The circuit
The 87\times324 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 |
|---|---|
| out 0 (135) | ·1·······1···1111·1·11··1·1·1···11···11····1···11111111·1111·1··1···111·1··1·····111·1·1···1·1·1·······1111····1···11·11···1·111····111····1···1··1··1·1·······1··1·1···1·····1····111·1·1·111··11···11··11·1···111·11·111··11·111·1······1·11·1···1···1111·1··1·1·1·······111··1···1···1··11···1111·····111··1·1··1··1·1·····1·1·1· |
| out 1 (63) | ·1····1········1·1·1·1·······11···1·········1··11····11····1····1·················1····1···········1·1·1······11··1·······1···11····11·····1····1·······················1··1·········1··1·1·1·····11···1·····1··11······11······1··1····················1···1··········1·111·······11··1·······1··11·····11···1··1·················· |
| out 2 (103) | ·1····1·1····1·111······111···1···1·11·1················1····1··1··1····1··1····1··1·1····1··1·1·····1·1·1···1···1·····1·1·1·1·1·1·11·1··1·1···1··1·1····1·1···1···1·1··1··1·1·····1·1·11····11·1··1···111·1················1····1·1····11·····1···1··1··11···1··1·1······11·1····1··1······1·1·11·1·1·1·1·1·11·1··1·1····11··1··1·1 |
| out 3 (119) | ·1·1·11·1·····111···1·····1··111··1·1·1·····1·1·1·1···1·111···1····1··1·1········11···1···1··1··1··1·1··1····11·11····1·1·····111··1111·····1···1·1·1·1··1····1·1·1·1···1111·1······11·1···1····1·111··11·1··11··1··1····1··11·1··1······1···1·1·······11··1··1··1··1····11·1·····11·1·····1·1····111··1·111···1·1·1·1·1··1··1·11·1· |
| out 4 (111) | 11···11··········1···1··1·1··1··11····11···1··111······1···1··1·····111·1··11·····11·11···1·1·1·11···1····1··111···1·111·········1·111···1··1····1·11·1········1····1··11·11············1···11··1·1··11···111·1·11·········1····1·1·······1·11·1···11···1111··1·1·1·1···1·1·····1·111···1··11········1·1·11··1·1··1·11·1······1···1· |
| out 5 (135) | ·1·1···11······1·11··1···1·1·1·1111·11······1·······111·1·1·····1··1·1111···1···1·1··1·1··111··1···1·1··111··111·11···1·1111··1·11·11····1··1··1···1·11····1···11····1··11··11·······1··11··1·1···1·111111···1·········111··1··1···1·····1··1111····1·1·1·1·1·111··1·····11·11··1·1111·1···1·1111·1·11·1·1···1·11···1·11···1··11···1 |
| out 6 (31) | ·····························11············11···11··11························································11·········11····11···1·····························································11········11···11····11··························································11·········11···11···11·························· |
| out 7 (127) | 1····1·········11·1111···1··1····11···1····1··11·1···1·1·11··1··1··1··11·1·········1·111··1·1·1·1····1·111··11·1·111··11·······111·1·11········1··1··1·1·1·1··1·1··1·1·1··1··········1·1·1111·1··1····11··1·1·1·1·1·····1·11·1·1·1·1·····1···11·1········1111·1·1·1·1·····1111···11·11·11··11······111·1··11····1··1··1·1·11·1·1·1·1 |
| out 8 (127) | ···1·1··1·····1··111····11··1·1·····1·1·1···1·1·1·1··1··1··1·1··1···1111·1·11····1····11··1··1··11·1·1·1·11·11···11·····1·····111··1··1··1·····111·1·1·1···1···1··11·1···11··1······1···111··11··1·1····1·1··11··1··1···1···1···11·1······1·111·1··11··1···11·1··1··1···1111·1··111··1·1·····1····111··1···1·1··111·1·1·1··1··1·11·1 |
| out 9 (143) | 11·1···11······1·11······1·····1111·11······1···1···111·1·1········1·1111·······111··1·1··1111·1···1·1·1111·11·1·11···1·1111··1111·11····1··1··11··1·11····1···11·1··1·111··11··1····1··11····1·····111111···1···1·····111··1··1·········1··1111······111·1·1·1111·1·····11111··111·11·1···1·1111·1111·1·1···1·111··1·11···1··111··1 |
| out 10 (135) | ·1·1··1111···11·1···11··111·1·11····111········1··11·11··1···1··1··11··1···11···1111···1··1·11·······1····1·11·1·1·1···11····1···1·11·1··1··1···1·11··11···1····1·1·11··11·1111····11··1···1111111·11···111·····1···11··11···1···1·1·····11···1····11·1111··1·1·11········1·····111·11··1···11···1···1·1·1·1·1·1·1·11··11··1···11·11 |
| out 11 (135) | 1··1··1··1·····11·1·····11··1···1·1··111···11··111·11··11··1····1··········1····1·11·1·1··11111··1·1·1·······1···11···111·····111··1111····1·····1111·11······111·1111·1·1·1··1······1·1·1···11··1···1·1·11111··111··1·1···11···1··1···1···········1··1·111·1·11111·····111·······1··1·1···111····111··1·111··1···1111·11····1111111 |
| out 12 (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 13 (127) | 1····11·11····1111·1·········1··1···11·1····1·11··111··1···1·1······1111·1······1111·11····11·1·1······1·11·1·11··1····1·11·····1····1···1·····11·1·1·1··1·1··1·1·1·1··1··11·11·····11·11·1·······1··1··11·1·11·1···11·1···1····11········11111·1·····111111···11·1·1······1·1··11·11··1····1·11····1·····1··1··11·1·1·1··11·1·11·1· |
| out 14 (135) | 11·1···111···11·11·111···1·····111··11········111·11·1·1·1·1·11·1··1·111····1···111··1·1·····11·11···1·1··1·11·1·1····1·11···11·······1·········111·1··1···1···11····1·111··111····11··11·111·1·····111·11····1·11··11··1··1·1··1111·····1··111·····1·111·1·1····11·1···1·11····111·11·····1·11··11········1·····111·1··1··11·11···1 |
| out 15 (119) | 1····1·1······11···1·1··1····111·11··11·······1·1···1·····1··1··1··11·1·11·11···1····11····111·111·····11····111·1·······111···1·1··111····11····1····11···1····1··1···1··1·1·······11····1·11····111·11·11···1··1·····1·······1·1·1·····11··1·11··11·1···11···111·11···1··11·····1111········111··1·11··111··11··1····11··1···1·1·· |
