The circuit
The 97\times358 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.
| 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 |
|---|---|
| out 0 (133) | 1··1·1·11····1··1·11·1·····1·1··11··1·111··1·····11·1111·1··1·1·11··1··1·······1·1··1·····1··1··11·11·····1111···1············1·1·1··11·1·1··1··11·1·······1···11·1·11·1····1···1·1···1·1··1·11····1··1·111·······1·1·11·1·11··1····11··1·111·1·1·1·11··1··1········1··11··1····1·1·1·1···1·····111·1··1·1······1·1··1·11·1·1·1···11·······1···11··1·11·1···1···1·1··· |
| out 1 (141) | 1··1111·1··11·1···11···1··1···1·····1111·11······1··11111·1···11··11··11·1·····11···11········1··1··111···1··1··111··1·1····111·111··1·1··1··1··11··1··········1·1··11·1······1····11·1·11·11·1··11·1···11··1···1····1···111111·····1···1·1111·1··11··11··11····1···11··11·······1··1·····111···1···1··1111·11·11·1·11·1·1··1·1···1·1··········1·1···11·1····1·····11· |
| out 2 (79) | ·······1·1····1······1·····1···1·1·····1·11·1····1···11·1·········1············1·····1·1··1·····11··1·····1·······1··1·1·····1·111······1····11·1·······1·················1·····1·1··1·······1·1····1·····1·······1····1····111·1···1·····11·1········1·············1····111······1·1·····1·····1·········1·11·1·11·1·····1···11··1·······1················1····1·1··1 |
| out 3 (135) | ··1·1111···111·········1·1111····11·1·········1··1·11·1··11····111·11·1··1··········1··1···1·1··1··11111··111·1··1·······1········11·1··1·1·1·1·1··1····1··1····111····1111····1111······1·111···111········11··1·11···111········1·1·1·1··1··11···111·11·1·····1·······1·1···1·1·1···1···1111··111··1···1····1······111··1·11·1··11······11····11·1····1111··1·111··· |
| out 4 (133) | 1···1·1·1··11·1···11···1··1···1··1··11·1·11······1··11·1··1···11··11··11·1·····11···1·····1·1····1··111···1··1··111··1·······11·111··1·1··1··11··1··1··········1·1··11·1······1·1··1111··1··1·1··11·1···11··1···1····1·1·11·111·····1···1·1·1··1··11··11··11····1···11··1··1········1·····111···1···1··1111·1··11·1·11·1·1··1·11····1··········1·1···11·1····1··1··111 |
| out 5 (149) | 1··1·1·11····1····11·1···1····1···1··1·1····1·1··1·1·1·1·1··1·1·111·1··1········1····1·1··1··1··11·11··1··11111·1····1···1···111···1···1····111·11·1····1··1···11·1·11··11····111111111·1··1·11····1····111··1·······1··1·1·1···1·1·1·1···1·1·1·1·1·111·1··1·········1···111····1·1·1·1···1··1··111·11·11··11·1111····1··1···111··11······11···11··1·11··11··11·111111 |
| out 6 (135) | ····1111·1·111··1······1···1·11·11···111···11····11··1···11·1··111111·1··1······11·······11··1··11·1111···111·····1··1·1······111·····11·····1··1··11······1····111·········1·1···11·····1·111·1·111··1·····1·····1·1111··111··11···11····1···111··111111·1·····1····1·1···1····1·1·1·1···111···111·······1·11··111·····11····1···111······1····11·1········11····11·· |
| out 7 (143) | ····1111·1·1111·1····1·1···1·11·11···111·111······1··11··11····11··11·1··1·····111···1·······1··11·1·11····11·····1··1·1······1··1····111····11·1··1····1··1····111·······1·1·1·1·1111···1·111·1·1111·1···1·1·····1·1111··111111·····1····11··11···11··11·1·····1···11·1·1······1·1·1·1····11····11·······1·11··1···1···111···11··11·····111····11·1·······111··1·1111 |
| out 8 (135) | ····1·11···111·········1·111·11·1····111·1·11·····1···1··11····111·1111··1······11·····1··1··11·1··11111··111·1·1·1··1········1·1·····111·····1·1··1····1·····1·111·········1·1····11····1··11···111········11··1·1·111···1111·11····1·····1··11···111·1111·1···1····1·1··11····111···1···1111··111··1··1·1·1···1·1·····111····1··11······1···1·11·1········11·····11· |
| out 9 (149) | 1··1111·1··11···1·11···1··1···1·····11···11······1··11111·1···11··111111·1·····11···11·1··1···1··1···111··1··1··111··1·1······1·111··1·1··1··1··11··1·····11···1·1··11·1······1···11111·11·11·1··11···1·11··1···1····1···11··11·····1···1·1111·1··11··111111····1···11··1111·····1··1······111··1···1··1111·11··1·1·11·1·1··1·1···1·1······1···1·1···11·1····1····1111 |
| out 10 (47) | ·······1·1······1····1···········1·1······1······1····1·····1··················1·····1··········11·····1··1············1·1······1·······1·····1·····1·····················1·····1············1·1······1···1············1······1·····1······1····1···················1····1········1·1········1··1············11···1·······1····1····1······················1····1····· |
| out 11 (111) | ··············1··1··········111·111·1111·1·11·1··11111··1·······················11··1·····1·········1···1·······111··1···1····1·1·11·111··1·11··1······················1111·1·1111111···············1··1···········11111111111·11·1·111·1·1··1·······················1·11··1··············1·············111·1·1·1·1··11111··111···1·····················1111111·11111· |
| out 12 (135) | 1···1111···111··1····1·1·1··1····11·1·····1···1····11····11·1··111·11·1··1·····1····11·1·····1··1··1111····11·1·111······1······1·11·1····1·1···1··11···1··1····111····111·····1·11···1··1·111···111··1···1·11·····1···111····1···1···1·1·····111··111·11·1·····1···1···111·1···1·1···1···111····11··1··111···1···1··111····11····111·····11····11·1····111···1··11··· |
| out 13 (135) | ····1111·1·1111······1·1·1·11·····1·1······1··1····11·1··11····111·11·1··1··········1··1·····1··11·1·111···11·1·11·····1·1········11·1····1·1·1·1··1····1··1····111····1111····1111······1·111·1·1111·····1·11····11····11·····1··1···1·1··1··11···111·11·1·····1·······1·1·····1·1·1·1····111···11··1··11···11····1·111····11·1··11······11····11·1····1111··1·111··· |
| out 14 (127) | ·····1···1······1····1······111·111·1111···1··1··1111···1·········1··1······1···11··1··1······1··1·····1··1·····111··1···1····111111·111··1·1···1·······1··1·········1·1111·1·1111·111·····1···1······1···1········1111111111··1··1·111·1····1········1··1···········1·11·1······1··1········1··1·······111·1·1·111·111111··11····1·······11··········1·1111111·11·111 |
| out 15 (133) | 11····11·1·1····111··1······111···1······1··1·1··111·1111···1····1·11····1·····1·1···1·1······1·1·11··1····1···1··1····1·····11·11···1····1··111·1···1··1·····11·1111··11·1···1··1·1··11····11·1·1····111·1········111··1····1··1·1·111···1111··1····1·11······11···1··1·11······11··11·····1····1····11··1··1·11·1·1··1····1·11·1···1····1···11·1·111··11·1·1···1·1·· |
| out 16 (143) | ·1·111·111··1····1·1·1·1····11···11·11······1·1·1·1111····1···11·11·1111········11··1·····1·····1111·1·1··11·1·1·1···1·1·····1··1·1··········1111····1··1··1··1··111·1··1·1······11·11·111·1·111··1····1·11·1······11··1111·····1·1··11·1·1····1··11·11·1111·········1·11··1······1·111····1·1··11··1·1··1··11·1··1··1········11·11··1····11··1··1·11·1··1·1·····11·11 |
| out 17 (63) | ·····1···1····1·1·········1············1·11··········11·1···1······1·1·········1·······1······1··1··1··1········1············1·11············11·1···1····1·1··············1·······1········1···1····1·1·········1···········111···········11·1··1······1·1··········1·····1······1··1·····1··1··········1······1·11···········11··1·1······1···············1······1··· |
| out 18 (133) | 1··11·1·11·11·1···11···1··1···1·····11·1·11······1··1111··1·1·11··11··11·1······1···11····1·········111···1··1··1·1··1·1·····11·111··1·1··1··1···1·············1·1··11·1··1···1····1111·11··1·11·11·1···11··1···11···1···11·111·····1···1·111··11·11··11··11····1····1··11·1··············111···1···1··11·1·11·11·1·11·1·1··1·1················1·1···11·1··1·1·····111 |
