magic State Factory Catalog

The circuit

The 206\times805 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 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \|
out 0 (805)	1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 1 (48)	1·111···1·1·1···11···1····111····1·1111···1··1··1·111··················································1·111···1·1·1···11···1····111····1·1111···1··1··1·111·········································································································································································································································································································································································································································································································································································································································································
check 2 (56)	111··1··111111··1·1··11···1··1···111···1··11·11·111··1·················································111··1··111111··1·1··11···1··1···111···1··11·11·111··1········································································································································································································································································································································································································································································································································································································································································
check 3 (56)	·111··1··111111··1·1··11···1··1···111···1··11·11·111··1·················································111··1··111111··1·1··11···1··1···111···1··11·11·111··1·······································································································································································································································································································································································································································································································································································································································································
check 4 (48)	1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1······································································································································································································································································································································································································································································································································································································································································
check 5 (48)	·1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1·····································································································································································································································································································································································································································································································································································································································································
check 6 (48)	··1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1····································································································································································································································································································································································································································································································································································································································································
check 7 (48)	···1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···································································································································································································································································································································································································································································································································································································································································
check 8 (48)	····1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1··································································································································································································································································································································································································································································································································································································································································
check 9 (64)	1·1111··1·1··1···1111·11·1·1·1·111·1·1····11·1111111········1··········································1·1111··1·1··1···1111·11·1·1·1·111·1·1····11·1111111········1·································································································································································································································································································································································································································································································································································································································································
check 10 (64)	111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1·········································111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1································································································································································································································································································································································································································································································································································································································································
check 11 (64)	·111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1·········································111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1·······························································································································································································································································································································································································································································································································································································································································
check 12 (64)	··111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1·········································111··11·11111·1·11111··11··1··1·1·11·1····111111·1···········1······························································································································································································································································································································································································································································································································································································································································
check 13 (48)	1·1··1···111·1111··11·11····1·1·····1···1·1···11·1·1············1······································1·1··1···111·1111··11·11····1·1·····1···1·1···11·1·1············1·····························································································································································································································································································································································································································································································································································································································································
check 14 (56)	111·1·1·1··1··11····1··11·1111·1·1·11·1··111·1·1···1·············1·····································111·1·1·1··1··11····1··11·1111·1·1·11·1··111·1·1···1·············1····························································································································································································································································································································································································································································································································································································································································
check 15 (56)	11··11·1111····1·1······111··11·1111··11···1111···11··············1····································11··11·1111····1·1······111··11·1111··11···1111···11··············1···························································································································································································································································································································································································································································································································································································································································
check 16 (56)	11·1111··1·11····11··1···1··1·11··1··1111·1·1·111·1················1···································11·1111··1·11····11··1···1··1·11··1··1111·1·1·111·1················1··························································································································································································································································································································································································································································································································································································································································
check 17 (56)	·11·1111··1·11····11··1···1··1·11··1··1111·1·1·111·1················1···································11·1111··1·11····11··1···1··1·11··1··1111·1·1·111·1················1·························································································································································································································································································································································································································································································································································································································································
check 18 (64)	1···1111··11111·11·111·1··1·1·1·1··1·11111··111··1·1·················1·································1···1111··11111·11·111·1··1·1·1·1··1·11111··111··1·1·················1························································································································································································································································································································································································································································································································································································································································
check 19 (64)	11111111··11·1111·1·1·1·1·1·11·1···1·1·111····111··1··················1································11111111··11·1111·1·1·1·1·1·11·1···1·1·111····111··1··················1·······················································································································································································································································································································································································································································································································································································································································
check 20 (56)	11···111··11··11···1···1·11·111·11·1·1··11···1·1·111···················1·······························11···111··11··11···1···1·11·111·11·1·1··11···1·1·111···················1······················································································································································································································································································································································································································································································································································································································································
check 21 (48)	11·11·11··11···1·1··11··1···1111··11·1···1···11·························1······························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1·····················································································································································································································································································································································································································································································································································································································································
check 22 (48)	·11·11·11··11···1·1··11··1···1111··11·1···1···11·························1······························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1····················································································································································································································································································································································································································································································································································································································································
check 23 (48)	··11·11·11··11···1·1··11··1···1111··11·1···1···11·························1······························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1···················································································································································································································································································································································································································································································································································································································································
check 24 (48)	···11·11·11··11···1·1··11··1···1111··11·1···1···11·························1······························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1··················································································································································································································································································································································································································································································································································································································································
check 25 (48)	····11·11·11··11···1·1··11··1···1111··11·1···1···11·························1······························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1·················································································································································································································································································································································································································································································································································································································································
check 26 (48)	·····11·11·11··11···1·1··11··1···1111··11·1···1···11·························1······························11·11·11··11···1·1··11··1···1111··11·1···1···11·························1················································································································································································································································································································································································································································································································································································································································