| out 16 (143) | 1··1·11111···1·111·111···11··11··1··1······11·11·1·11·1··11············111··1····1·1·111··11···111·1·1··1···1111··11···11··1·1··1··111···1·1····1111·······1·······111·1·111111····1·1·11·111·1·1·11··1·1···111·1·1··1·1·1···1·1··············111···1··1·1111111···11···111·1····1111··11···11··11··1··1·11··11··1111······1·····111 |
| out 17 (127) | 11···1·1·1···1··1·111·····1·1··1·····1·····11··11··1····11·1·······1·1···1··1···1111··11····1···11·······11··1·1··11··11·1··111111··11······1··1·11··11····1···11·111··11·1·1·1····1···1·111····11··1····1··11··11···1······11··1········1··1···1···1·1111·11···1···1···1····1··1·1·1··11··11·1··11111···11····11·11··11···1··11111· |
| out 18 (127) | ···1·1·11·······1··111··1···11111·1·111·······1·11··1··111·1·1··1····11·11······11·1··1····1··111·········1···11··11···11··1········1····1·11···1·11··11·1·1··11··11·····11·11·········1··1111···11111·1111···1··11····1···111··11·1········11·11·····11·1·1···1··111·········1·1··11··11···11··1········1···111·1·11··11·11·11·11·· |
| out 19 (111) | ···1··1·1·····1······1···11·1···111·1·······1·····1····11··1·11·······1111··1······1·1·1····111····111·1·1··1····1·1···111·····111···11····11··1····1111···········111···1·1·1······1·······1·1·11···1111····1······1······11···111··········1111···1····11·1···111······111·1···1···1··1···111····111····11··111····1111········111 |
| out 20 (111) | ·············11·····11··11···1·······111······1·1·1···1··111·11·1·····1····1····111111·········11·······11····1·······111111·11·11···1···1··1··11··········1··111·1111·············11······1111···1······111··1··1··1····1···1·11111·········1·····1··11111········11·······11·····1·······11111111·11····1··1·111·········1·1111111 |
| out 21 (127) | 11···1·1·1···1··1·111·····1·1111··1··1·····1··11·1·1·1··11······1··1·1··········1111··11····1···11·······11··11····1··11·11··11··1···1·····11··1111··11····1·1·11··11··11·1·1·1····1···1·111····11111··1·1··1·1·1·1··1··1···11·····1·····1··1·········1111·11···1···1···1····1··1·11····1··11·11·11··1····1···111111··11···1··11·11· |
| out 22 (103) | ·1······11····111···············1·1·11·1···1··1··1111··1·····1·1····11·1·1······1··1·1·1···11·1·1··1·1·1·11·1··1·······1······1······1···1·1····1·1·1·1·······1·1·1·1···1····11·····11·1·············1·111·11·1···1·11·1···1·····1········1·1·1·1·····1··11·1··11·1·1····111·1··11··1·······1·····1·······1··11··1·1·1·1·····1·11·1· |
| out 23 (119) | ·1······11····111············1··1·1·11·1···11·11·1111·11·····1··1···1111·1·1····1··1·1·1···11·1·1··1·1·1·11·1·11·······1··1··············1·1···1··1·1·1····1··1·111·1···1····11·····11·1··········1··1·111·1111·1·1·11·1·1·1·····1·1······1·111·1··1··1··11·1··11·1·1····111·1··11·11·······1··1·············11·1··1·1·1···1·1·11·1· |
| out 24 (135) | 11···1···1···11····1····111··1··1·11·······1··11111111111··1·······111·111·1·····11···1···1111111····1····1·111··111·····1·1·1···1·1··1····1·············1·1··111·1111·11·1···1····11·····1··11·1·1··1·1····1·1·111·11·111·11···1········11·1·111··1···11··1··1111111·····1·····1111·1·11·····1·11···1·1···1··1···········11·1111111 |
| out 25 (119) | ·1······11····111············1··1·1·11·1···11·1·111111·1·····1··1···1··1·1··1···1··1·1·1···11·1·1··1·1·1·11·1·11·······1··1···11····11···1·1···1··1·1·1···1···1·1···1···1····11·····11·1··········1··1·111·1111··11·11·11··1·····1·1······1···1·1···1·1··11·1··11·1·1····111·1··11·11·······1··1··11·····11··11·1··1·1·1·····1·1··1· |
| out 26 (135) | ·1····1········1111·11···1··111··1····1····11·1··1····11·111·1·····1··1··1··1····111·1····1·1·1·1··1···111··111··1·1··11··1···1111·11······1···11·1··1·1·1·11·1·1·11·1··1··1·········1·111·11·1··111··1···1·111···1······1·1·1·111·······1···1··1···1··1111···1·1·1·1····1·111···111·1··1··11··1··1111·1·1····1·11·1··1·1·11·1·111·1 |
| out 27 (135) | 11···1···1···11····1····111··11·1·1···1·······1··1111··11··1·······111·111·1·····11···1···1111111····1····1·1111·11········1·111·1·1111····1·············1·1··111·1111·11·1···1····11·····1··11·1·11·1·1··1···1···1·11·1···11···1········11·1·111··1···11··1··1111111·····1·····111111·1··1·····1111·1·1·111··1···········11·1111111 |
| out 28 (119) | 1··1····1·····1111··11··1·····1·11··1·····111···1·1··1·11111·······111·····11····1·1·1······111··1·1····1·1····1·111···1········11··111··1······1111·····1····111·1····1·1···1······11·11··111·····1·11·1···11···1··1···1··111·11········11·1······11··1·11·····111·····11··1···1···11·11···1·······11···111·1···1111·····1··1111··· |
| out 29 (111) | 11···11··········1···1··1·1···1··11···1··1··1·1······111···1··1·····111·1··11·····11·11···1·1·1·11···1····1··1···111··1··11···11·1·1·····1··1····1·11·1········1····1··11·11············1···11··1··1··11··1··11·········11·1····1·1·······1·11·1···11···1111··1·1·1·1···1·1·····1·1··1·11··1··11··11·1·1·····1·1··1·11·1······1···1· |
| out 30 (111) | ······11·1···1··111111··1···1··1111··11·········1··1·1··11····1····11·1·11·1····11···1·1··1···1······1···1···············11··11·1··11····1·····1··1111·····1····1·11·······11·1····1···1111111···1··1111·11······1···1··1···11····1······11··1·11··1··11··1·1·1···1·······1··1················11·11·1··1·1··11··1··1111····1···111·· |
| out 31 (119) | ······1··1···11··1······111··1··1···········1·11111111111··········111·111·1···········1··1111111··1······1·111··1········11·1···1·1··1··1···············1·1··111·1111·····1··1····11···1····11·1·1··1·······11·111·11·111·11·1··········11·1·111··1········1·1111111····1······1111·1·········111···1·1···1·1············11·1111111 |