| out 19 (157) | 11·1·1·111···1··1·11·····1··1·1··11··1·1··1·1·1····1·1·1·1··1·1·111·1··1········1····1·1··1··1··1··11······1111·1····1·1·1···1111··1···11···111·11·1····1··1···11·1·11··11····11111111111··1·111···1··1·11···1·····1·1·11·1·1·1·1·1···1···1·1·1·1·1·111·1··1·········1···111·1··1·1···1···1······11·11·11···1111111···1··11··111··11······11···11··1·11··11··11·111111 |
| out 20 (143) | ····111····1111······1·1·11·1·····1·1····11·1·1····11···111·1··111111·1··1·····11···11·1··1··1·····1·111···11·1··11····1·1·····11111·1····1·1······11······1····111····111·1···1·11··1···1·11····1111·····1·11··1··1····11···11·1·1···1·1····1111··111111·1·····1···11··1111····1·····1····111···11··1···11··11··11·1111····11·····11······1····11·1····111···1··11··1 |
| out 21 (135) | ····1·1··1·111··1····1·1·1111·····1·1··1··1···1····111··111·1··111·11·1··1·····1···111·······11··1·1111····11·1··1·····1·1···1··1·11·1····1·11·····11···1··1····111····111·······1·······1··1··1·111··1···1·11··1·11····11··1·1···1···1·1·1··1111··111·11·1·····1···1···11······11··1·1···111····11··1···1···111··1··111····111····11·····11····11·1····111······1···· |
| out 22 (135) | ·1·1··1111·1·11·11·1·1···11··1···1···1······1·····1···1··1····1·1·11·1·1·1·····111···1·1··1··1··111···11····1111··1··1···1···1··1··1·1·1··1·1··1···1··········1·1··1·1·1·11····1····11·11···1111·1·11·11·11··1··1···1··1··1·····1····1·····1··1··11·1·11·1·1····1···11·1·111····1·1·11······11····1·111···1·1·11··1···11·1··11···1·1··········1·1···1·1·1·11··1·····11 |
| out 23 (133) | 11·······1·1·····11··1···111····1···111··111········1··1····1····11111···1·····11···1··1······11··11··11···1··11·11··1···1·····11111··11····1··111···1·····1··11··111····1··1··1··1·1111·······1·1·····11·1··1··1·1···1··111·111········1···1···1····11111······1···11··1·1······1···11·····11···1···111·11·1·1··11·111·11···1···11··1·····1··11···111····1·1·1···1·11 |
| out 24 (31) | ·····················1···1··················1·1·······1·1····························1····1···············1···1··················1··1·········1·1·······························1····1····················1··1··················1·1········1·1···························1·1····················1····1··············1··········1··1·····························1····1 |
| out 25 (127) | ··············1·1····1···1··111·111·1111·111··1··111111·····1·····1·············11··1···1···········1··1··1···1·111··1···1····1··111·111··1·111·····1···1··············1111·1·11111·11··············1·1···1··1·····1111111111111··1·111·1·11····1·····1··············1·11·················1··1··1····1··111·1·1·1···111111··1111····1·····1·············1111111·111·11 |
| out 26 (141) | 11··11·1·1··111··11··1·1·11··1······1··1··1······11·1111·11····11·1··11··········1··1········11·1·1··1····1·1·11·1··1····1····11··11········1111·1·111··1·····1111·11····11···11··11··11·1·1·1·1··111··11·1·11··1···1····1··1·1·····11··1·111·11···11·1··11············11·······111··1·····1····1·1··111·1····1·11···11······111·1·111····1···1111··11····11·11···11·· |
| out 27 (119) | ·····1···1····1··········1··1·1·1·1·1111·1·1··1···11111·························11··11········1··1··1·········1·1111·1·1·1····1·1111·1111·1·111························1111·1·11·11111·····1···1····1········1·····1·11·111111·1··1··11·1·11·························1·111·······1··1·····1··········1··111·111·1·1·1111111·1111························1111111··11111 |
| out 28 (143) | ·1·1··1111·1·1··11·1·11··11··1···1···1···········11··11··1····1·1·11·1·1·1······11·····1··1··1··111·1·11···11111··1··1···1···1··11·1·1·11·1·11·1···1·1········1·1··1·1·1·1·····11···11·11···1111·1·1··11·11··1··1···1··1··1·········11····11··1···1·1·11·1·1····1····1·1··11····1·1·11····1·11···11·111···1·1·11··1·1·11·11·111··1·1·1········1·1···1·1·1·1···1·1···11 |
| out 29 (143) | ····1111·1·1111······1·1·1111····11·1·········1··1·1111··11·1··111·1111·············1··1·····1··11·1·111···11·1··1·······1········11·1··1·1·111·1··11···1·······111····1111····1111······1·111·1·1111·····1·11··1·11···111········1·1·1·1·11··111··111·1111·············1·1·····1·1·1·1····111···11··1···1····1······111··1·1111··111·····1·····1111····1111··1·111··· |
| out 30 (135) | ·1·1··1·1··1·1··11·1·····1·1·1···1···1···11······11··11·11·1··1·1·11·1·1·1······11···········1····1·1·11··1·11111····1···1···1·1·1·1·1·11·1·11·11····1········1·1··1·1·1·1·····11·1·1··11···1·1··1·1··11·1···1····1·1··1··1··11·····11····11·11···1·1·11·1·1····1····1·1········1····1····1·11··1·1·111·1···1·11·1··1·11·11·111··11··1········1·1···1·1·1·1···1·1·1·1· |
| out 31 (149) | 1··1·1·111·1·11···11·····1·11·1··11··1···11···1····1···1·1··1·1·11··1··1·······11····1····1··1··1··1···1···1111·1·1··1·1·1····1·11·1···11···1·1·11·1·······1···11·1·11··111···1111·1111·1··1·111·1·11···11···1····11·1·11·1··11···1···1·····1·1·1·1·11··1··1········11···1·1····1·1···11·····1···11·11·11·1·111·1·1·1·1··11··1·1··11·······1···11··1·11··111·11·11·111 |
| out 32 (141) | 11··1·······111·111····1·111·11··1··1·············1·1··1111····11····11········1·1··11·1··1······11··1·1····1·11·11····1·1···1111·11····1···1··111·111········1111·11····1····111··1·111·11·······111·111···11··1·1·11·1·1···········1··1···1111···11····11·········1··11111········11·····1·1····1··111·11··111111··11···1··1···11111········1111··11····1··11·1··1·1 |
| out 33 (141) | ·1·111··1···1·1···1·11·····111···11·11·1·1111·········1·111·1·11·1·1·····1·····111··11····1·······11··1·····1·1··11··1·1········11·1·11·1·1·1··1·1··11·····1·1·11···1·1·1·······111·11·111·1··1···1·1···1·1·······111··1111·11111··········1·1111·11·1·1········1···11·111·1·········11·····1·····1··1·1·11·11····1·1·111·1·11···1··11·····1·1·11····1·1·1······111·11 |
| out 34 (135) | ····1·1··1·111·········1·11·1····11·1··1·1····1····11·1·111·1··111·1111··1··········11·······11··1·11111··111·1··11······1···1·1··11·1····1·1·1····11···1········11····1111····1·1·······1··1··1·111········11··1··1···111··11····1···1·1··1·1111··111·1111···1·1·······11······11··1·1···1111··111··1···11···11·1···111····11·1···11·····1······1·1····1111··1··1···· |
| out 35 (135) | ·1·1··1111·1·11··111······1··1···1···1···1········1·····11····1·1··1·1·1·1·····111···1·······1··111···1··11·11·1··1··1···1···1·111·1·1·1··1·1·111··1·1··1·····1·1··1·1·1·11····1··1·1··11···1111·1·11··111······1···1··1··1··1·······1·······11···1·1··1·1·1····1···11·1·1······1·1·11······1···1·1·1·1···1·1·11·11·1·11·1··11·1·111·1····1···1·1···1·1·1·11··1···1·1· |
| out 36 (157) | 1··1·1·11····1····11·1···1·11·1···1··1·1·11·1·1··1·1··11·1··1·1·111·1111········1····1·1··1··1··11·11··1··11111·1·1··1···1···11·1··1···1····1···11·1····1······11·1·11··11····111111111·1··1·11····1····111··1····11·1··1·1·111·1·1·1·1····11·1·1·1·111·1111·········1···111····1·1·1·1···1··1··111·11·11·1·1·111·1···1··1···1····11······1·1··11··1·11··11··11·111111 |
| out 37 (79) | ·····1···1····1·1····1···111·············11·1····1···1··1············1·····1···1·····1·1··1···1··1··1··1··1···1·1·1············111······1····1··1··········1·······1······1·····1·1··1·····1···1····1·1···1··1··1·1··········11·1···1·····1··1···········1··········1····111·····1··1·····1··1··1····1··1·1······11·1·····1···1···1········1········1······1····1·1··1 |
| out 38 (135) | ····1111···1111·1····1·1···1·11·1····11··111······1··11··11·1··111·11·1··1·····111·····1·····1··1····11····11·····1··1·······11··1····111····11·1··11···1··1····111·······1·1·1····111···1·111··11111·1···1·1·····1·111···11·111·····1····11··111··111·11·1·····1···11·1··1·····1·1········11····11·······1·1··11···1···111···11··111·····11····11·1·······111·····111 |
