The circuit
The 79\times300 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 |
|---|---|
| out 0 (111) | ·11·11·1111··11······1··1·······111····1·········111111········1·111······1·1111·1··1·1··········11····1111····1··11111······11········11·1·1····1···1·11·11·11··1111·11······11······11···1····11·1111······1··1·11······1·11111·11········11··111·1·······1·1111·1·······1··1··········11·1··1····1····111 |
| out 1 (95) | ···1·11·111·1·1····11·········11·····1·1·····1·····111·····1·11···1······1·1····11··1··1·········11····1··1··1·1·····11···111····1····1···111···11·····11···1·1·1·1111·1····11······11···1·1··1····111····111·····1·····1··1····1·1·1·······11··1···1····1··1····1·1····111······1···1······1·11···11·····11 |
| out 2 (111) | 11·1··111····1··111··········111·1·1·11··1··1······111··111······1111·1··111111·····1··11··1···1··········1····1·1·111·11········11······11··1··1···1····11·1···111···1··111·······111·1111·11·····111·111······1·11·1··1·11111···1·11··1·1·········1·······11·111···11··········11········11····1·1····1··· |
| out 3 (111) | 1···11·11·1··1····1········1·1··11···1···1···1····11·1··1··1·····1····111·11···1·1··1·1·1··1······1····111··111··1···1·1··1···11·11···1·1··111····1111···1···11··11·1·1····1······11··11·1··1·1··1·1·1·1··1·····1····111··11···11·11·1··1····1··111·····11·1·1···1···1··1·····11·11··1····1···11·1····1·11·· |
| out 4 (111) | 1111111···1·······111···1··1·11·1··1·1···1·······1·1·1·······111·1·····111···11··1··1···1······1··1·········1··1···1·1·1···111·1·111···1·1·11···1··111···111111·1···1······111·1··111·1·11··1···1··1·1·····111··1·····111····11·1·1··1····1··1··········1···1··1·1···1···111···1·11······1·1··11···1··1·11·· |
| out 5 (47) | ·1·1··1·1····················1··1··················1··1··1······1·····1······1······1·1···11·················1·1···············1·1··1···1····1·····1······1·1···1·1················1··1············1··1·1······1·····1·······1····11····1················1··1··················1·1·1······1······1····1····· |
| out 6 (135) | 11·11··1111··11·111·1··········1·1·1···1·1··11·····1····1·11·11·11·1··1·1·1·1111·1····11·········11··1·1······1··1·111111·111··1··1·1·1·11·1·1···1···1·1111·11···1111·11·111·1·······1·11··1111····1···1·1111··11··1·1·1··1·11111··11·······11·11··········1·1·111·1·11·111····1··11·1····11··1··11·1····111 |
| out 7 (119) | 1····111·11·11··11··1···1··1·1···1···111·1··1····111··1···1··1···1·1···1·1111····1····1·1········11····1·111···1···11·····11······1···11111111···1··1··1·1····1·11·1111··11··1·1··11···1·11111··11·1··1··1·1····1··1··1·1·111···1··1·1······111·1·1·1·1·····1··11·······11········1··1···1111·11·1··1···1·1· |
| out 8 (111) | ··1·1··1·1··11··1·11····1····11·11·1·111····1·····11·1··111···11···1··1·1·111·1················1·1·····1·11111·······1·1··1·11······1·1·1·1·····11···1·1···1·1···1·1·11··1·11··1···11·111111·1···1·1·1·111··11·····1·1·1··111·1···········1·1···1·111·1·11·······1···1··1·11·······1·1····1·1······11····11· |
| out 9 (103) | 111······1····1···1··1··1··1·1·····1·1·1·1···1···1·11···1··1···1······111··1·111········1··1·····1········1·1111···11·11··1··1····1···11··1··1···1·1···11111·······1···1···1··11··11····11·11·1·1··11··1··1··1·······111···1·111·····1··1···1·······1···11·11··11··1·1··1··1······1··1···1··11···1··1·1···11 |