check 27 (48)	1·111·1111···1·········1····1·1··11···1·1111·1·11·1···························1························1·111·1111···1·········1····1·1··11···1·1111·1·11·1···························1···············································································································································································································································································································································································································································································································································································································································
check 28 (48)	·1·111·1111···1·········1····1·1··11···1·1111·1·11·1···························1························1·111·1111···1·········1····1·1··11···1·1111·1·11·1···························1··············································································································································································································································································································································································································································································································································································································································
check 29 (56)	1··1·11··1·11··111···1···1111·1·11···11·1··11··111·1····························1······················1··1·11··1·11··111···1···1111·1·11···11·1··11··111·1····························1·············································································································································································································································································································································································································································································································································································································································
check 30 (48)	1111··111····1····1··11······1·1··1111·1·11·1····1·1·····························1·····················1111··111····1····1··11······1·1··1111·1·11·1····1·1·····························1············································································································································································································································································································································································································································································································································································································································
check 31 (48)	11·····1·11·1·1·11·1·111··111·1·11······1··1····1··1······························1····················11·····1·11·1·1·11·1·111··111·1·11······1··1····1··1······························1···········································································································································································································································································································································································································································································································································································································································
check 32 (64)	11·11······111·11·1·11111·1··1·1··11111··11·11··1111·······························1···················11·11······111·11·1·11111·1··1·1··11111··11·11··1111·······························1··········································································································································································································································································································································································································································································································································································································································
check 33 (48)	11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1··················11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1·········································································································································································································································································································································································································································································································································································································································
check 34 (48)	·11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1··················11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1········································································································································································································································································································································································································································································································································································································································
check 35 (48)	··11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1··················11·1·1··1·1··11····1··11111·1·1·11·····1···1··1·11··································1·······································································································································································································································································································································································································································································································································································································································
check 36 (40)	1·1···1···1111·······11··1···1·1·····11······11·111····································1···············1·1···1···1111·······11··1···1·1·····11······11·111····································1······································································································································································································································································································································································································································································································································································································································
check 37 (40)	·1·1···1···1111·······11··1···1·1·····11······11·111····································1···············1·1···1···1111·······11··1···1·1·····11······11·111····································1·····································································································································································································································································································································································································································································································································································································································
check 38 (48)	1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·············1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1····································································································································································································································································································································································································································································································································································································································
check 39 (48)	·1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·············1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1···································································································································································································································································································································································································································································································································································································································
check 40 (48)	··1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·············1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1··································································································································································································································································································································································································································································································································································································································
check 41 (48)	···1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·············1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·································································································································································································································································································································································································································································································································································································································
check 42 (48)	····1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1·············1··1······1··11111···1·11·1·1··1···111111·1··1·1·········································1································································································································································································································································································································································································································································································································································································································
check 43 (56)	1·1111····1·1··111111·1····1·1·1···1·11·11·11··11··1··········································1········1·1111····1·1··111111·1····1·1·1···1·11·11·11··11··1··········································1·······························································································································································································································································································································································································································································································································································································································
check 44 (56)	111··11·1·1111····111··1··11··1·11·1·1·1·1··1····111···········································1·······111··11·1·1111····111··1··11··1·11·1·1·1·1··1····111···········································1······························································································································································································································································································································································································································································································································································································································
check 45 (48)	11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1·····························································································································································································································································································································································································································································································································································································································
check 46 (48)	·11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1····························································································································································································································································································································································································································································································································································································································
check 47 (48)	··11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1···························································································································································································································································································································································································································································································································································································································
check 48 (48)	···11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1······11··1·111111·11·11·11···1·1····1··11·1··1·······1···············································1··························································································································································································································································································································································································································································································································································································································
check 49 (56)	1·11·1·····1·1111·1·1··11·11··1··1··11·1·11·11··1·11················································1··1·11·1·····1·1111·1·1··11·11··1··1··11·1·11·11··1·11················································1·························································································································································································································································································································································································································································································································································································································
check 50 (48)	111···1·1·1···11···1····111····1·1111···1··1··1·111··················································1·111···1·1·1···11···1····111····1·1111···1··1··1·111··················································1························································································································································································································································································································································································································································································································································································································
check 51 (48)	·111···1·1·1···11···1····111····1·1111···1··1··1·111··················································1·111···1·1·1···11···1····111····1·1111···1··1··1·111··················································1·······················································································································································································································································································································································································································································································································································································································
check 52 (40)	··············································································································································································································1··11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11·······························································································································································································································································································································································································································································································
check 53 (48)	··············································································································································································································11·1·111···1··11···1··1111··1·1·11·11111·1·····································11·1·111···1··11···1··1111··1·1·11·11111·1······························································································································································································································································································································································································································································································