| out 39 (111) | ··············1······1······111·111·1111·1·1··1··11111······1··················111··1···············1·····1·····111··1···1····1·1111·111··1··1······1··················111··1·11111111··············1·····1········11111111111·1··1·111·111·····1···················11·11·················1·····1·······111·1·1·1·1·111111··1·1·····1···················111·111·111111 |
| out 40 (135) | ·1·111··1···1····1·1·1·1··11··1·1·····11···1·········11·1·1·1·11·1··1111·············1·1··········11·1·1··11·1·1·······1·1···111···1··1·1·1·11·1····11·····1··1··111·1·1·1··1·11··11·1·111·1··1···1····1·11·1···1·1··11····11··1···1······11·1·11·11·1··1111·············11··········11····1·1··11··1·1······11111····1·1·1·111··1··11·····1··1··1·11·1·1·1·111···11·1 |
| out 41 (135) | ····1111·1·111··1······1···11·····1·1····1····1··1·1·1···11·1··111111·1··1··········11·······1··11·1111···111···11·····1·1·····1··11·1··1·1111··1··11······1····111····1111····1·1·······1·111·1·111··1·····1·····11····11···1····1·1·1···1···111··111111·1·····1·······11······1·1·1·1···111···111·····11···11··1···111··1·111···111······1····11·1····1111··1··1···· |
| out 42 (119) | ··············1··········1··111·111·1111·1·1··1···11111·1···1···················1···1···············1·········1·111··1···1····1·1111·1111·1·111·1···1··················1111·1111111111··············1········1·····11111111111·1··1··11·1·11·1··1····················1··1·················1··········1··111·1·1·1·1·1111111·1111··1·1···················1111111·111111 |
| out 43 (125) | 11···11···11····111··1····11111··11····1·11·1·1···11··11····1····1·111···1·······1···1···········1·1··1····1···11·············1··1···1··1·1···1111···1··1··1··11··111··11·····1··111··11···11····1····111·1·····1·1111·11···111·1·1··11····11···1····1·111······1······1·1··········1·1·····1····1····111·······1···1··1··1·1··1·11··1····11··11···111··11···1···111·· |
| out 44 (143) | ····1·1··1·111·········1·1111·····1·1··1······1··1·1111·111·11·111·11·1··1··········11·······11··1·11111··111·1··1·····1·1···1····11·1··1·1·111····11·1·1··1····111····1111····1·1·······1··1··1·111········11··1·11····11··1·····1·1·1·1·11·1111··111·11·1·····1·······11······11··1·1···1111··111··1···1···111·····111··1·1111···11·1···11····11·1····1111··1··1···· |
| out 45 (159) | ·1·11··11···1····1·1···1·1·111···11·11·1······1··111111···1·1·11·11·1111·······111··11····1···1·1·11·1·1···1·111·11··1·1········1111···11····1·11···11··1··1··1··111·1··1·······111·11·111···11···1····1·1··11····111··1111·1····11·111·1·11···11·11·11·1111········11·111·1·····11··11····1·1···1··111··11·11····1·111··11···1··11·11····11··1··1·11·1··1······111·11 |
| out 46 (135) | ····1·1··1·1111·1····1·1··111····11·1·········1··1·111···11·1··111111111·1··········1··1·····11··1·1·11····11····1·······1········11·1··1·1·11··1··11·······1···111····1111····1111······1··1··1·1111·1···1·1···1·11···111········1·1·1·1·1···111··111111111····1·······1·1·····11··1·1····11····11······1····1······111··1·111···111···········11·1····1111··1·111··· |
| out 47 (151) | ·1·111·111··1·1··1·1·1·1·1····1·1·····11···1·····1····1·1·1·1·11·11·1111···············1········111111·1··11·1111·1····1·1···111···1·11···1·1··1····11··1··1··1··111·1·1·1····111·11·1·111·1·111··1·1··1·11·11·······11····11··1····1······1·1·11·11·11·1111··········1···1·······1·111···11·1··11··111·1·1··11111····111···11···1··11····11··1··1·11·1·1·1··11·1·11·1 |
| out 48 (151) | ·1·1·11·11·1·1··11·1·····1···1···1···1·1·11······11··11·11······1·11·1·1·1·····111········1··11··11·1·11··1·11111·1··1···1·····1·1·1·1·11·1·11·11··1·1·1······1·1··1·1·1·11····11·1·11·11··11·11·1·1··11·1···1······1··1··1·111·····11····11·11·····1·11·1·1····1···11·1···1····11··11····1·11··1·1·111·1·1·1·1··1··1·11·11·111··111·1········1·1···1·1·1·11··1·1·1·11 |
| out 49 (133) | 11··1··1····11··111··1·1·1···11·····1··1·11·······1·1··1·11·1··11·····1···1····1·1··1··1·····1··111·11·1··1·1·1111·······1····1···11····1···1··1·1·1·1·····1··1111111····1····11···1··11·1···1····11··111·1·11······11···1··111······1··1···1·111··11·····1·········1··11·1·····1·1·11····11·1··1·1··11111····1·1····11···1··1···1·1·1·····1··1111·111····1··11····1·· |
| out 50 (141) | 11··1··1····11··111··1·1·11··11···1·1··1·11·1····11·1·11·11····11····11········1·1··1··1·····1··111·11·1··1·1·11·1······11····1··111········1·11·1·111········1111·11····1····11···1··11·1···1····11··111·1·11··1···11··11··111·1···11··1··11·11···11····11·········1··11·1·····1·1·11····11·1··1·1··111·1····1·1···111······1·1·1·111········1111··11····1··11····1·· |
| out 51 (141) | 1··1111·1··11·····11·1·1··1111··111···1··111··1···11·1111·1·1·11···1·111·1·······1···1········1··1···11······1····1····1·1···1·1···1··1·····11··11······1··1···1·1···1··11··1··1111··11·11·11·1··11·····111·1···1·111·111··1·111··1··11···1111·11·11···1·111····11·····1·1·······1··1······11·······1··1··1··111·1····1·1····11···1·······11···1·1····1··11·1·1·111··1 |
| out 52 (127) | ····1··1········1········1·1111·111·111····11·1···111·1·1···1·····1·············11··11·1··1·····1······1······1·11···1···1···1111·11·1111·1·1·1·1···1···1··············1111·1·11·1·11····1···1········1······1····1111111111···11·1··11·1··1·1··1·····1··············1·11111···1··1··········1·······1··11··1·11111··111111·11·1··1·1·····1·············1111111··1·11· |
| out 53 (135) | ····1·1··1·111··1··1·1·1··111·····1·1··1······1··1·111···11·1··111111·1··1··········11·······11··1·1111····11····1·····1·1···1····11·1··1·1·11··1··11······1····111····1111····1·1·······1··1··1·111··1··11·1···1·11····11··1·····1·1·1·1·1···111··111111·1·····1·······11······11··1·1···111·1··11······1···111·····111··1·111···111······1····11·1····1111··1··1···· |
| out 54 (141) | 11··11·1·1··111··11····1·····11·····1··1··1······11·1111·11····11·1···1··········1··11····1··11·1·1··1······1··111·······1····11··11········1111·1·111··1··1··1·11·11····11···111·11·111·1·1·1·1··111··11···1·······11···1··1·1·····11··1·111·11···11·1···1··1·········111·1····111··1·····1······1···1111····1·11···11······111·1·111····11··1·11··11····11·11·1·11·1 |
| out 55 (151) | ····1·11···111··1····1·1····1·····1·1··1·11·1·1····11·1·111·1··111·11·1··1·····1····1··1··1··11·1··1111····11··1111····1·1···1·11111·1····1·1·1····11···1··1····111····111·····1111··1···1··11···111··1···1·1·1····1····11··111·1·1···1·1··1·1111··111·11·1·····1···1···1·11····111···1···111····11···1·111··111·11·1111····11·1···11·····11····11·1····111···1·111··1 |
| out 56 (31) | ···············1·····1······················1····1····1·····1··················1·····1···············1····1······················1······1·····1·····1·····················1·····1·························1·····················1···1······1····1···················1····1·················1····1···················1·····1····1····1······················1····1····· |
| out 57 (143) | ····1111·1·111··1······1·1·11·····1·1····11···1··1·11····11·1··111·11·1··1·····1····11·1·····1··11·111····111·1·11·····1·1·····11·11·1··1·1·1···1··11···1··1····111····111·····1·11······1·111·1·111·11·····11····11····11···11···1·1·1·1·····111··111·11·1·····1···1···111·····1·1·1·1···11····111··1··11···11··11··111··1·11····111·····11····11·1····111···1··11··· |
| out 58 (31) | ··············1·1························1··1··················1··1····················1··1·········1··1·······················1·1······················1·························1··1··············1·1······················1··1··················1··1···················11··············1··1···················1··1··················1··1·······················1··1 |