| out 10 (103) | ·1·1111···1·····11·········1··1····1·1······11····1·1····111····111····11111··11·1····11·······1··1····1111·11·····1·1··1·1···11······1···1·····11···1····1·111·1···1····11·······1·1···11···11··1··1···111····11·1···111·11··111··11·····1··1··111·1···11·····1·1····1·1·····11·····1······1······111···1·· |
| out 11 (111) | ·1······111···1·11··1······1····1··1··11····1·····11·11···1··11··1·1··111··1·111····1·11·····1···1···1··11··1·1····1·11·1··11·11····1···1···11···1·1···11·1·······111··1·11··1····1···1·1·11·1···1·1·11··1·11···1··1·111···1·111··111·······1··1·11·····1··1···1·1·1··1··11···11···1······1····1·1··1·1···11 |
| out 12 (95) | ······1·111·1·1·····11·······11······1·1·····1·····111·····1·11···1······1·1·····11·1·111········11··1····1···11·····11···111····1····1···111···11···1··1·······1·1111·1·····11····11····1·1··1····111····111·····1·····1··1····1·1111······11·1····1······11····1·1····111······1···1······1·11···11····1·1 |
| out 13 (119) | 11·11111111·1···1···1···1··1·1··11·····1·1··1····11···1···1··1·····1··11·1111····1··1··11··1····111····1·111·······1·1····11···1··1···111·111····1··1··1·11·111·111111···1···1·1··11··11···111··11····1··1·1·······1·11·1·111···1·1·11··1···11··1·1·1·1········1·1······11·····1··1··1···11·1·11····1···1·1· |
| out 14 (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 15 (119) | ··1··11111···11·11·1····1··1·11··1····11····11···1···1···111····11·1···1111·11······1·111······1·1···1·1····1····1···11·1·1··1···1····1111··1···11·····11··1··1·1111··11·11·1··1··111··1··11·11·1····1··111····11··1··111·1·11····1111····1·1··11·······1····1···1·1··1·1··1·····1···1··1111···1···11·····11 |
| out 16 (119) | ·111··111····1·····11···1····111·1·1·11······1···111··1···11·11111····1··111111·······1····1···1·······111·····1·1·111····111111·1···111·····1··1···1·····111···111···1·····11·1···111·1111···1·11·1··1··11111·11····1··1·11111····1····1·1·····111·········11·111······1111··11·1···1···1·······1·1····1··· |
| out 17 (111) | ·1·······1····1·11·111·····1···11····1·1·1··1·····11·1···11··11·1·····111·11··11····1·11···1·····1·····111··1·····111·1·1··11·11·1·······1·111·········11·1········1···1·11·111···1··11··1·111···1·1·1··11·11··1·····111··11··11··111···1···1···111·····1·····111··11·1··11···11·1·········1··11·1········11 |
| out 18 (103) | ·····11·11··1···1···1···1····1········11····11···1···11·1·11·1·····1··1·11··········1··11··1·····1··1···1·111·1··1·111·1···1··11·1·····1·11······1·111·1······1·1·11·1···1···1·1···1······11·11·1····111·111·······1·1·11·········1·11··1···1····1··1·1·1··1·1·111···1···1····11·1·······1·11·······1·1·111· |
| out 19 (127) | 1·1···1·111·1·1·1111·1··1···1·111··1···1·1··1····111··1·1·1····11·····1··111·1···1···············11··1·111··11····1·11111····111·11·1··1·1···1··1··1·1·111·1····1·1111·1·1111·11····111·1··111··11·1··11·1···1·1·····1··1·11·1··1···········11·1111·····11····1·11·1·11····1··11·111·····1·1·····1·1··1··111 |
| out 20 (103) | ···11···11······11·11······1·1·1···1·1·1····1·····1··11···1··11··1····111·11·111·················1······11··11·1···11·1·1··11·1·····1···1··111·····1···11···11····11·····11·11····11·1··11·1·1···1···11··1·11···1····111··11·111···········11····11·····11··1··11··1··1··11···1····1······1···11·1····1···11 |