check 54 (48)	··············································································································································································································1111···11··1·1···11·1·11·11·1··111111·1···1····································1111···11··1·1···11·1·11·11·1··111111·1···1·····························································································································································································································································································································································································································································································
check 55 (48)	···············································································································································································································1111···11··1·1···11·1·11·11·1··111111·1···1····································1111···11··1·1···11·1·11·11·1··111111·1···1····························································································································································································································································································································································································································································································
check 56 (48)	··············································································································································································································1·1··11··1111···11111····1·1·11·111·1·11····1··································1·1··11··1111···11111····1·1·11·111·1·11····1···························································································································································································································································································································································································································································································
check 57 (40)	··············································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1··························································································································································································································································································································································································································································································
check 58 (40)	···············································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·························································································································································································································································································································································································································································································
check 59 (40)	················································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1························································································································································································································································································································································································································································································
check 60 (40)	·················································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·······················································································································································································································································································································································································································································································
check 61 (40)	··················································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1······················································································································································································································································································································································································································································································
check 62 (40)	···················································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·····················································································································································································································································································································································································································································································
check 63 (40)	··············································································································································································································1··11··1··111··1·11··1··1111·11·····1·1············1···························1··11··1··111··1·11··1··1111·11·····1·1············1····················································································································································································································································································································································································································································································
check 64 (40)	···············································································································································································································1··11··1··111··1·11··1··1111·11·····1·1············1···························1··11··1··111··1·11··1··1111·11·····1·1············1···················································································································································································································································································································································································································································································
check 65 (48)	··············································································································································································································1·1111···1·1··111·111·111·11···1···1·111·············1·························1·1111···1·1··111·111·111·11···1···1·111·············1··················································································································································································································································································································································································································································································
check 66 (40)	··············································································································································································································11···1····11·1····111111·1·1·1·····1111···············1························11···1····11·1····111111·1·1·1·····1111···············1·················································································································································································································································································································································································································································································
check 67 (40)	···············································································································································································································11···1····11·1····111111·1·1·1·····1111···············1························11···1····11·1····111111·1·1·1·····1111···············1················································································································································································································································································································································································································································································
check 68 (40)	··············································································································································································································1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················1·1·1·11···1····111·11·1·1·11··11··1··1·················1···············································································································································································································································································································································································································································································
check 69 (40)	···············································································································································································································1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················1·1·1·11···1····111·11·1·1·11··11··1··1·················1··············································································································································································································································································································································································································································································
check 70 (48)	··············································································································································································································1·11····11·11··111·11··111·11·1·1111···1··················1····················1·11····11·11··111·11··111·11·1·1111···1··················1·············································································································································································································································································································································································································································································
check 71 (40)	··············································································································································································································11····1··111···1····111··11····1111·11·1···················1···················11····1··111···1····111··11····1111·11·1···················1············································································································································································································································································································································································································································································
check 72 (48)	··············································································································································································································11111·11··1··1·1·11··1·11·1111···11···11····················1··················11111·11··1··1·1·11··1·11·1111···11···11····················1···········································································································································································································································································································································································································································································
check 73 (40)	··············································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1··········································································································································································································································································································································································································································································
check 74 (40)	···············································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1·········································································································································································································································································································································································································································································
check 75 (40)	················································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1········································································································································································································································································································································································································································································
check 76 (32)	··············································································································································································································1····11·111·11······1···1····11·11·····1························1··············1····11·111·11······1···1····11·11·····1························1·······································································································································································································································································································································································································································································
check 77 (56)	··············································································································································································································11·11··1·11·1·11111··11·11··11111111·1·1·························1·············11·11··1·11·1·11111··11·11··11111111·1·1·························1······································································································································································································································································································································································································································································
check 78 (48)	··············································································································································································································1111·11·1·1·1······1···1111·1·11·11·1111··························1············1111·11·1·1·1······1···1111·1·11·11·1111··························1·····································································································································································································································································································································································································································································
check 79 (40)	··············································································································································································································111····1·1··1··1111·1·1··1111··1··1···1····························1···········111····1·1··1··1111·1·1··1111··1··1···1····························1····································································································································································································································································································································································································································································
check 80 (40)	···············································································································································································································111····1·1··1··1111·1·1··1111··1··1···1····························1···········111····1·1··1··1111·1·1··1111··1··1···1····························1···································································································································································································································································································································································································································································
check 81 (40)	··············································································································································································································1·1···1··1··11111··11······1··1·11·111·1·····························1·········1·1···1··1··11111··11······1··1·11·111·1·····························1··································································································································································································································································································································································································································································