| out 32 (127) | 1··1·1··1·····1··111·1··11····1·····1·1·····1·1·1·1··11·1····1··1···11·1·1·11·········11··1··11·11·1·1···11·1····11···1·1·····111··1·11··1·1···111·1·1·1·······1··11·1·1·11··1···1··1···111·111····1····1·1··11··1··1···11··1····1·1······1·1·1·1··11······11·1··11·1···111··1··11···1·1···1·1····111··1··11·11·111·1·1·1·····1·11·1 |
| out 33 (119) | ········1····1····1·11··1·1·11···11·1111······1·1·····111111····1·1····111·11···111·········11111··1·1··1···1·1····1··1····1·111······1··1······1···111····1··111·1··········1·····1·····1·111··111···111111··1··1·······1·111·11··1··········111··11·111·······11111····11·1····1·1····1··1····1111·······1·1···1···111···1·1111··· |
| out 34 (135) | 11·1···111···11·11··1···111····1··1·111····11··1·111····11···1··1··11·11···1····1·11······1·11·····1·1·1····1····111···1111··1··11·1·111·1··1···1·11··11········1···11·111··111····11··11··1·11·1···1··1111·11··1·1·11······11···1·1·····11··11····1··1·11····1·11·······111·····1···1·11···1111·1··11·1··11·1·1·1·11··11······1··11 |
| out 35 (135) | ·1·1··111··1····11·111······11111···111····11·1111··1··111···1··1····1··11······1111···1···11·111··1······1···11···1···11111··1·····1····1··1···1·11··11·1····11··11····11·111·········11·111····11111··111·111·111····1···111···1·1········1··11·····1111··1··11·111····1······1··11···1···11111·1······1···1·1·1·11··11·1··11·11·· |
| out 36 (119) | ···············11·1·1···1·1···1·············1··111····1··11··11····111·111·11····················1·1·1·1111·11·1··········1···111····1···1·11··111111111·1·1··111··111···············1·1·1·1·1··1··1·········1··111······1···1·1·11······11·1·111··11···················111111·1111·1··········1··111·····1··111111111111·11·111·111 |
| out 37 (127) | 1··1···11······1·11··1···1··1··1·11·11······1·······111·1·1·····1··1·1111······111···1·1··111··1···1·1··111·1··1··1···1·1111··1·11·11····1··1··1···1·11····1···11·1····1·1··11·······1··11··1·1··1··1·1111···1·········111··1··1···1·····1··1111······11··1·1·111··1·····11·11··11··1··1···1·1111·1·11·1·1···1·11···1·11···1··111··· |
| out 38 (127) | ···1·1·11·······1···1·····1·11·11·1·111····1··1··1··11·111·1·1··1····11·11······11·1··1····1··111····1·1··11··1···11···111·1···1·········1·11···1·11··11·1·1··11··11·····11·11·········1···1····111·11·1111·1·1···1····11··111··11·1········11·11·····11·1·1···1··111·····11····1··1···11···111·1··1·········111·1·11··11·11·11·11·· |
| out 39 (127) | 1····11·11····1111·1·········11·1···11·1······11·11111·1···1·11·1···1111·1··1···1111·11····11·1·1······1·11·1·1···1····1·1··········11···1····11··1·1·1····1··1·1···1··1··11·11·····11·11·1·······11·1··11·1··1·1·1·11·11··1····1111······1·111·1···1·111111···11·1·1······1·1··11·1···1····1·1··········11··1··1··1·1·1···1·1·1··1· |
| out 40 (119) | 1··1··1··1·····11·11·1···11·11··11···1·1···11·1··1·11···1··11·1·····111·1···1···111········1·1··1····1····1···11···1····11····1111····1··1······1·1··1·1······1·1·11·1·1·1·1··1······1·1·11·1·1·111··11··1·1111···1··1·1····1···1·1·······1·11·1····1·111······1·1··1·····1·····1··11···1····11···1111·····1·1···1·1··1·1····1·111·1 |
| out 41 (119) | ···1·1··1·····1··111····11··1·1·1···1·1·····1·1···1··11·1····1··1···11·1·1·1·····1····11··1··1··11·1·1·1·11·11····1···1·1·····1·1··1·11··1·1···111···1·1·······1···1·1···11··1······1···111··11··1·1·1··1·1··11·····1···11··1····1·1·1····1·1·1·1··1···1···11·1··1··1···1111·1··111····1···1·1····1·1··1··11·11·111···1·1·····1··1·1 |
| out 42 (55) | 11···11··········1·1··············1·········1··1·····1·····1·····1····1·····1····11···11···········1·1············1·······1···1·····1······1·····1·········1······1····11·11············1·1············1·····1··1·······1·······1············1······1··11··11············11············1·······1··1······1····1···1········1····1··· |
| out 43 (127) | ·1·1··11··1··1·1·1·11···111·11·11·····11····1·1·1···1··1·1·1·······1·1···1·1·····1···1····1··11·1····1···11··111·111····111··1·111·1··1·····1··11··11··1···1··1···1··1··11·11······1·1··1·11·11·111·11····11·11··1·····1···1·1··1········1··1···1··1···1··1···1··11·1·····1··1··1·1111·11····111·1·111·1···1···111··11··1··1·1··1··1 |
| out 44 (127) | ·1····111····111·11111··1···11·1·11·1·11····1·1···1·1···11·1·11····1·1111··11····1·1······111···1··1···1··1·1·11··1····1·····1·1···1·1··········1··1·11····1······111···1··111·····111··111111···11·1·111·11·11·····1··1····11··111······1··1111·1·11··1·1····111···1····1·1····11·11··1····1····1·1···1··1······1··1·11···1····111· |
| out 45 (127) | ·1·1·111·····1·1···11···111··1·11·····11······1·11··1··1·1·········1·1···1·1·····1···11···11·11·1··1·1···11···11·111····11···1·1·1·1··1····11··11··11··1···1··11··1··1··11111······1·1····11·11·1·1·11····11··1··11····1···1·1···········1··1···1·11···1··11··11·11·1····11··1··1··111·11····11··1·1·1·1···1··1111··11··1··1·11·1··1 |
| out 46 (135) | 11·1··111·······1··111··1·1··11111··11······1···11··1·1·11···11·1···1····1·11···111··1····111··1·1·1·1·1······1··1····1·1111··11···1·······1····111·1··1·1·1··1···111··111·111·········1··1111··1·11111·11···1···111···1·1··11···111······1·····1··11·111·1···111··1····1111·······1·1·····1·1111·11···1······1··111·1··1·11·1··111· |
| out 47 (127) | ·1·······1···1111·1·11··1·1·11··11····1····1···1·11111··1·11·1······11··1··11····111·1·1···1·1·1·······1111···11···1··11···1·11·····1·1·1··1···11·1··1·1···1···1····1···1·····1····111·1·1·111··111··11···1·1···1·1·11·11···1··111········1·1··1···11··1111·1··1·1·1·······111··1··11···1··11···111······1·1··1·11·1··1·1··1··1···1· |