| out 59 (111) | ··············1··········1··111·111·1111·1·1··1···1111··········1··············111··11····1·········1·········1·111··1···1····1·1111·1111·1·11·························111··1·11·1111···············1········1·····11111111111·1··1··11·1·1·········1···············11·111·1··············1··········1··111·1·1·1·1·1111111·111·········1···············111·111··1111· |
| out 60 (133) | 11···111···1··1··11··1····11111···1·1··1··1···1···11··11····1····1·111···1·······1···1··········11111·11···1···11······1··1···11·····1··1·1···1111···1··1··1··11··111··11·····1··111··11···111···1··1··11·1·····1·1111··11··1·1···1··11····11···1····1·111······1······1·1········1·111···1·11···1····111····1··11·····1··1·1··1·11··1····11··11···111··11···1···111·· |
| out 61 (151) | ····1·11·1·1·11·1······1·1111····11·1····1··1·1··1·1111·111·1··111111·1··1··········1·····1··11·11·1·11···111·1··1·······1·····1·111·1··1·1·111····11······1····111····1111····111···1···1··11·1·1·11·1·····11··1·11···111···1··1·1·1·1·1·11·1111··111111·1·····1·······1··1····111·1·1·1··11···111··1···1····1··1··1111··1·1111···11······1····11·1····1111··1·11···1 |
| out 62 (63) | ·····1···1····1······1·····1···········1·11·1····1···1··1·····················11·····1·1······1··1··1·····1·······1··········1·111······1····1··1·······················1·1·····1·1········1···1····1·····1·······1·········111·1···1·····1··1······················1····11······1··1·····1·····1·········1····1·11·1·····1···1···1······················1·1····1·1··· |
| out 63 (159) | ·1·111··1···1····1·1·1·1··1111···11·11···1····1··111111·1·1·1·11·1··1111·······1111·11·1··1·······11·1·1··11·1·1111··1·1·····1·1111····11····1·1····11·····1··1··111·1··1·····1·11··11·111·1··1···1····1·11·1···1·111··1111··1····1·111·1·11·1·11·11·1··1111········11·11111·········11····1·1··11··1·1·111·11·1·11·11···11···1··1··11·····1··1··1·11·1··1···1··11··11 |
| out 64 (151) | ·1·111··1···1·1·11·1·1·1··1111···11·11······1·1··1111·1···1···11·11·1111········11··111···1·······1111····11·1·1111··1·1·····1··1·1····11······11····1··1··1··1··111·1··1·1·····1·1·11·111·1··1···1·1·11·11·1···1·111··1111·····1·1·111·1··1···1··11·11·1111·········1·111·1·········11···11····11··1·1·111·11·1··1··1···11······11··1····11··1··1·11·1··1·1····1·1·11 |
| out 65 (135) | ·1·1··1·1··1·1··11·1·1·1·1·1·1···1···1····1·1····11··11··1····1·1·11·1·1·1······11·····1··1··1····1·1·11····11111····1···1···1·····1·1·11·1·11·1···1·1········1·1··1·1·1·1·····11···11·11···1·1··1·1··11·11·11····1·1··1··1···1·1···11····11··1···1·1·11·1·1····1····1·1··11····1····1····1·11····11111·1···1·11······11·11·111··1·1·1········1·1···1·1·1·1···1·1···11 |
| out 66 (119) | ·····1···1····1······1·····1111·111·111····11·1··11·11··1·······················11··1·····1···1··1··1·····1·····11···1···1···1111·11·111··1·11··1······················1111·1·1111111······1···1····1·····1·······1111111111···11·1·11··1·1··1·······················1·11··1·····1··1·····1·····1·······11··1·11111··11111·1111···1·····················1111111·11111· |
| out 67 (133) | 1··1111·11·111····11···1·11·11··1·1···1···11··1··111··111·1·1·11··11··11·1·······1···1········1······11···1··11··········1···1·····1··1·1···1···11·············1·1··11··11··1··1111··11·11·11·11·111····11··11··1··11·1·1··1··11··1·111····111·11·11··11··11····1······1·1·······1·······1·11···1···11·1······11······1·1·1··1····1············1·1···11··11·1·1·111··1 |
| out 68 (135) | ····111····1111·1······1·11·1·····1·1····11···11···11····11·1··111·11·1··1·····1····11·1·····1·····1·11···111·1··11····1·1·····11·11·11···1·1···1··11···1··1····111····111·····1·11······1·11····1111·1·····11··1··1····11···11···1···1·1·····111··111·11·1·····1···1···111·····1·····1····11···111··1···11··11··11··1111···11····111·····11····11·1····111···1··11··· |
| out 69 (141) | 11···111···1·····11··1···11······1··1111·111········11·11········1·111···1·····11···1·····1·····1111··11···1··11·1···111·1···1·11111··11····11·1·1··11··1··1··11··111····1··1··1····1·11···111···1·····11·1··1··1······1·1111111········1·1·11·······1·111······1···11··1··1······1·111·····11···1···111·1··1111·11·111·11···11··1··11····11··11···111····1·1·1·····1· |
| out 70 (127) | ····111····111··1······1··1··11·11···111···11····11··1··11··1··111111·1··1······11·····1··1··1·····1111···111···1····1·1······111·····11·····1····111······1····111·········1·1····11····1·11····111··1·····1···1···1111··111··11···11····1··11·1··111111·1·····1····1·1··11····1·····1···111···111·····1···11··111·····11····1····11······1····11·1········11·····11· |
| out 71 (149) | 1··1···111···1····11·······11·1···1··1·1·11···1····1···111··1·1·111·11·1·······11······1··1··11·1··11··1···111··1·1··1···1···11·11·1···11···1·1··1·1····1······11·1·111·111···11·111111·1····111···1····11········11·1··1·1·111···1···1·····111·1·1·111·11·1······1·11····11····111···1···1··1···11·1··11·1·1·111·1·1·1··11··1·1···1······1····11··1·111·111·11··11111 |
| out 72 (133) | 11··1···1···111·111····1·11··11··1··1··1··········1·1··1·11·1··11····11··········1··11·1·····1···11··1·1····1·11·1·····1·1····111·11····1···1··1·1·1·1········1111·11····11···111··1··11·1····1···111·111···11··1···11·1·1··1········1··1···1·111··11····11············1111·····1··111·····1·1····1··111·1···11·111··11···1··1···1·1·1········1111··11····11·11·1··1·· |
| out 73 (147) | ····111····1111··111·1···1···11·11···11··1····1····111····1·1··1111··1·1·······111···1·······1·····11·····1··1·1·····1·1·····111··11·1····1·11·111·11······1·111···1111···1·1·1·1·1111···1·11····1111··1111··1······1111··11·1····1···1·1·1····11··1111··1·1········11·1·1······1·····1···1····11···1·11····11·111···111····111··1111······1·111····1111···111··1·1111 |
| out 74 (151) | ·1·111··1···1···11·1···1··1111···11·11········1··1·1111···1·1·11·11·1111·······111··11····1·······11·1·····1·1·1111··1·1·····1··111····111···1·11···11··1··1··1··111·1··1·······111·11·111·1··1···1···11·1··1···1·111··1111·······1·1·1·1·11···11·11·11·1111········11·111·1·········11····1·····1··1·1·111·11·1··1·11···11···1··11·11····11··1··1·11·1··1······111·11 |
| out 75 (159) | ·1·11··11···1····1·1·1·1···111···11·11·1·1····1··11111··1·1·1·11·11·1111·······111···1·1··1···1·1·11·1·1··11·1·1·11··1·1·······1111····11····111····11··1··1··1··111·1··1·······11··11·111···11···1····1·11·1·····111··1111·11····1·111·1·1··1·11·11·11·1111········11·1·111·····11··11····1·1··11··1·1··11·11···11·11···11···11·1··11····11··1··1·11·1··1·····111··11 |
| out 76 (119) | ··············1·1····1··1···111·111·1111···1··1··1111·······1·····1·············11··1··1············1··1··1··1··111··1···1····111111·111··1·1·······1···1··············1111·1·1111·111··············1·1···1········1111111111··1··1·111·1·······1·····1··············1·11·1···············1··1··1···1···111·1·1·111·111111··11······1·····1·············1111111·11·111 |
| out 77 (79) | ·····1···1····1·1····1···1·1···········1·11······1···11·1·········1············1·····1·1··1···1··1··1··1··1···1···1··········1·11·······1·1··11·1·······1·················1·····1·1··1·····1···1····1·1···1··1····1·········111·····1··1··11·1········1·············1····111·····1··1·····1··1··1····1····1····1·11·······1·1·11··1·······1················1····1·1··1 |
| out 78 (141) | 11····11·1·1··1·111········1····11··111····1········1·11····1····1·11···11······1···11·1······1·1·111·1···11···1111··1·1·1·······111··11····1·1111···1··1····111··111····11·1··11·1·1111····11·1·1··1·111·········1···11·111···1········1··11···1····1·11·······1····1··111······11··11···1·1···11····11111·111·····111·11···1·1·11··1····1··111···111····111·1·1·1·11 |