check 82 (48)	··············································································································································································································11··1·11··111·1···1·111·1····1·111111·11······························1········11··1·11··111·1···1·111·1····1·111111·11······························1·································································································································································································································································································································································································································································
check 83 (48)	··············································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1································································································································································································································································································································································································································································
check 84 (48)	···············································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1·······························································································································································································································································································································································································································································
check 85 (48)	················································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1······························································································································································································································································································································································································································································
check 86 (48)	·················································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1·····························································································································································································································································································································································································································································
check 87 (48)	··············································································································································································································1··1·1·1111··1·1111·11·111·1·····111··11···································1···1··1·1·1111··1·1111·11·111·1·····111··11···································1····························································································································································································································································································································································································································································
check 88 (40)	··············································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1···························································································································································································································································································································································································································································
check 89 (40)	···············································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1··························································································································································································································································································································································································································································
check 90 (40)	················································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1·························································································································································································································································································································································································································································
check 91 (40)	············································································································································································································································································································································································1··11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11·································································································································································································································································································································
check 92 (48)	············································································································································································································································································································································································11·1·111···1··11···1··1111··1·1·11·11111·1·····································11·1·111···1··11···1··1111··1·1·11·11111·1································································································································································································································································································································
check 93 (48)	············································································································································································································································································································································································1111···11··1·1···11·1·11·11·1··111111·1···1····································1111···11··1·1···11·1·11·11·1··111111·1···1·······························································································································································································································································································································
check 94 (48)	·············································································································································································································································································································································································1111···11··1·1···11·1·11·11·1··111111·1···1····································1111···11··1·1···11·1·11·11·1··111111·1···1······························································································································································································································································································································
check 95 (48)	············································································································································································································································································································································································1·1··11··1111···11111····1·1·11·111·1·11····1··································1·1··11··1111···11111····1·1·11·111·1·11····1·····························································································································································································································································································································
check 96 (40)	············································································································································································································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1····························································································································································································································································································································
check 97 (40)	·············································································································································································································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1···························································································································································································································································································································
check 98 (40)	··············································································································································································································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1··························································································································································································································································································································
check 99 (40)	···············································································································································································································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·························································································································································································································································································································
check 100 (40)	················································································································································································································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1························································································································································································································································································································
check 101 (40)	·················································································································································································································································································································································································11··1··1··1····11··1111·1·1··111111··········1·································11··1··1··1····11··1111·1·1··111111··········1·······················································································································································································································································································································
check 102 (40)	············································································································································································································································································································································································1··11··1··111··1·11··1··1111·11·····1·1············1···························1··11··1··111··1·11··1··1111·11·····1·1············1······················································································································································································································································································································
check 103 (40)	·············································································································································································································································································································································································1··11··1··111··1·11··1··1111·11·····1·1············1···························1··11··1··111··1·11··1··1111·11·····1·1············1·····················································································································································································································································································································
check 104 (48)	············································································································································································································································································································································································1·1111···1·1··111·111·111·11···1···1·111·············1·························1·1111···1·1··111·111·111·11···1···1·111·············1····················································································································································································································································································································
check 105 (40)	············································································································································································································································································································································································11···1····11·1····111111·1·1·1·····1111···············1························11···1····11·1····111111·1·1·1·····1111···············1···················································································································································································································································································································
check 106 (40)	·············································································································································································································································································································································································11···1····11·1····111111·1·1·1·····1111···············1························11···1····11·1····111111·1·1·1·····1111···············1··················································································································································································································································································································
check 107 (40)	············································································································································································································································································································································································1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················1·1·1·11···1····111·11·1·1·11··11··1··1·················1·················································································································································································································································································································
check 108 (40)	·············································································································································································································································································································································································1·1·1·11···1····111·11·1·1·11··11··1··1·················1······················1·1·1·11···1····111·11·1·1·11··11··1··1·················1················································································································································································································································································································
check 109 (48)	············································································································································································································································································································································································1·11····11·11··111·11··111·11·1·1111···1··················1····················1·11····11·11··111·11··111·11·1·1111···1··················1···············································································································································································································································································································
check 110 (40)	············································································································································································································································································································································································11····1··111···1····111··11····1111·11·1···················1···················11····1··111···1····111··11····1111·11·1···················1··············································································································································································································································································································