| out 48 (119) | ·1·1··1·1······11···11····1·111···1·1·1·····1·1·111···1·1111··1····1····1········11·······1··1··1··1·1·11·····1··1····1·1·····11···1111····11···1·1·1·1··1·1··1·1·1·1···11·1·1·······1·1···11···1111···11·1··11··11·1····1··11·11·1······1·····1·······11·····1··1··1·1··1111······1·1·····1·1····11···1·111··11·1·1·1·1··11·1·11·1· |
| out 49 (103) | ·11·····1····1·11····1··111···1·1·1·11·1···1············1··1·1··1··1····1··1····1····1·1··1··1·1···1·1···1···1·········1···1·1·1·1·11·1··1·····1··1·1·1··1·1···1···1·1··1····1·····1·1·1····111·1··1·1·111·11···············1···11·1·····1·····1···1··1···1·1·1··1·1·····11··1····1·········1···11·1·1·1·1·1·1··1··1·1·1··11··1··1·1 |
| out 50 (135) | 1····11·11····1111···1··1·1··11··1··1111···1···111111········11·1·····1111·11···1·1···11··11·····1·1···1·1··1111··11··1··1····1··1·11·······1··1·1111·········111·1····1··11·11·····11·11···11··1·11··1·11111···111·11·1·········111··1······1111··11·1·1··11·11········11·1·1···1111··11··1··1···1··1·1·1·····11·1111·······1111··· |
| out 51 (135) | 1····11111·····1·1111···11··1·111·1·1··1····1·111··1··1··1···1··1···11··11·1·····11··111··1·11·111···1·1··1····1··11··1··1·1··1·1··1··1··1··1····1··11··11······1···11·1··11111······1··1111·11··1·111·11··1·11·11···1···1···1···1·1······1·1··11··1···11·111·1·11·11···1·11····1···1··11··1··1·1·1·1··1···1·1·1··1··11···1····1··11 |
| out 52 (119) | ·1··1·1·11····111··1·1·······1··1·1·11·1···11·1111111111·····1··1···11·1·1······1··1·······11·1·1··1·····11·1·11·······1··1····1····1····1·1···1··1·1·1·······1·1·1·1···1··1·11·····11·1··1·1·····1··1·111·1111·111·11·111·1·····1·1······1·1·1·1·····1··1·····11·1·1····1···1··11·11·······1··1···1·····1···11·1··1·1·1·····1·11·1· |
| out 53 (111) | ···1··1··1·····11·1··1···11··1···1···1·1···11·1··1·111··1··1··1·····111·1·······1·1········1·1············1··111·1·1····11····1111··1·1··1··1···1·1··1·1······1·1··1·1···1·1··1···1··1·1·1··1·1·1·1···1··1·1111···1··1·11···1···1·1·······1·11·1······1·1······1·1··············1·1111··1····11···1111···1·1·1·1·1·1··1·1····1·1·1·1 |
| out 54 (135) | ···1·11111···11·1···11···1···11111··11·····1111··111·1·1·1·1·11·1··1·1·11···1···1····11······11·11·1···1··1·111··1····1·1·11·1·11·····1·········111·1··1·······11····1···111111····11··1···11·1···11111·11··111···1·11··1··1·1··1111·····1··1·11····1·1···11·····11·1···11·1····1111·1·····1·1·111·11······1·····111·1··1·····11···1 |
| out 55 (127) | ·1···1·········1111······1··111··1····1····11·1·1·····11·111·1·····1···1·1··1····111·111··1·1·1·1··1··1·11··111··1·1··11··1···1··1·11······1···11·1··1·1·1····1·1·11·1··1·1··········1·111····1··111··1···1·111··1·······1·1·1·111·······1····1·1···1··111111·1·1·1·1····1··11···111·1··1··11··1··1··1·1·1····1·11·1··1·1·1··1·111·1 |
| out 56 (119) | ······1········11·1111···1··1····11···1····1··111····111·11··1··1··1··11·1······11·1·1····1·1·1·1····1·111··11·1·111··11·········1·1···········1··1··1·1·1·1··1·1··1·11····1·········1·1·1111·1··1····11··1·1·1·11······11·1·1·1·1·1·····1···11·1·····11·11···1·1·1·1·····1111···11·11·11··11········1·1········1··1··1·1·11·1·1·1·1 |
| out 57 (135) | 1····1·········11·1111···1··111··11···1·····1·1··1···111·11··1··1··1··11·1·········1·111··1·1·1·1····1·111··111··111··11·11··11111·1···········1··1··1·1·1·1··1·1··1·1·1··1··········1·1·1111·1··111··11··1··111··1·····11·1·1·1·1·1·····1···11·1········1111·1·1·1·1·····1111···111·1·11··11·11·11111·1········1··1··1·1·11·1·1·1·1 |
| out 58 (127) | ······1·11····1··11·11···1··1·1··1··1111·······11111111··11··1··1··1111·········111····1··11·········1··1·1··1·1··11··1·······1··1·1·1···1·1·1··1···1111·1·1······1111·····1·11·····1···11·11·1··1·1··1·1111····111·11·111···1·1·1·1·····11·11········111···1·11··········1·1···1·1·1··11··1······1··1·1··1··11··1···1111·11····1111 |
| out 59 (135) | 1····1··11····1111·1·1··1·1·111·11··1111···1···1111111·······11·1······111·11···1·1···1····1·····1·1·1·1·1··1·11·111··1··1····1··1·1········1··1·111·······1··111·1····1··1··111····11·11·1·11··1111·11·11111···111·11·11········111··········111··11·1·1··1···1········1111·1···1·111·11··1··1···1··1·1·······11·111······1·1111··· |
| out 60 (135) | 1··1···1·1···11·1111·1···1·····1·1·····1···11·1··111··111·1··1··1··11·1·11·······111······1···111····1·11····1···11···111111····11·1·1·····11···1·1111·····1··11····11·1·1··1·1····11··1111·1·1·····1·1····1111···1·11···1·11··1·1·1·····11··1·11······111····1···1111····111·····1··1·1···111111···11·1··1···11·1·1111····1·11···11 |
| out 61 (127) | 11·1·1··1·····1··111·11·11··111·····1·1·····1·1···1··11·1····1······11·1·1·1······1···11··1··1··11·1·1··111·111··11···1·1·····1·1··1·11··1·1···1·1·1·1·1·······1···1·1·1111··1······1···111·111··111····1·1··11·····1···11··1····1········1·1·1·1··1····1··11·1··1··1···111·11··1111·1·1···1·1····1·1··1··11·11·1·1·1·1·1·····1··1·1 |
| out 62 (127) | 11·1··1·1·····1···11·1···11·1···1·1·1··········1··1··1·11····11·1······111·······111·1·1····111····1···1·1··1····1·1···1111···1111··111·····1··11···1111···1······1111·111·1·1······1····11·1·1·11···1·11·······1···1···1··11····111··········111······1111·1···111······1·1·1···1···11·1···1111··1111···111···111···1111··1····1111 |
| out 63 (135) | 11·1·1···········1·111··1···111··11··1·1······111··1111·111··1··1··1··11·1·11···11····11·1·1·1··11·····111··111··111····1·1······1··111········111·11·1··1·1···1····1··1111·············1·1111···111··11·1·1··1·11···1·111··11·1·1·1·····1···11·1··11·11···11··1·1··1···1··111···111·1·11····1·1·····1···111····111·11·1··11··1···1· |