| out 79 (143) | ····1·1··1·1111······1·1·111·11·11···11··111·1···11······11····111111·1··1·····111···1·······11··1·1·111···11·1·1·1··1·1·····11··11···11········1··1·······1····111·······1·1·1·1·1111···1··1··1·1111·····1·11··1·1·1111··11·111····11········11···111111·1·····1···11·1·1······11··1·1····111···11··1··1·1·11·11···11··11········11·······1····11·1·······111··1·1111 |
| out 80 (127) | ····111····1111········1·11·1·····1·1····1····1····11·1··11····111·11·1··1··········1··1·····1·····1·111··11··1··11····1·1·····1··11·1····1·1·1·1··1····1··1····111····1111····1111······1·11····1111······111··1··1····11···1····1···1·1··1··11···111·11·1·····1·······1·1·····1·····1····111··11···1···11··11··1···111····11·1··11······11····11·1····1111··1·111··· |
| out 81 (31) | ·····1···1·················1···········1················1···1················1·········1······1··1················1··········1··················1···1··················1··········1········1···1··················1·········1················1··1·························1······1··1·····················1····1··················1·1···················1·········1··· |
| out 82 (143) | ····1111·1·111·········1·1·11·····1·1·········1··1·1111··11·1··111·11·1··1··········11·1·····1··11·11111··111·1·11·····1·1········11·1··1·1·111·1··11···1··1····111····11·1····1·11······1·111·1·111········11····11····11········1·1·1·1·11··111··111·11·1·····1··1····111·····1·1·1·1···1111··111··1··11···11······111··1·1111··111·····11····11·1····11·1··1··11··· |
| out 83 (127) | ·····1···1······1········11·111·111·1·11···11·1···111·1·1···1·····1·············11··11·1··1···1··1·····1······1··11··1···1·1··111·11·1111·1·1·1·1···1···1··············1111·1·11·1·11······1···1······1······1··1··1111111·11··11·1··11·1··1·1··1·····1··············1·11111·····1··1········1·······1···11·1·1·111··111111·11·1··1·1·····1·············1111111··1·11· |
| out 84 (133) | ·1·1·1111··1·11··1·1······11·1···1···1·1·········11·········1·1·1·11·1·1·1·····111·····1·····11·1·1···1···1·11·1·····1···1······11·1·1·11·1·1·11·1·111········1·1··1·1·1·11····11···1··11··1111··1·11··1·1·····11·1·1··1··1·1·······11··········1·1·1·11·1·1····1···11·1··1·····111··1······1···1·1·1·11····1·1···1·1·11·11·11·1·1·111········1·1···1·1·1·11··1·1···1· |
| out 85 (135) | ····1·11···111··1····1·1·1··1·····1·1··1··1···1····11··1111·1··111·11·1··1·····1····1········11·1··1111····11·1·111····1·1···1··1·11·1····1·1······11···1··1····111····111·····111·······1··11···111··1···1·11·····1····11··1·1···1···1·1···11111··111·11·1·····1···1···1·······111···1···111····11··1··111··111··1··111····11··1··11·····11····11·1····111···1·11···· |
| check 86 (134) | ·····1·11··1111········1··········1·111··········111111··1··1·1111···1···1··········11·1··1···1··1111·····111111·······1·1···11·······11··1·111··1···11·1··1····1111111········1·1·11······1·11··1111·······1···········1111········111·1·11··1·1·1111···1······1·······1111·····1··111···1·····111·1111·····1111·······11··1111·····11···11····11·11111······1··1·11· |
| check 87 (142) | 11·1···1·1·111············1··11·111·1··1·1··1·1···1··1····1···1···1····1·1·····1··········11····11·11111·····1111····1···1···1·1·111·1111····1··11·1111·1····111111····111········111·111····1·1·111············1···111111··11··1·1··1····1····1··1···1····1····1···1······1··1···1·1·1···1111······11111···1·11·1··1111111···1···11111···1··11111·1····111·······111· |
| check 88 (136) | ·1·1··1·1··1·11··1·1·····1111·1·1·1·1·1···11··1··1·11·111·1····1·1··1·1·········11·····1··1··1····1···1···1·1111111···········111·1···1······11·····1·1······1·1·11·1·11·1·····11···11·11···1·1··1·11··1·1···1··1·11·11·11·1··11··1·1·1·1··111·1···1·1··1·1··········1·1··11····1····1······1···1·1·111·111·····111··1··1·····11····1·1······1·1·1·1·1·11·1···1·1···11 |
| check 89 (176) | 11·1··1··1·1···111·111·1·1···1···1···1·1·11·····1111·11111·11·1··111·1111··1·1··11··1·······1·1···111··11·1·11··11·1·111·11·11······11·1··1··111···1·1·1·1······11·1·111·11·11·1····11·1··111·1·11·1·11··1····1··11···1··111··1·111··1···11···1·····1·1··1·11··11·1·111··1111···1··111···11111·1··11111·1·1·1·1··1··1·11··11111·111·11··11··111·1·1···1···1···111·1·1· |
| check 90 (174) | ···1··11··1···111·1·1·1···1·11·······1·11111··1·11·11·1·11·1··1···1·11··1·1···11111·11111···1··11·1·11·1·1·1·····11·1111111·1····111·11··11·1·1·11·1···11·11·1····1····1·1··1··1····11·1··1··11··1·11·······11·111··111·111111·11111111111···1···1··1····11··1·1·11··111·111·1··1·11···1·11········1·1·1··11111·1·1··1··11·······11··1··1··11··1·1···1·11111·111·1·11· |
| check 91 (180) | 1111···1·111····111·1·····1111111·111··11·1······1·11111··11·11··1·111···11·1··1··1···1··1·11·111··1··1···11···11····111·11····1····11···111·111111111111··1··11···111·11·1··1··1·111·11···111···111·1·111·11·111···11··1·····111·11·11··111··········111·1·11····11···1·1·1······1·111·11···11·1111····1·11·1·111·11·····1·11111·1·11···1··1·····1111·1111··1···111·1 |
| check 92 (182) | ·1·1···11··1·1···1··1··11·1·11·1··1·11··1·1·111···1·1·1··1111·1·1·1·1·111··11··1111·11·1111··1·11·1··1·111·1·11·11·1111····11·····1111·1··111··1··1·11······1··1·111111·1··111··111·1··11111111·1·1·····11··11111··1·11·11·11·1·11·1·111·1·1·1··1·11·1··1·1·11···11·1·1·11·····1·11··11111·1·111·1····1·11·····11········1·1·····11111·1111··11··1·1·····1···1··11·1·1 |
| check 93 (176) | ·1·11··1111·1·1··1·1··111···11···1·1··1·111·1·1111·1··1·1·1··1·1·1··1·11··111···11·11·1·111···1·11·111·1·······1·1···1·111111111··1···1·11·1···1·····111······1··1······1·1····1··11·1·111······11·11··1·111·111···11···111·111·1·1··1·111·1·1·1111·1·1·1·11··11111··1·1·11······1·1·1·11111·1··111111·1·1··1····1···1···1·111···1··1··1111···1·1·111111·1·1···111··1· |
| check 94 (176) | 11··11······11·1·111111·1·111···111··11···1··11111···1·1··1····11·1··1··11111···1····1·······11··11··11111····1·1····1·········1···11·11·1·111·1···111··11111······1··111···1····1··1111·1·1······11111····111111·11··111·11·1·111·1·111111·1··1···11·111·111111·11··1···1······11··11····1···1111111·111···1·····1111·1··111·1··1·111····1·11111111·11·11··1····1··11 |
| check 95 (168) | ····111····111··1······1··1·111111·1·111111·11·11·11·11·111····111·11·1··1···11111111·1·111··1·····1111···111····111111·1·11111111·11111·111111····1····1··1····111······1·1·11·1··111···1·11····111··1·····1····11·····11·····1·1111··11111·111···111·11·1·····1··1··1··11·····1·····1···111···111·····1··1·11····1·1····11··11···1······11····11·1····11·11·11·11··· |
| check 96 (166) | 11··1····1··11··1··1······1··11·····1····1·11·1··1·1···1·1·1·1111·1··1··111111111·111·11111··1····1···1···11·11··1·······1···111·····1111·1····1·11·111111111······1··1111·1·1···1··1111·1·····1··11··1··1······1···11···1···1·11·1·1·1···11·1·111···1·11·111111·111··11·1······1····1······1··111··11···1····1111·····1111·1·111·11···111··11111111·11····111111·11·· |
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 n358Noisy T states per run.
outputs k86
distance d3Exact, proved and witnessed here.
error coefficient A_{3}3,116Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.
wires N97
checks r11
V_{\mathrm{ex}}86T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.2982Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.2982Overhead per output qubit.
\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.
T-countnot computedMinimal T-count of the output gate. Not computable at this width.
phase-polynomial degreenot computedMinimised over changes of output basis.
effective width86Rank of the output rows modulo the check rows.