check 111 (48)	············································································································································································································································································································································································11111·11··1··1·1·11··1·11·1111···11···11····················1··················11111·11··1··1·1·11··1·11·1111···11···11····················1·············································································································································································································································································································
check 112 (40)	············································································································································································································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1············································································································································································································································································································
check 113 (40)	·············································································································································································································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1···········································································································································································································································································································
check 114 (40)	··············································································································································································································································································································································································111··1111···1111·1·1·····1·1··1·1·1··1·······················1·················111··1111···1111·1·1·····1·1··1·1·1··1·······················1··········································································································································································································································································································
check 115 (32)	············································································································································································································································································································································································1····11·111·11······1···1····11·11·····1························1··············1····11·111·11······1···1····11·11·····1························1·········································································································································································································································································································
check 116 (56)	············································································································································································································································································································································································11·11··1·11·1·11111··11·11··11111111·1·1·························1·············11·11··1·11·1·11111··11·11··11111111·1·1·························1········································································································································································································································································································
check 117 (48)	············································································································································································································································································································································································1111·11·1·1·1······1···1111·1·11·11·1111··························1············1111·11·1·1·1······1···1111·1·11·11·1111··························1·······································································································································································································································································································
check 118 (40)	············································································································································································································································································································································································111····1·1··1··1111·1·1··1111··1··1···1····························1···········111····1·1··1··1111·1·1··1111··1··1···1····························1······································································································································································································································································································
check 119 (40)	·············································································································································································································································································································································································111····1·1··1··1111·1·1··1111··1··1···1····························1···········111····1·1··1··1111·1·1··1111··1··1···1····························1·····································································································································································································································································································
check 120 (40)	············································································································································································································································································································································································1·1···1··1··11111··11······1··1·11·111·1·····························1·········1·1···1··1··11111··11······1··1·11·111·1·····························1····································································································································································································································································································
check 121 (48)	············································································································································································································································································································································································11··1·11··111·1···1·111·1····1·111111·11······························1········11··1·11··111·1···1·111·1····1·111111·11······························1···································································································································································································································································································
check 122 (48)	············································································································································································································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1··································································································································································································································································································
check 123 (48)	·············································································································································································································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1·································································································································································································································································································
check 124 (48)	··············································································································································································································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1································································································································································································································································································
check 125 (48)	···············································································································································································································································································································································································111111111·······1111·1·111··111··11·1··································1·······111111111·······1111·1·111··111··11·1··································1·······························································································································································································································································································
check 126 (48)	············································································································································································································································································································································································1··1·1·1111··1·1111·11·111·1·····111··11···································1···1··1·1·1111··1·1111·11·111·1·····111··11···································1······························································································································································································································································································
check 127 (40)	············································································································································································································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1·····························································································································································································································································································
check 128 (40)	·············································································································································································································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1····························································································································································································································································································
check 129 (40)	··············································································································································································································································································································································································11·1····111·1111···1·1···11··1··1·1·11······································1··11·1····111·1111···1·1···11··1··1·1·11······································1···························································································································································································································································································
check 130 (24)	··········································································································································································································································································································································································································································································································································1···11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11···················································································································································································································
check 131 (32)	··········································································································································································································································································································································································································································································································································11··1·1·1·11·1·11·1111·1·1·····················11··1·1·1·11·1·11·1111·1·1··················································································································································································································
check 132 (32)	··········································································································································································································································································································································································································································································································································111·1··11·····111111·111··1····················111·1··11·····111111·111··1·················································································································································································································
check 133 (24)	··········································································································································································································································································································································································································································································································································11111······11···11·1··1····1···················11111······11···11·1··1····1················································································································································································································
check 134 (24)	···········································································································································································································································································································································································································································································································································11111······11···11·1··1····1···················11111······11···11·1··1····1···············································································································································································································
check 135 (32)	··········································································································································································································································································································································································································································································································································1·11··1·11·11111···111·1·····1·················1·11··1·11·11111···111·1·····1··············································································································································································································
check 136 (32)	··········································································································································································································································································································································································································································································································································11·1·1·11·11·11·1·1··111······1················11·1·1·11·11·11·1·1··111······1·············································································································································································································
check 137 (24)	··········································································································································································································································································································································································································································································································································111··11·······1··1111·1········1···············111··11·······1··1111·1········1············································································································································································································
check 138 (24)	···········································································································································································································································································································································································································································································································································111··11·······1··1111·1········1···············111··11·······1··1111·1········1···········································································································································································································