| out 64 (119) | ······1··1···111··1·1···1·1·1····1····1····1···11111111·111··1······111·1··1·····1·1·1·····1·1·1··1·····111····1·1·1··11···1·111····111········11·1··1·1·······1··1·1······1··1····111···1·1·1··11····1···1·1···111·11·111··11·1·1········1·11·1···1···1·11····1·1·1········11··1···11··1··11···1111·····111····11·1··1·1·····1·1·1· |
| out 65 (135) | ······1·11····1··11·11···1··11··111·1111···11··1··111····111····1··1111···1·1···111····1··11·········1··1·1··11··1·1··1··11···1111·11····1······1···1111·1·1····1··111·····1·11·····1···11·11·1··11··111111111··1···11·1·····1·11··1·····11·11······1·111···1·11··········1·1···1·11·1··1··1··11··1111·1·1···1···1···1111·11···1·111 |
| out 66 (127) | ·1·······1···1111·1·11··1·1·11··11··1·1····11····1111···1111·1··1···111·1··1·····111·1·1···1·1·1·······1111···11···1··11··11·1········1····1···1··1··1·1·······1··1·1···1·····1····111·1·1·111··111··11·1·1·11····1·11·1····11·111·1······1·11·1···1···1111·1··1·1·1·······111··1··11···11·11··111·········1··1·1··1··1·1·····1·1·1· |
| out 67 (135) | 11···11·11··1·111··1········11··1···11·1···11·111·111··1···1·1··1···1111·1······11·1·11····11·111··1···1·11·1111··1····1··1····11····1···1·····1··1·1·1····1··1·1·1·1··11·11·11·····11·1··1······11··1··11·1111·11··11·1···1····11·1······1·111·1·····11·111···11·111····1·1·1··11111··1····1··1···11·····1··1··1··1·1·1···1·1·11·1· |
| out 68 (119) | 1····1·········11·1·1···111·1·1·············1··11········111·11····111·111·11····1····1··········1·1·1·1111·1··1··········1···11·········1··1··111·11111·1·1··111··111·1··1··········1·1·1·1·11·11·1·········1··11···········1·1111·1····11·1·111··11··1···1············111111··11··1··········1··11·········1·1111·11111·11·111·111 |
| out 69 (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 70 (119) | ···1·111·1····1·1·1·····111·1·11··1···11···1····1111·1··1·11·11······1···1·11····11··11·····1··1·1···1·11·1··1·····1····1··1··1·1····1···1·1·····11··11····1··1······1···1111·1·····1··1·1···11·11·11··1··111····11·11··1···1··1111·········1···1··11··11·11····1··1····1·111···1·1·····1····1··1·1·1·····1··11···11··11·1·1·1·····1 |
| out 71 (127) | ·1····1··1····1···1·1····1··1·1·11··1111···1···11111111··11········1111·········11·····11·11·······1·1·11·1··1·1·111··1··1····1··1·1·1···1·1········1111·1·1······1111··1··1··1·····1····1·1··1··1·1·11·11111···111·11·111···1·1·········11·11········11····1·11·········1111···1·1·11·11··1··1···1··1·1··1··11······1111·11····1111 |
| out 72 (135) | ·······1······1·1·1111···11·1111111··11·····1·11·11·1····1·1··1······111····1·1·11···1·····111·11··1·1···11·1111·········1·1··1·11··111··1·1···1··1111···1····11··1··1······1·······1··1·1111·1·11111111·11··11·1·1·1··1·····1··1·1·········111·····1·11··1····111·11····11··1··11111·········1·1·1·11···111·11·1··1111···1··11·1··1 |
| out 73 (119) | ·1····11······11·1·1······1····11····1············111·11··11·11·1··1·1···1······1·11······11·111·····1·11·1····1·111··11··11··11··11·11··1·1·······11··1···1···11··11···1··11·······11··1·1·····1···11···1··········11·1·1·1···11111·····1··1···1·····1·11····11·111······111···1···11·11··11··11·11···1··11·11·····11··1··1··11·11· |
| out 74 (111) | ···1·1··1·····1··11··1···11·1···111·1······1······1····11·1··11·······1111··1······1·11·····111······1·1·1··1····1·1···11·1····111···11···1·1··1····1111···········111···11··1······1···11··1·1·11···1111···1·······1······11··1·11··········1111···1····111····111·······11·1···1···1··1···11·1···111····11···11····1111········111 |
| out 75 (135) | ···1·1·11·······11·11········111··1·111····1··1··1··1··111·1·1··1····11·11······11·1··1····1··111··1···1··1··111·111···111·1···1···11····1·11···1·11··11·1·1··11··11·····11·11·········11·11······111··1111·1·1···1···11···111··11·1········11·11·····11·1·1···1··111····1·1····1·1111·11···111·1··1···1·1···111·1·11··11·11·11·11·· |
| check 76 (72) | 11···11··········1·1·········11···1·········1··111···1·····1····1·····1······1···11···11···········1·1········11··1·······1···111···1······1····1··········1·······1···11·11············1·1·······11···1·····1··111·····1·······1··1·········1·······1·11··11············11········11··1·······1··111····1····1··1·········1·····1·· |
| check 77 (120) | 11·1·1··1·····1·11111···1······1·1···11·····1···1··1·1·11·11·1·······1·1····1····1·1···1···111·11····1·1·1···1···11······1···11·1··11·······1···11····11·1·1··11··1·11·1111··1······1··11111·1······1·1··11··1···1···1··1··11··111··········1·1·····1··1·1··1··111·11·····11·1····1··1·1······1··11·1··1·1·····1·11····11·11·11·1·11 |
| check 78 (128) | ·1·····1·1···1·1·····1···11·········1··1···11·1··11·111··1·1··1·1··11·1·11·1····111··1····1···1··1···1·11·1·1·11···1··111111····11····1··1·1···11·1111·····1····1·11····1···1·1····1·1······1·1·1·······1··1111···1·1··111···1··1·11·····11··1·11··1··111·1···1···1·····1·111···11·11···1··111111···11·····1·11·11·1111····1···111·· |
| check 79 (160) | 11··1····11111··1·1·1·······11·1····111·1·1··1·11··1111111····1·11111···11·11·1···1·11·11·····1··11···11·1·1··11111·1·····1··11··1··1··111·1·1111··1·1··11·1·11·11····1111·11111···1··1·11···1··1111··1···1·1····111·11·1··1····11·11·1··1·1·1·1·1··111·1····1111·11·····1·1·11····1·111·1·1·11111··1··1111··1··1111111·1······1·11· |