Output gate
86 T0 CS0 CCZon 86 output wires
As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}\cdot \mathrm{T}_{77}\cdot \mathrm{T}_{78}\cdot \mathrm{T}_{79}\cdot \mathrm{T}_{80}\cdot \mathrm{T}_{81}\cdot \mathrm{T}_{82}\cdot \mathrm{T}_{83}\cdot \mathrm{T}_{84}\cdot \mathrm{T}_{85}
As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85 (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 92 single-wire gates and 469 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{S} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23 and 537 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 561 correction gates
\mathrm{Z} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{S} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{Z} on output 26, \mathrm{S} on output 27, \mathrm{S} on output 28, \mathrm{S} on output 29, \mathrm{S} on output 30, \mathrm{Z} on output 31, \mathrm{Z} on output 32, \mathrm{Z} on output 33, \mathrm{S} on output 34, \mathrm{S} on output 35, \mathrm{Z} on output 36, \mathrm{S} on output 37, \mathrm{S} on output 38, \mathrm{S} on output 39, \mathrm{S} on output 40, \mathrm{S} on output 41, \mathrm{S} on output 42, \mathrm{Z} on output 43, \mathrm{S} on output 44, \mathrm{S} on output 45, \mathrm{S} on output 46, \mathrm{S} on output 47, \mathrm{S} on output 48, \mathrm{Z} on output 49, \mathrm{Z} on output 50, \mathrm{Z} on output 51, \mathrm{S} on output 52, \mathrm{S} on output 53, \mathrm{Z} on output 54, \mathrm{S} on output 55, \mathrm{S} on output 56, \mathrm{S} on output 57, \mathrm{S} on output 58, \mathrm{S} on output 59, \mathrm{Z} on output 60, \mathrm{S} on output 61, \mathrm{S} on output 62, \mathrm{S} on output 63, \mathrm{S} on output 64, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{Z} on output 67, \mathrm{S} on output 68, \mathrm{Z} on output 69, \mathrm{S} on output 70, \mathrm{Z} on output 71, \mathrm{Z} on output 72, \mathrm{S}^\dagger on output 73, \mathrm{S} on output 74, \mathrm{S} on output 75, \mathrm{S} on output 76, \mathrm{S} on output 77, \mathrm{Z} on output 78, \mathrm{S} on output 79, \mathrm{S} on output 80, \mathrm{S} on output 81, \mathrm{S} on output 82, \mathrm{S} on output 83, \mathrm{Z} on output 84, \mathrm{S} on output 85, \mathrm{S} on check 86, \mathrm{S} on check 87, \mathrm{S} on check 90, \mathrm{Z} on check 91, \mathrm{S} on check 92, \mathrm{S} on check 96, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 4, \mathrm{CZ} on output 0, output 5, \mathrm{CZ} on output 0, output 9, \mathrm{CZ} on output 0, output 15, \mathrm{CZ} on output 0, output 18, \mathrm{CZ} on output 0, output 19, \mathrm{CZ} on output 0, output 23, \mathrm{CZ} on output 0, output 26, \mathrm{CZ} on output 0, output 31, \mathrm{CZ} on output 0, output 32, \mathrm{CZ} on output 0, output 33, \mathrm{CZ} on output 0, output 36, \mathrm{CZ} on output 0, output 43, \mathrm{CZ} on output 0, output 49, \mathrm{CZ} on output 0, output 50, \mathrm{CZ} on output 0, output 51, \mathrm{CZ} on output 0, output 54, \mathrm{CZ} on output 0, output 60, \mathrm{CZ} on output 0, output 67, \mathrm{CZ} on output 0, output 69, \mathrm{CZ} on output 0, output 71, \mathrm{CZ} on output 0, output 72, \mathrm{CZ} on output 0, output 73, \mathrm{CZ} on output 0, output 78, \mathrm{CZ} on output 0, output 84, \mathrm{CZ} on output 0, check 86, \mathrm{CZ} on output 0, check 87, \mathrm{CZ} on output 0, check 91, \mathrm{CZ} on output 0, check 92, \mathrm{CZ} on output 1, output 4, \mathrm{CZ} on output 1, output 5, \mathrm{CZ} on output 1, output 9, \mathrm{CZ} on output 1, output 15, \mathrm{CZ} on output 1, output 18, \mathrm{CZ} on output 1, output 19, \mathrm{CZ} on output 1, output 23, \mathrm{CZ} on output 1, output 26, \mathrm{CZ} on output 1, output 31, \mathrm{CZ} on output 1, output 32, \mathrm{CZ} on output 1, output 33, \mathrm{CZ} on output 1, output 36, \mathrm{CZ} on output 1, output 43, \mathrm{CZ} on output 1, output 49, \mathrm{CZ} on output 1, output 50, \mathrm{CZ} on output 1, output 51, \mathrm{CZ} on output 1, output 54, \mathrm{CZ} on output 1, output 60, \mathrm{CZ} on output 1, output 67, \mathrm{CZ} on output 1, output 69, \mathrm{CZ} on output 1, output 71, \mathrm{CZ} on output 1, output 72, \mathrm{CZ} on output 1, output 73, \mathrm{CZ} on output 1, output 78, \mathrm{CZ} on output 1, output 84, \mathrm{CZ} on output 1, check 86, \mathrm{CZ} on output 1, check 87, \mathrm{CZ} on output 1, check 91, \mathrm{CZ} on output 1, check 92, \mathrm{CZ} on output 4, output 5, \mathrm{CZ} on output 4, output 9, \mathrm{CZ} on output 4, output 15, \mathrm{CZ} on output 4, output 18, \mathrm{CZ} on output 4, output 19, \mathrm{CZ} on output 4, output 23, \mathrm{CZ} on output 4, output 26, \mathrm{CZ} on output 4, output 31, \mathrm{CZ} on output 4, output 32, \mathrm{CZ} on output 4, output 33, \mathrm{CZ} on output 4, output 36, \mathrm{CZ} on output 4, output 43, \mathrm{CZ} on output 4, output 49, \mathrm{CZ} on output 4, output 50, \mathrm{CZ} on output 4, output 51, \mathrm{CZ} on output 4, output 54, \mathrm{CZ} on output 4, output 60, \mathrm{CZ} on output 4, output 67, \mathrm{CZ} on output 4, output 69, \mathrm{CZ} on output 4, output 71, \mathrm{CZ} on output 4, output 72, \mathrm{CZ} on output 4, output 73, \mathrm{CZ} on output 4, output 78, \mathrm{CZ} on output 4, output 84, \mathrm{CZ} on output 4, check 86, \mathrm{CZ} on output 4, check 87, \mathrm{CZ} on output 4, check 91, \mathrm{CZ} on output 4, check 92, \mathrm{CZ} on output 5, output 9, \mathrm{CZ} on output 5, output 15, \mathrm{CZ} on output 5, output 18, \mathrm{CZ} on output 5, output 19, \mathrm{CZ} on output 5, output 23, \mathrm{CZ} on output 5, output 26, \mathrm{CZ} on output 5, output 31, \mathrm{CZ} on output 5, output 32, \mathrm{CZ} on output 5, output 33, \mathrm{CZ} on output 5, output 36, \mathrm{CZ} on output 5, output 43, \mathrm{CZ} on output 5, output 49, \mathrm{CZ} on output 5, output 50, \mathrm{CZ} on output 5, output 51, \mathrm{CZ} on output 5, output 54, \mathrm{CZ} on output 5, output 60, \mathrm{CZ} on output 5, output 67, \mathrm{CZ} on output 5, output 69, \mathrm{CZ} on output 5, output 71, \mathrm{CZ} on output 5, output 72, \mathrm{CZ} on output 5, output 73, \mathrm{CZ} on output 5, output 78, \mathrm{CZ} on output 5, output 84, \mathrm{CZ} on output 5, check 86, \mathrm{CZ} on output 5, check 87, \mathrm{CZ} on output 5, check 91, \mathrm{CZ} on output 5, check 92, \mathrm{CZ} on output 9, output 15, \mathrm{CZ} on output 9, output 18, \mathrm{CZ} on output 9, output 19, \mathrm{CZ} on output 9, output 23, \mathrm{CZ} on output 9, output 26, \mathrm{CZ} on output 9, output 31, \mathrm{CZ} on output 9, output 32, \mathrm{CZ} on output 9, output 33, \mathrm{CZ} on output 9, output 36, \mathrm{CZ} on output 9, output 43, \mathrm{CZ} on output 9, output 49, \mathrm{CZ} on output 9, output 50, \mathrm{CZ} on output 9, output 51, \mathrm{CZ} on output 9, output 54, \mathrm{CZ} on output 9, output 60, \mathrm{CZ} on output 9, output 67, \mathrm{CZ} on output 9, output 69, \mathrm{CZ} on output 9, output 71, \mathrm{CZ} on output 9, output 72, \mathrm{CZ} on output 9, output 73, \mathrm{CZ} on output 9, output 78, \mathrm{CZ} on output 9, output 84, \mathrm{CZ} on output 9, check 86, \mathrm{CZ} on output 9, check 87, \mathrm{CZ} on output 9, check 91, \mathrm{CZ} on output 9, check 92, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 19, \mathrm{CZ} on output 15, output 23, \mathrm{CZ} on output 15, output 26, \mathrm{CZ} on output 15, output 31, \mathrm{CZ} on output 15, output 32, \mathrm{CZ} on output 15, output 33, \mathrm{CZ} on