check 139 (32)	··········································································································································································································································································································································································································································································································································1·11·1·1·1·11··11·11·111·········1·············1·11·1·1·1·11··11·11·111·········1··········································································································································································································
check 140 (32)	··········································································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1············11·1·11··111·1·11111··1···········1·········································································································································································································
check 141 (32)	···········································································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1············11·1·11··111·1·11111··1···········1········································································································································································································
check 142 (24)	··········································································································································································································································································································································································································································································································································1·111··1·1···1···1·1·1·1············1··········1·111··1·1···1···1·1·1·1············1·······································································································································································································
check 143 (24)	··········································································································································································································································································································································································································································································································································11·1·····1111·11······11·············1·········11·1·····1111·11······11·············1······································································································································································································
check 144 (24)	··········································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1·····································································································································································································
check 145 (24)	···········································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1····································································································································································································
check 146 (24)	············································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1···································································································································································································
check 147 (24)	·············································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1··································································································································································································
check 148 (24)	··········································································································································································································································································································································································································································································································································1·····1·1··1·111·11···11··················1····1·····1·1··1·111·11···11··················1·································································································································································································
check 149 (24)	··········································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1································································································································································································
check 150 (24)	···········································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1·······························································································································································································
check 151 (24)	············································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1······························································································································································································
check 152 (24)	·············································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1·····························································································································································································
check 153 (24)	········································································································································································································································································································································································································································································································································································································································1···11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11·····················································································································
check 154 (32)	········································································································································································································································································································································································································································································································································································································································11··1·1·1·11·1·11·1111·1·1·····················11··1·1·1·11·1·11·1111·1·1····················································································································
check 155 (32)	········································································································································································································································································································································································································································································································································································································································111·1··11·····111111·111··1····················111·1··11·····111111·111··1···················································································································
check 156 (24)	········································································································································································································································································································································································································································································································································································································································11111······11···11·1··1····1···················11111······11···11·1··1····1··················································································································
check 157 (24)	·········································································································································································································································································································································································································································································································································································································································11111······11···11·1··1····1···················11111······11···11·1··1····1·················································································································
check 158 (32)	········································································································································································································································································································································································································································································································································································································································1·11··1·11·11111···111·1·····1·················1·11··1·11·11111···111·1·····1················································································································
check 159 (32)	········································································································································································································································································································································································································································································································································································································································11·1·1·11·11·11·1·1··111······1················11·1·1·11·11·11·1·1··111······1···············································································································
check 160 (24)	········································································································································································································································································································································································································································································································································································································································111··11·······1··1111·1········1···············111··11·······1··1111·1········1··············································································································
check 161 (24)	·········································································································································································································································································································································································································································································································································································································································111··11·······1··1111·1········1···············111··11·······1··1111·1········1·············································································································
check 162 (32)	········································································································································································································································································································································································································································································································································································································································1·11·1·1·1·11··11·11·111·········1·············1·11·1·1·1·11··11·11·111·········1············································································································
check 163 (32)	········································································································································································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1············11·1·11··111·1·11111··1···········1···········································································································
check 164 (32)	·········································································································································································································································································································································································································································································································································································································································11·1·11··111·1·11111··1···········1············11·1·11··111·1·11111··1···········1··········································································································
check 165 (24)	········································································································································································································································································································································································································································································································································································································································1·111··1·1···1···1·1·1·1············1··········1·111··1·1···1···1·1·1·1············1·········································································································
check 166 (24)	········································································································································································································································································································································································································································································································································································································································11·1·····1111·11······11·············1·········11·1·····1111·11······11·············1········································································································
check 167 (24)	········································································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1·······································································································
check 168 (24)	·········································································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1······································································································
check 169 (24)	··········································································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1·····································································································
check 170 (24)	···········································································································································································································································································································································································································································································································································································································································111··1··111··1··1·1·1·················1········111··1··111··1··1·1·1·················1····································································································
check 171 (24)	········································································································································································································································································································································································································································································································································································································································1·····1·1··1·111·11···11··················1····1·····1·1··1·111·11···11··················1···································································································
check 172 (24)	········································································································································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1··································································································
check 173 (24)	·········································································································································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1·································································································