| check 80 (160) | 11···11··1···1·····1···1··11·11·····1·1·1·1···1·1··111111··1···1·111111111·11··1··1·1·1·1··11·11·1··11·1····111··11·······1111···1··1··1·1···1·····1·1··111·111·11··11··111··1111·111·1··11·11111·1··1·1·····1··111·1111·111··1··1···1·1·1···1·1··1·11·11··11·1111111·1···1··1111·111····111·1··111·1111···1··1·1·1·····1·1··111·11· |
| check 81 (156) | 11·11·11111···111···1·11····111····1··1·1··11··1·111··1··111··111·1·11·11111··11········1··11··1··11····1···1·1·1·1··11·1·11···11···1··1··1·1·1····11····11··1·1·1·1·1·1·1·1··1··1·1·1····11·111··1111··1·11···1··11·1·111·111·····111··1·11··1·········1·1··1··1·11·11··11··1111111·1·111···11·1111111·1···1·111··1·1·11···1·11·11· |
| check 82 (168) | ··1·11·111·1··11··111··11··11··111·1···1·1111·11·111·1·1·1·111·11·1··11··1·11·11··1·111·1·1·1·1111··1··1··11·1····11··1··111··1·11·11··1·1·1111··1····1··1··11··1··111···11·1·1·11···1··1··1·11·1···11·11··1··1·11·1·1··111·11··1·11··111···1·11···1·1··11·1··1··1·11·1·1111·1·111····1··1·111··1·11··11·111111·1·1··11·1·111··11··· |
| check 83 (156) | ·1·1····1···111··1····11·1·11·1·111·····11111··1··11···1111··1···11·11··1·11··111······11·1·1·1··1···11···111·····111111·1·1·11·1·1111·1·······1···11·11···1··1··1·11···11111·····1·····1··11·111··1·111·111····1···1·11111··1·1·1·111111·1·1··1·11·111····1·11·1·11111·1·1111····1····11·1··1·1111·1···1··11···1111··1····1··111··1 |
| check 84 (168) | 1····1··111111·11··1·····111·11··11·1111···1·1··11·1·111···1·11····1···1·111··111·1···1··1·1·11·11···1···1111·11···1··1··1··11111·1·1·11···11··11111····111·11··1111···1··1··1·1111·11·1··1··1·1·111··1111111·111··11·11··1·1···111·······1111·1·11·111·1··1··1·1··1·11·1·1··111··111···1··1··1·1····1111·1·1·1111111····1·1111···11 |
| check 85 (160) | 11·1·····1······1·11··111·11····111··1·1···11·1····111··1···1·11·11111····1·1·1111·····1···1·1··11111·1····1···1··11····11····11·1··1·1·1·1·111····11·11111·11·111···1·111····1······11·1··11·11·1···111·1·1111······1·11···111111·111111··1·1111111·111····1··1·1··1··1··111111111·1··11····11···11·1···1·1·11·1111··1··1·111··111· |
| check 86 (168) | ·1······11····111·············11··111···111··1··1·1·111111111·11·11·······11··111··1·1·1···11·1·1··1·1·1·11·1···11·1111·11·11·111·1·1··1111·111·111·1·111·1·111··11··1··1····11·····11·1··········1··11··11111111·11·11···1···1··1·1111111111111111·111··11·1··11·1·1····111·1··11·11·11·11·1··1·1···1111·111·1·1···1·1··1111·11·11· |
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 n324Noisy T states per run.
outputs k76
distance d3Exact, proved and witnessed here.
error coefficient A_{3}3,022Faults 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 N87
checks r11
V_{\mathrm{ex}}76T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3199Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3199Overhead 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 width76Rank of the output rows modulo the check rows.
Output gate
76 T0 CS0 CCZon 76 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}
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 (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 78 single-wire gates and 262 \mathrm{CZ} gates: \mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{S} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23 and 316 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 340 correction gates
\mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{S} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{S} on output 26, \mathrm{S} on output 27, \mathrm{S} on output 28, \mathrm{S} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{S} on output 32, \mathrm{S} on output 33, \mathrm{S} on output 34, \mathrm{S} on output 35, \mathrm{S} on output 36, \mathrm{S} on output 37, \mathrm{S} on output 38, \mathrm{S} on output 39, \mathrm{S} on output 40, \mathrm{S} on output 41, \mathrm{S} on output 42, \mathrm{S} on output 43, \mathrm{S} on output 44, \mathrm{S} on output 45, \mathrm{S} on output 46, \mathrm{S} on output 47, \mathrm{S} on output 48, \mathrm{S} on output 49, \mathrm{S} on output 50, \mathrm{S} on output 51, \mathrm{S} on output 52, \mathrm{S} on output 53, \mathrm{S} on output 54, \mathrm{S} on output 55, \mathrm{S} on output 56, \mathrm{S} on output 57, \mathrm{S} on output 58, \mathrm{S} on output 59, \mathrm{S} on output 60, \mathrm{S} on output 61, \mathrm{S} on output 62, \mathrm{S} on output 63, \mathrm{S} on output 64, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{S} on output 69, \mathrm{S} on output 70, \mathrm{S} on output 71, \mathrm{S} on output 72, \mathrm{S} on output 73, \mathrm{S} on output 74, \mathrm{S} on output 75, \mathrm{Z} on check 81, \mathrm{Z} on check 83, \mathrm{CZ} on output 0, check 81, \mathrm{CZ} on output 0, check 83, \mathrm{CZ} on output 0, check 84, \mathrm{CZ} on output 0, check 85, \mathrm{CZ} on output 2, check 79, \mathrm{CZ} on output 2, check 81, \mathrm{CZ} on output 2, check 82, \mathrm{CZ} on output 2, check 85, \mathrm{CZ} on output 3, check 81, \mathrm{CZ} on output 3, check 84, \mathrm{CZ} on output 4, check 81, \mathrm{CZ} on output 4, check 83, \mathrm{CZ} on output 5, check 79, \mathrm{CZ} on output 5, check 80, \mathrm{CZ} on output 5, check 81, \mathrm{CZ} on output 5, check 82, \mathrm{CZ} on output 5, check 83, \mathrm{CZ} on output 5, check 85, \mathrm{CZ} on output 7, check 79, \mathrm{CZ} on output 7, check 81, \mathrm{CZ} on output 7, check 83, \mathrm{CZ} on output 7, check 84, \mathrm{CZ} on output 8, check 79, \mathrm{CZ} on output 8, check 81, \mathrm{CZ} on output 9, check 