output 15, output 36, \mathrm{CZ} on output 15, output 43, \mathrm{CZ} on output 15, output 49, \mathrm{CZ} on output 15, output 50, \mathrm{CZ} on output 15, output 51, \mathrm{CZ} on output 15, output 54, \mathrm{CZ} on output 15, output 60, \mathrm{CZ} on output 15, output 67, \mathrm{CZ} on output 15, output 69, \mathrm{CZ} on output 15, output 71, \mathrm{CZ} on output 15, output 72, \mathrm{CZ} on output 15, output 73, \mathrm{CZ} on output 15, output 78, \mathrm{CZ} on output 15, output 84, \mathrm{CZ} on output 15, check 86, \mathrm{CZ} on output 15, check 87, \mathrm{CZ} on output 15, check 91, \mathrm{CZ} on output 15, check 92, \mathrm{CZ} on output 18, output 19, \mathrm{CZ} on output 18, output 23, \mathrm{CZ} on output 18, output 26, \mathrm{CZ} on output 18, output 31, \mathrm{CZ} on output 18, output 32, \mathrm{CZ} on output 18, output 33, \mathrm{CZ} on output 18, output 36, \mathrm{CZ} on output 18, output 43, \mathrm{CZ} on output 18, output 49, \mathrm{CZ} on output 18, output 50, \mathrm{CZ} on output 18, output 51, \mathrm{CZ} on output 18, output 54, \mathrm{CZ} on output 18, output 60, \mathrm{CZ} on output 18, output 67, \mathrm{CZ} on output 18, output 69, \mathrm{CZ} on output 18, output 71, \mathrm{CZ} on output 18, output 72, \mathrm{CZ} on output 18, output 73, \mathrm{CZ} on output 18, output 78, \mathrm{CZ} on output 18, output 84, \mathrm{CZ} on output 18, check 86, \mathrm{CZ} on output 18, check 87, \mathrm{CZ} on output 18, check 91, \mathrm{CZ} on output 18, check 92, \mathrm{CZ} on output 19, output 23, \mathrm{CZ} on output 19, output 26, \mathrm{CZ} on output 19, output 31, \mathrm{CZ} on output 19, output 32, \mathrm{CZ} on output 19, output 33, \mathrm{CZ} on output 19, output 36, \mathrm{CZ} on output 19, output 43, \mathrm{CZ} on output 19, output 49, \mathrm{CZ} on output 19, output 50, \mathrm{CZ} on output 19, output 51, \mathrm{CZ} on output 19, output 54, \mathrm{CZ} on output 19, output 60, \mathrm{CZ} on output 19, output 67, \mathrm{CZ} on output 19, output 69, \mathrm{CZ} on output 19, output 71, \mathrm{CZ} on output 19, output 72, \mathrm{CZ} on output 19, output 73, \mathrm{CZ} on output 19, output 78, \mathrm{CZ} on output 19, output 84, \mathrm{CZ} on output 19, check 86, \mathrm{CZ} on output 19, check 87, \mathrm{CZ} on output 19, check 91, \mathrm{CZ} on output 19, check 92, \mathrm{CZ} on output 23, output 26, \mathrm{CZ} on output 23, output 31, \mathrm{CZ} on output 23, output 32, \mathrm{CZ} on output 23, output 33, \mathrm{CZ} on output 23, output 36, \mathrm{CZ} on output 23, output 43, \mathrm{CZ} on output 23, output 49, \mathrm{CZ} on output 23, output 50, \mathrm{CZ} on output 23, output 51, \mathrm{CZ} on output 23, output 54, \mathrm{CZ} on output 23, output 60, \mathrm{CZ} on output 23, output 67, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, output 71, \mathrm{CZ} on output 23, output 72, \mathrm{CZ} on output 23, output 73, \mathrm{CZ} on output 23, output 78, \mathrm{CZ} on output 23, output 84, \mathrm{CZ} on output 23, check 86, \mathrm{CZ} on output 23, check 87, \mathrm{CZ} on output 23, check 91, \mathrm{CZ} on output 23, check 92, \mathrm{CZ} on output 26, output 31, \mathrm{CZ} on output 26, output 32, \mathrm{CZ} on output 26, output 33, \mathrm{CZ} on output 26, output 36, \mathrm{CZ} on output 26, output 43, \mathrm{CZ} on output 26, output 49, \mathrm{CZ} on output 26, output 50, \mathrm{CZ} on output 26, output 51, \mathrm{CZ} on output 26, output 54, \mathrm{CZ} on output 26, output 60, \mathrm{CZ} on output 26, output 67, \mathrm{CZ} on output 26, output 69, \mathrm{CZ} on output 26, output 71, \mathrm{CZ} on output 26, output 72, \mathrm{CZ} on output 26, output 73, \mathrm{CZ} on output 26, output 78, \mathrm{CZ} on output 26, output 84, \mathrm{CZ} on output 26, check 86, \mathrm{CZ} on output 26, check 87, \mathrm{CZ} on output 26, check 91, \mathrm{CZ} on output 26, check 92, \mathrm{CZ} on output 31, output 32, \mathrm{CZ} on output 31, output 33, \mathrm{CZ} on output 31, output 36, \mathrm{CZ} on output 31, output 43, \mathrm{CZ} on output 31, output 49, \mathrm{CZ} on output 31, output 50, \mathrm{CZ} on output 31, output 51, \mathrm{CZ} on output 31, output 54, \mathrm{CZ} on output 31, output 60, \mathrm{CZ} on output 31, output 67, \mathrm{CZ} on output 31, output 69, \mathrm{CZ} on output 31, output 71, \mathrm{CZ} on output 31, output 72, \mathrm{CZ} on output 31, output 73, \mathrm{CZ} on output 31, output 78, \mathrm{CZ} on output 31, output 84, \mathrm{CZ} on output 31, check 86, \mathrm{CZ} on output 31, check 87, \mathrm{CZ} on output 31, check 91, \mathrm{CZ} on output 31, check 92, \mathrm{CZ} on output 32, output 33, \mathrm{CZ} on output 32, output 36, \mathrm{CZ} on output 32, output 43, \mathrm{CZ} on output 32, output 49, \mathrm{CZ} on output 32, output 50, \mathrm{CZ} on output 32, output 51, \mathrm{CZ} on output 32, output 54, \mathrm{CZ} on output 32, output 60, \mathrm{CZ} on output 32, output 67, \mathrm{CZ} on output 32, output 69, \mathrm{CZ} on output 32, output 71, \mathrm{CZ} on output 32, output 72, \mathrm{CZ} on output 32, output 73, \mathrm{CZ} on output 32, output 78, \mathrm{CZ} on output 32, output 84, \mathrm{CZ} on output 32, check 86, \mathrm{CZ} on output 32, check 87, \mathrm{CZ} on output 32, check 91, \mathrm{CZ} on output 32, check 92, \mathrm{CZ} on output 33, output 36, \mathrm{CZ} on output 33, output 43, \mathrm{CZ} on output 33, output 49, \mathrm{CZ} on output 33, output 50, \mathrm{CZ} on output 33, output 51, \mathrm{CZ} on output 33, output 54, \mathrm{CZ} on output 33, output 60, \mathrm{CZ} on output 33, output 67, \mathrm{CZ} on output 33, output 69, \mathrm{CZ} on output 33, output 71, \mathrm{CZ} on output 33, output 72, \mathrm{CZ} on output 33, output 73, \mathrm{CZ} on output 33, output 78, \mathrm{CZ} on output 33, output 84, \mathrm{CZ} on output 33, check 86, \mathrm{CZ} on output 33, check 87, \mathrm{CZ} on output 33, check 91, \mathrm{CZ} on output 33, check 92, \mathrm{CZ} on output 36, output 43, \mathrm{CZ} on output 36, output 49, \mathrm{CZ} on output 36, output 50, \mathrm{CZ} on output 36, output 51, \mathrm{CZ} on output 36, output 54, \mathrm{CZ} on output 36, output 60, \mathrm{CZ} on output 36, output 67, \mathrm{CZ} on output 36, output 69, \mathrm{CZ} on output 36, output 71, \mathrm{CZ} on output 36, output 72, \mathrm{CZ} on output 36, output 73, \mathrm{CZ} on output 36, output 78, \mathrm{CZ} on output 36, output 84, \mathrm{CZ} on output 36, check 86, \mathrm{CZ} on output 36, check 87, \mathrm{CZ} on output 36, check 91, \mathrm{CZ} on output 36, check 92, \mathrm{CZ} on output 43, output 49, \mathrm{CZ} on output 43, output 50, \mathrm{CZ} on output 43, output 51, \mathrm{CZ} on output 43, output 54, \mathrm{CZ} on output 43, output 60, \mathrm{CZ} on output 43, output 67, \mathrm{CZ} on output 43, output 69, \mathrm{CZ} on output 43, output 71, \mathrm{CZ} on output 43, output 72, \mathrm{CZ} on output 43, output 73, \mathrm{CZ} on output 43, output 78, \mathrm{CZ} on output 43, output 84, \mathrm{CZ} on output 43, check 86, \mathrm{CZ} on output 43, check 87, \mathrm{CZ} on output 43, check 91, \mathrm{CZ} on output 43, check 92, \mathrm{CZ} on output 49, output 50, \mathrm{CZ} on output 49, output 51, \mathrm{CZ} on output 49, output 54, \mathrm{CZ} on output 49, output 60, \mathrm{CZ} on output 49, output 67, \mathrm{CZ} on output 49, output 69, \mathrm{CZ} on output 49, output 71, \mathrm{CZ} on output 49, output 72, \mathrm{CZ} on output 49, output 73, \mathrm{CZ} on output 49, output 78, \mathrm{CZ} on