check 174 (24)	··········································································································································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1································································································
check 175 (24)	···········································································································································································································································································································································································································································································································································································································································11··11·11··1··1·1··11······················1···11··11·11··1··1·1··11······················1·······························································································
check 176 (16)	······································································································································································································································································································································································································································································································································································································································································································································1·1··1··11111··········1·1··1··11111···························································
check 177 (16)	······································································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1··························································
check 178 (16)	·······································································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1·························································
check 179 (16)	········································································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1························································
check 180 (16)	·········································································································································································································································································································································································································································································································································································································································································································································1111·11·1····1·········1111·11·1····1·······················································
check 181 (16)	······································································································································································································································································································································································································································································································································································································································································································································1·1·1·111··1·····1·····1·1·1·111··1·····1······················································
check 182 (16)	······································································································································································································································································································································································································································································································································································································································································································································1111···1··11······1····1111···1··11······1·····················································
check 183 (16)	······································································································································································································································································································································································································································································································································································································································································································································11·111···11········1···11·111···11········1····················································
check 184 (16)	·······································································································································································································································································································································································································································································································································································································································································································································11·111···11········1···11·111···11········1···················································
check 185 (16)	······································································································································································································································································································································································································································································································································································································································································································································1··1··11111··········1·1··1··11111··········1··················································
check 186 (16)	·······································································································································································································································································································································································································································································································································································································································································································································1··1··11111··········1·1··1··11111··········1·················································
check 187 (8)	·····················································································································································································································································································································································································································································································································································································································································································································································································11····11·········11····11·······················
check 188 (8)	····················································································································································································································································································································································································································································································································································································································································································································································································1···1········1··11···1········1··1···············
check 189 (8)	························································································································································································································································································································································································································································································································································································································································································································································································1····11··1·······1····11··1··················
check 190 (8)	··························································································································································································································································································································································································································································································································································································································································································································································································111·····1········111·····1·················
check 191 (8)	························································································································································································································································································································································································································································································································································································································································································································································································1····1·····11····1····1·····11···············
check 192 (8)	·······················································································································································································································································································································································································································································································································································································································································································································································································1·1·····11·······1·1·····11···················
check 193 (8)	·····················································································································································································································································································································································································································································································································································································································································································································································································11··1······1·····11··1······1···················
check 194 (16)	····················································································································································································································································································································································································································································································································································································································································································································································································11·1··11····1··1111·1··11····1··11···············
check 195 (8)	······················································································································································································································································································································································································································································································································································································································································································································································································································1·111··1·111···
check 196 (8)	······················································································································································································································································································································································································································································································································································································································································································································································································································111··1·111··1··
check 197 (8)	·······················································································································································································································································································································································································································································································································································································································································································································································································································111··1·111··1·
check 198 (8)	·····························································································································································································································································································································································································································································································································································································································································································································································································································11111111
check 199 (32)	·····································································································································································································································································································································································································································································································································································································································································································································································································11111111111111111111111111111111
check 200 (72)	·····························································································································································································································································································································································································································································································································································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111
check 201 (142)	·······················································································································································································································································································································································································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 202 (236)	·························································································································································································································································································································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 203 (362)	···························································································································································································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 204 (520)	·····························································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 205 (702)	·······································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