79, \mathrm{CZ} on output 9, check 80, \mathrm{CZ} on output 9, check 81, \mathrm{CZ} on output 9, check 82, \mathrm{CZ} on output 9, check 83, \mathrm{CZ} on output 9, check 85, \mathrm{CZ} on output 10, check 79, \mathrm{CZ} on output 10, check 80, \mathrm{CZ} on output 10, check 82, \mathrm{CZ} on output 10, check 84, \mathrm{CZ} on output 11, check 79, \mathrm{CZ} on output 11, check 82, \mathrm{CZ} on output 13, check 81, \mathrm{CZ} on output 13, check 82, \mathrm{CZ} on output 14, check 79, \mathrm{CZ} on output 14, check 80, \mathrm{CZ} on output 14, check 81, \mathrm{CZ} on output 14, check 82, \mathrm{CZ} on output 14, check 83, \mathrm{CZ} on output 14, check 84, \mathrm{CZ} on output 15, check 80, \mathrm{CZ} on output 15, check 82, \mathrm{CZ} on output 15, check 83, \mathrm{CZ} on output 15, check 85, \mathrm{CZ} on output 16, check 79, \mathrm{CZ} on output 16, check 83, \mathrm{CZ} on output 16, check 84, \mathrm{CZ} on output 16, check 85, \mathrm{CZ} on output 17, check 80, \mathrm{CZ} on output 17, check 81, \mathrm{CZ} on output 17, check 82, \mathrm{CZ} on output 17, check 84, \mathrm{CZ} on output 18, check 80, \mathrm{CZ} on output 18, check 82, \mathrm{CZ} on output 18, check 84, \mathrm{CZ} on output 18, check 85, \mathrm{CZ} on output 19, check 79, \mathrm{CZ} on output 19, check 83, \mathrm{CZ} on output 20, check 79, \mathrm{CZ} on output 20, check 82, \mathrm{CZ} on output 20, check 84, \mathrm{CZ} on output 20, check 85, \mathrm{CZ} on output 21, check 80, \mathrm{CZ} on output 21, check 81, \mathrm{CZ} on output 21, check 82, \mathrm{CZ} on output 21, check 84, \mathrm{CZ} on output 22, check 81, \mathrm{CZ} on output 22, check 82, \mathrm{CZ} on output 23, check 81, \mathrm{CZ} on output 23, check 82, \mathrm{CZ} on output 24, check 79, \mathrm{CZ} on output 24, check 85, \mathrm{CZ} on output 25, check 81, \mathrm{CZ} on output 25, check 82, \mathrm{CZ} on output 26, check 79, \mathrm{CZ} on output 26, check 81, \mathrm{CZ} on output 26, check 83, \mathrm{CZ} on output 26, check 84, \mathrm{CZ} on output 27, check 79, \mathrm{CZ} on output 27, check 85, \mathrm{CZ} on output 28, check 83, \mathrm{CZ} on output 28, check 84, \mathrm{CZ} on output 29, check 81, \mathrm{CZ} on output 29, check 83, \mathrm{CZ} on output 30, check 80, \mathrm{CZ} on output 30, check 82, \mathrm{CZ} on output 30, check 83, \mathrm{CZ} on output 30, check 84, \mathrm{CZ} on output 31, check 79, \mathrm{CZ} on output 31, check 85, \mathrm{CZ} on output 32, check 79, \mathrm{CZ} on output 32, check 81, \mathrm{CZ} on output 33, check 82, \mathrm{CZ} on output 33, check 83, \mathrm{CZ} on output 33, check 84, \mathrm{CZ} on output 33, check 85, \mathrm{CZ} on output 34, check 79, \mathrm{CZ} on output 34, check 80, \mathrm{CZ} on output 34, check 82, \mathrm{CZ} on output 34, check 84, \mathrm{CZ} on output 35, check 80, \mathrm{CZ} on output 35, check 82, \mathrm{CZ} on output 35, check 84, \mathrm{CZ} on output 35, check 85, \mathrm{CZ} on output 36, check 79, \mathrm{CZ} on output 36, check 84, \mathrm{CZ} on output 37, check 79, \mathrm{CZ} on output 37, check 80, \mathrm{CZ} on output 37, check 81, \mathrm{CZ} on output 37, check 82, \mathrm{CZ} on output 37, check 83, \mathrm{CZ} on output 37, check 85, \mathrm{CZ} on output 38, check 80, \mathrm{CZ} on output 38, check 82, \mathrm{CZ} on output 38, check 84, \mathrm{CZ} on output 38, check 85, \mathrm{CZ} on output 39, check 81, \mathrm{CZ} on output 39, check 82, \mathrm{CZ} on output 40, check 79, \mathrm{CZ} on output 40, check 81, \mathrm{CZ} on output 40, check 82, \mathrm{CZ} on output 40, check 83, \mathrm{CZ} on output 41, check 79, \mathrm{CZ} on output 41, check 81, \mathrm{CZ} on output 43, check 79, \mathrm{CZ} on output 43, check 80, \mathrm{CZ} on output 43, check 81, \mathrm{CZ} on output 43, check 84, \mathrm{CZ} on output 44, check 80, \mathrm{CZ} on output 44, check 81, \mathrm{CZ} on output 44, check 83, \mathrm{CZ} on output 44, check 84, \mathrm{CZ} on output 45, check 79, \mathrm{CZ} on output 45, check 80, \mathrm{CZ} on output 45, check 81, \mathrm{CZ} on output 45, check 84, \mathrm{CZ} on output 46, check 80, \mathrm{CZ} on output 46, check 81, \mathrm{CZ} on output 46, check 82, \mathrm{CZ} on output 46, check 83, \mathrm{CZ} on output 46, check 84, \mathrm{CZ} on output 46, check 85, \mathrm{CZ} on output 47, check 81, \mathrm{CZ} on output 47, check 83, \mathrm{CZ} on output 47, check 84, \mathrm{CZ} on output 47, check 85, \mathrm{CZ} on output 48, check 81, \mathrm{CZ} on output 48, check 84, \mathrm{CZ} on output 49, check 79, \mathrm{CZ} on output 49, check 81, \mathrm{CZ} on output 49, check 82, \mathrm{CZ} on output 49, check 85, \mathrm{CZ} on output 50, check 82, \mathrm{CZ} on output 50, check 83, \mathrm{CZ} on output 51, check 79, \mathrm{CZ} on output 51, check 80, \mathrm{CZ} on output 51, check 84, \mathrm{CZ} on output 51, check 85, \mathrm{CZ} on output 52, check 81, \mathrm{CZ} on output 52, check 82, \mathrm{CZ} on output 53, check 79, \mathrm{CZ} on output 53, check 81, \mathrm{CZ} on output 53, check 82, \mathrm{CZ} on output 53, check 83, \mathrm{CZ} on output 54, check 79, \mathrm{CZ} on output 54, check 80, \mathrm{CZ} on output 54, check 81, \mathrm{CZ} on output 54, check 82, \mathrm{CZ} on output 54, check 83, \mathrm{CZ} on output 54, check 84, \mathrm{CZ} on output 55, check 79, \mathrm{CZ} on output 55, check 