output 49, output 84, \mathrm{CZ} on output 49, check 86, \mathrm{CZ} on output 49, check 87, \mathrm{CZ} on output 49, check 91, \mathrm{CZ} on output 49, check 92, \mathrm{CZ} on output 50, output 51, \mathrm{CZ} on output 50, output 54, \mathrm{CZ} on output 50, output 60, \mathrm{CZ} on output 50, output 67, \mathrm{CZ} on output 50, output 69, \mathrm{CZ} on output 50, output 71, \mathrm{CZ} on output 50, output 72, \mathrm{CZ} on output 50, output 73, \mathrm{CZ} on output 50, output 78, \mathrm{CZ} on output 50, output 84, \mathrm{CZ} on output 50, check 86, \mathrm{CZ} on output 50, check 87, \mathrm{CZ} on output 50, check 91, \mathrm{CZ} on output 50, check 92, \mathrm{CZ} on output 51, output 54, \mathrm{CZ} on output 51, output 60, \mathrm{CZ} on output 51, output 67, \mathrm{CZ} on output 51, output 69, \mathrm{CZ} on output 51, output 71, \mathrm{CZ} on output 51, output 72, \mathrm{CZ} on output 51, output 73, \mathrm{CZ} on output 51, output 78, \mathrm{CZ} on output 51, output 84, \mathrm{CZ} on output 51, check 86, \mathrm{CZ} on output 51, check 87, \mathrm{CZ} on output 51, check 91, \mathrm{CZ} on output 51, check 92, \mathrm{CZ} on output 54, output 60, \mathrm{CZ} on output 54, output 67, \mathrm{CZ} on output 54, output 69, \mathrm{CZ} on output 54, output 71, \mathrm{CZ} on output 54, output 72, \mathrm{CZ} on output 54, output 73, \mathrm{CZ} on output 54, output 78, \mathrm{CZ} on output 54, output 84, \mathrm{CZ} on output 54, check 86, \mathrm{CZ} on output 54, check 87, \mathrm{CZ} on output 54, check 91, \mathrm{CZ} on output 54, check 92, \mathrm{CZ} on output 60, output 67, \mathrm{CZ} on output 60, output 69, \mathrm{CZ} on output 60, output 71, \mathrm{CZ} on output 60, output 72, \mathrm{CZ} on output 60, output 73, \mathrm{CZ} on output 60, output 78, \mathrm{CZ} on output 60, output 84, \mathrm{CZ} on output 60, check 86, \mathrm{CZ} on output 60, check 87, \mathrm{CZ} on output 60, check 91, \mathrm{CZ} on output 60, check 92, \mathrm{CZ} on output 67, output 69, \mathrm{CZ} on output 67, output 71, \mathrm{CZ} on output 67, output 72, \mathrm{CZ} on output 67, output 73, \mathrm{CZ} on output 67, output 78, \mathrm{CZ} on output 67, output 84, \mathrm{CZ} on output 67, check 86, \mathrm{CZ} on output 67, check 87, \mathrm{CZ} on output 67, check 91, \mathrm{CZ} on output 67, check 92, \mathrm{CZ} on output 69, output 71, \mathrm{CZ} on output 69, output 72, \mathrm{CZ} on output 69, output 73, \mathrm{CZ} on output 69, output 78, \mathrm{CZ} on output 69, output 84, \mathrm{CZ} on output 69, check 86, \mathrm{CZ} on output 69, check 87, \mathrm{CZ} on output 69, check 91, \mathrm{CZ} on output 69, check 92, \mathrm{CZ} on output 71, output 72, \mathrm{CZ} on output 71, output 73, \mathrm{CZ} on output 71, output 78, \mathrm{CZ} on output 71, output 84, \mathrm{CZ} on output 71, check 86, \mathrm{CZ} on output 71, check 87, \mathrm{CZ} on output 71, check 91, \mathrm{CZ} on output 71, check 92, \mathrm{CZ} on output 72, output 73, \mathrm{CZ} on output 72, output 78, \mathrm{CZ} on output 72, output 84, \mathrm{CZ} on output 72, check 86, \mathrm{CZ} on output 72, check 87, \mathrm{CZ} on output 72, check 91, \mathrm{CZ} on output 72, check 92, \mathrm{CZ} on output 73, output 78, \mathrm{CZ} on output 73, output 84, \mathrm{CZ} on output 73, check 86, \mathrm{CZ} on output 73, check 87, \mathrm{CZ} on output 73, check 90, \mathrm{CZ} on output 73, check 92, \mathrm{CZ} on output 73, check 96, \mathrm{CZ} on output 78, output 84, \mathrm{CZ} on output 78, check 86, \mathrm{CZ} on output 78, check 87, \mathrm{CZ} on output 78, check 91, \mathrm{CZ} on output 78, check 92, \mathrm{CZ} on output 84, check 86, \mathrm{CZ} on output 84, check 87, \mathrm{CZ} on output 84, check 91, \mathrm{CZ} on output 84, check 92, \mathrm{CZ} on check 86, check 87, \mathrm{CZ} on check 86, check 91, \mathrm{CZ} on check 86, check 92, \mathrm{CZ} on check 87, check 91, \mathrm{CZ} on check 87, check 92, \mathrm{CZ} on check 90, check 91, \mathrm{CZ} on check 90, check 96, \mathrm{CZ} on check 91, check 92, \mathrm{CZ} on check 91, check 96
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 0, 1, 6, 10, 16, 18, 25, 28, 36, 45, 52, 55, 56, 57, 59, 61, 70, 79, 95, 98, 99, 106, 107, 108 and 118 more (listed below); \mathrm{T}^5 on rotations 3, 7, 12, 14, 20, 27, 31, 42, 49, 54, 73, 74, 78, 82, 83, 91, 93, 184; \mathrm{T}^\dagger on rotations 2, 11, 17, 19, 23, 32, 33, 37, 38, 39, 41, 43, 47, 48, 53, 60, 65, 67, 68, 69, 80, 92, 96, 183 and 2 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 142 rotations at T³
0, 1, 6, 10, 16, 18, 25, 28, 36, 45, 52, 55, 56, 57, 59, 61, 70, 79, 95, 98, 99, 106, 107, 108, 110, 112, 117, 119, 121, 125, 128, 130, 131, 132, 134, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 148, 149, 151, 155, 160, 161, 162, 163, 166, 175, 180, 181, 182, 186, 188, 192, 193, 202, 210, 212, 213, 216, 221, 223, 225, 227, 231, 232, 233, 234, 236, 237, 238, 240, 241, 245, 251, 256, 263, 264, 265, 266, 267, 268, 269, 271, 274, 275, 277, 278, 279, 280, 281, 282, 283, 284, 285, 287, 292, 294, 295, 297, 298, 304, 306, 307, 309, 310, 312, 313, 314, 315, 317, 319, 320, 321, 322, 324, 325, 327, 328, 329, 333, 334, 335, 341, 342, 344, 345, 346, 347, 348, 349, 352, 353, 354, 355
All 26 rotations at T†
2, 11, 17, 19, 23, 32, 33, 37, 38, 39, 41, 43, 47, 48, 53, 60, 65, 67, 68, 69, 80, 92, 96, 183, 196, 208
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/358.86.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-358.86.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 3,116 faults of weight 3 are undetectable and damaging, so A_{3}=3{,}116. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).
A damaging fault of weight 3 sits on columns [0,2,311].
A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.
Original source
S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535
Provenance
built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows
Found by: AI search (gamma frontier): from Wills parent codes
Discovery: AI search
1 recorded source
[
{
"regime": "AI search (gamma frontier): from Wills parent codes",
"file": "gamma_frontier_release/protocols/paired_column_contraction_358_86_3_63543349f23e.json",
"label": "paired_column_contraction_358_86_3_63543349f23e",
"N": 97,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=112), with searched graph punctures; 2 paired-column contractions",
"provenance": "gamma frontier release record paired_column_contraction_358_86_3_63543349f23e (source catalogue id paired_column_contraction_358_86_3_63543349f23e); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=112), with searched graph punctures; 2 paired-column contractions; matrix 63543349f23e4369...; the release states d=3 (exact), gamma=1.2981701596258428 (exact)",
"notes": "matrix gamma_frontier_release/matrices/63543349f23e43695d89847d4b65368ffa8284f980a1ec03f1fa5b152bcf2c63.matrix"
}
]Use it in code
Load this factory and re-derive every number from its circuit with the catalogue's own verifier.
# git clone https://github.com/shubhamj810/magic-state-factory-repo
# cd magic-state-factory-repo/master_catalog
import json, urllib.request
import verify_catalog as VC
url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/358.86.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]
facts, problems = VC.derive(columns, k, N) # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N) # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
problems or "verified")
Raw record
Show the JSON this page is built from
Source: master_catalog.json, factories[996].