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 n805Noisy T states per run.

outputs k1

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

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

wires N206

checks r205

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

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d3.7342Overhead per extractable T state. Lower is better. At the certified d=17: 2.3616.

\gamma = \log(n/k)/\log d3.7342Overhead per output qubit. At the certified d=17: 2.3616.

\gamma_T = \log(n/T)/\log d3.7342Overhead per unit of T-count. At the certified d=17: 2.3616.

T-count1Minimal T-count of the output gate.

phase-polynomial degree1Minimised over changes of output basis.

effective width1Rank of the output rows modulo the check rows.

Output gate

1 T0 CS0 CCZon 1 output wire

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

As monomials: 0 (output wires per term, separated by +)

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

Clifford correction

With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 5 single-wire gates and 9 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{S} on check 201, \mathrm{Z} on check 202, \mathrm{S}^\dagger on check 203, \mathrm{S} on check 205, \mathrm{CZ} on output 0, check 201, \mathrm{CZ} on output 0, check 203, \mathrm{CZ} on output 0, check 205, \mathrm{CZ} on check 201, check 202, \mathrm{CZ} on check 201, check 203, \mathrm{CZ} on check 201, check 204, \mathrm{CZ} on check 201, check 205, \mathrm{CZ} on check 203, check 204, \mathrm{CZ} on check 203, check 205. The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

Or no Clifford gate at all: run \mathrm{T}^\dagger on rotations 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and 434 more (listed below), and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.

All 458 rotations at T†

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, 199, 200, 201, 202, 203, 204, 205, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709

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/805.1.6.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-805.1.6.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

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

A damaging fault of weight 17 sits on columns [0,103,206,285,364,443,522,569,616,663,710,733,756,773,790,797,804].

Its source certifies d\ge 17, as a lower bound. That certificate is not re-checked here, but rankings on this site may use it. With the damaging fault of weight 17 above, it makes the distance exactly d=17. Source: Jain and Albert (arXiv:2408.12752), Table II: [[103,1,19]] quantum QR code (extended QR [104,52,20]) doubled onto [[599,1,15]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 17, with d_sd at least the classical distance less one (their Lemma 2.4).

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

Original source

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

Provenance

a code of the weak triply even family of Jain and Albert (arXiv:2408.12752, Table II; transversal_t_codes/): quadratic-residue CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction, where T on some qubits and T-dagger on the rest is a logical T; a verified witness, not a maximum

Found by: Jain-Albert doubling: weak triply even family

Discovery: pre-existing

1 recorded source

[
 {
  "regime": "Jain-Albert doubling: weak triply even family",
  "file": "transversal_t_codes/factories.json",
  "label": "JA-805",
  "N": 206,
  "d": 6,
  "d_is_exact": false,
  "origin": "S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance\", IEEE J. Sel. Areas Inf. Theory 6, 127 (2025), arXiv:2408.12752",
  "provenance": "[[103,1,19]] quantum QR code (extended QR [104,52,20]) doubled onto [[599,1,15]] (Table II)"
 }
]

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/805.1.6.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]

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

Raw record

Show the JSON this page is built from

Source: master_catalog.json, factories[1231].

[\![805,\,1,\,6]\!] factory