81, \mathrm{CZ} on output 55, check 83, \mathrm{CZ} on output 55, check 84, \mathrm{CZ} on output 56, check 79, \mathrm{CZ} on output 56, check 81, \mathrm{CZ} on output 56, check 83, \mathrm{CZ} on output 56, check 84, \mathrm{CZ} on output 57, check 79, \mathrm{CZ} on output 57, check 81, \mathrm{CZ} on output 57, check 83, \mathrm{CZ} on output 57, check 84, \mathrm{CZ} on output 58, check 79, \mathrm{CZ} on output 58, check 82, \mathrm{CZ} on output 58, check 83, \mathrm{CZ} on output 58, check 84, \mathrm{CZ} on output 59, check 82, \mathrm{CZ} on output 59, check 83, \mathrm{CZ} on output 60, check 79, \mathrm{CZ} on output 60, check 80, \mathrm{CZ} on output 60, check 83, \mathrm{CZ} on output 60, check 85, \mathrm{CZ} on output 61, check 79, \mathrm{CZ} on output 61, check 81, \mathrm{CZ} on output 62, check 79, \mathrm{CZ} on output 62, check 83, \mathrm{CZ} on output 63, check 81, \mathrm{CZ} on output 63, check 82, \mathrm{CZ} on output 63, check 83, \mathrm{CZ} on output 63, check 84, \mathrm{CZ} on output 64, check 81, \mathrm{CZ} on output 64, check 83, \mathrm{CZ} on output 64, check 84, \mathrm{CZ} on output 64, check 85, \mathrm{CZ} on output 65, check 79, \mathrm{CZ} on output 65, check 82, \mathrm{CZ} on output 65, check 83, \mathrm{CZ} on output 65, check 84, \mathrm{CZ} on output 66, check 81, \mathrm{CZ} on output 66, check 83, \mathrm{CZ} on output 66, check 84, \mathrm{CZ} on output 66, check 85, \mathrm{CZ} on output 67, check 81, \mathrm{CZ} on output 67, check 82, \mathrm{CZ} on output 68, check 79, \mathrm{CZ} on output 68, check 84, \mathrm{CZ} on output 70, check 79, \mathrm{CZ} on output 70, check 80, \mathrm{CZ} on output 70, check 81, \mathrm{CZ} on output 70, check 85, \mathrm{CZ} on output 71, check 79, \mathrm{CZ} on output 71, check 82, \mathrm{CZ} on output 71, check 83, \mathrm{CZ} on output 71, check 84, \mathrm{CZ} on output 72, check 79, \mathrm{CZ} on output 72, check 80, \mathrm{CZ} on output 72, check 82, \mathrm{CZ} on output 72, check 83, \mathrm{CZ} on output 72, check 84, \mathrm{CZ} on output 72, check 85, \mathrm{CZ} on output 73, check 80, \mathrm{CZ} on output 73, check 81, \mathrm{CZ} on output 73, check 82, \mathrm{CZ} on output 73, check 85, \mathrm{CZ} on output 74, check 79, \mathrm{CZ} on output 74, check 83, \mathrm{CZ} on output 75, check 80, \mathrm{CZ} on output 75, check 82, \mathrm{CZ} on output 75, check 84, \mathrm{CZ} on output 75, check 85, \mathrm{CZ} on check 77, check 79, \mathrm{CZ} on check 77, check 80, \mathrm{CZ} on check 77, check 82, \mathrm{CZ} on check 77, check 83, \mathrm{CZ} on check 78, check 79, \mathrm{CZ} on check 78, check 80, \mathrm{CZ} on check 78, check 82, \mathrm{CZ} on check 78, check 83, \mathrm{CZ} on check 79, check 81, \mathrm{CZ} on check 79, check 83, \mathrm{CZ} on check 79, check 84, \mathrm{CZ} on check 79, check 85, \mathrm{CZ} on check 80, check 82, \mathrm{CZ} on check 80, check 85, \mathrm{CZ} on check 81, check 83, \mathrm{CZ} on check 81, check 84, \mathrm{CZ} on check 81, check 86, \mathrm{CZ} on check 82, check 86
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 1, 19, 20, 23, 24, 25, 26, 31, 32, 33, 34, 38, 42, 43, 44, 51, 61, 62, 66, 68, 70, 78, 82, 84 and 120 more (listed below); \mathrm{T}^5 on rotations 2, 4, 7, 10, 13, 16, 17, 21, 36, 46, 49, 50, 52, 54, 57, 58, 60, 65, 67, 72, 81, 89, 110, 167 and 2 more (listed below); \mathrm{T}^\dagger on rotations 0, 8, 11, 14, 18, 22, 30, 59, 63, 69, 80, 168, 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 144 rotations at T³
1, 19, 20, 23, 24, 25, 26, 31, 32, 33, 34, 38, 42, 43, 44, 51, 61, 62, 66, 68, 70, 78, 82, 84, 86, 88, 92, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 107, 108, 112, 116, 117, 119, 120, 122, 124, 125, 126, 128, 129, 131, 133, 134, 136, 137, 138, 139, 140, 141, 143, 145, 146, 148, 150, 152, 154, 158, 161, 163, 164, 165, 166, 171, 173, 174, 175, 177, 178, 179, 184, 185, 187, 188, 189, 191, 192, 196, 199, 205, 210, 211, 212, 214, 215, 220, 225, 228, 231, 233, 234, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 251, 252, 253, 255, 256, 257, 258, 260, 263, 266, 268, 270, 276, 277, 280, 281, 283, 285, 286, 287, 288, 290, 293, 295, 298, 300, 304, 307, 308, 314, 316, 319, 322
All 26 rotations at T⁵
2, 4, 7, 10, 13, 16, 17, 21, 36, 46, 49, 50, 52, 54, 57, 58, 60, 65, 67, 72, 81, 89, 110, 167, 181, 194
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/324.76.3.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-324.76.3.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 3,022 faults of weight 3 are undetectable and damaging, so A_{3}=3{,}022. 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 [0,4,19].
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/restricted_light_324_76_3.json",
"label": "restricted_light_324_76_3",
"N": 87,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived restricted-light construction",
"provenance": "gamma frontier release record restricted_light_324_76_3 (source catalogue id restricted_light_324_76_3); construction: Wills-derived restricted-light construction; matrix 10a93620b1e2f697...; the release states d=3 (exact), gamma=1.3198561407536247 (exact)",
"notes": "matrix gamma_frontier_release/matrices/10a93620b1e2f697ccff693579bed7d65c1eb4538ed1b7afc6f661b965e10101.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/324.76.3.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[977].