| out 21 (111) | 1111111···1·······111···1··1·1111··1·····1·······1···1··1····111······1111···111·1··1···1······1··1·········1·11···111·1····11···11····1···111··1··1·1···111111·1···1······111·1··11111·1···1··11····1·1···111·······1111····1111·1··1····1··1··········1··11··111···1····11·····11······1····11·1·1··1··1·· |
| out 22 (127) | ·111···1·11·111····1·1··1··1·1·1·1···111·········11·111··1·····1··1·········1·1··1··1··11··1···1·11··1·1111··11··111··1······111····1··111111······111·11·111····1·11111····1·11··11·1·1·111····11··111·1····1····1·········1·1·1·1·11··1·1·11·1111·1··1·1·1·111···1·······1··11···1·····1111·11······1·1111 |
| out 23 (119) | ·1·······1····1·11·111·····1·1·11··1··11····1·····11·11···1··11··1····111··1·111····1·11···1·····1·····111··11·····1·11·1··11·11····1···1·1111···1·1···11·1········1···1·11·111···11·11·1·11·1···1·1·11··1·11···11···111···1·111··111···1···1···111·····11·····1·1·1··1··11···11···1······1·1·11·1··1·1···11 |
| out 24 (111) | ·111·····1···1··1·11··········11·1···1·1····1·····11·11·1·1···1111·1····1··1111·····1·11·········1·····1·1111·11··1····1··1·11···1····1··11··1··1··1·1·1··111······1··1··1·11·······11·1·1·1·1···1·1·111·1··11·11··1···1···1111···111··1····1···1·1·1·1·1··11·1······1··1·11·····1···1·····11····1·1··1··11· |
| out 25 (111) | 111······1····1···1··1··1··1····1··1·1·1·1···1···1··1·1·1··1···1··11··111·11·111········1··1·····1········1·1·1····11·11··1··1·1·11···11··11·1··1··1···11111·······1···1···1··11··1···1·11·11·1·1···1·11··1··1····11·111·111·111·····1··1···1·······1···1··1···11··1·1··1··1···1·11··1···1··1·1··1·1··1···11 |
| out 26 (103) | ·1·1·1···1····1·11··1······1·1·····1··11····1·····1··1····1··11·1··1····1··1··1·····1··11··1·····1···1··11··1111···1·11·1··11·1··1··1····1··1·1··1··1··11·1·1·1····1···1·11··1····11····1·11·1···1···1···1·11··1···1···1···1··1···1·11··1···1··1·11·····11·11··1·1·1··1··11···1··1·1·······1···1····1···1·11 |
| out 27 (119) | 1·11··1·1·1·1·····111···1··1·1111··1··1··1·······1·1·11·1····111···1··11111··111·1·····1···1······1·······1·1·11···11··1···111·1··1····1····11··11·1·1···1·11···1·1·11·····111·11·11111·1·1·1···1··1·111···111·····1·1111·1··1111···1···1····1······1···1··11··11····1···111···1··1······1·····1·1·11·1··1·· |
| out 28 (111) | ··1·1··11··1111··1111······1·111·1···1··················1····1·1·1·····1··1·11········11······11·····1·11·11·1·····1··111·11·111·1··1·1···1·11··1··111··1··1·1···11··111··1111····1111·1·1·············1···1·1··1·····1···1·11·····11····11····111··1·1··1·····1···1·11·11·1··11·1·1·1······1··1·1·1··1·11·1 |
| out 29 (111) | ·1·1111···1·····11·········1··11·····1·······1····1·1·1···11····1111···1111···1··1····11·······1··1····1111·111···11·1··1·1···11·1··1·1···11····11··11····1·111·1···1····11·······1·11···1····1··1··1·1··11····11·11··111·1···1·1··11·····1··1··111·1···11·1··11·1····111·····11·1·1·1······1·1····11···11·· |
| out 30 (111) | 1111111···1·······111···1··1··1····1··1··1·······1·1111·11···1111······111····11·1··1···1······1··1·········11·····11··1···111·1··1·1··11··11···1····1···111111·1···1······111·1··1·1···1·1·1···1··111111··111·1······111·····111·1··1····1··1··········11·····11····1···111···11·11·····11···11···1·····1·· |
| out 31 (119) | ··11·1·11·1··1··11······1··1·1··11····1·····1····1·11·1···1··111111···111·1111·1·1····1····1······1··11···1·111··1··1···1··111···1··1··1111··1······11·····11·1··11·1·1··11····1··11··11··1··1··1··11·1··1·111·11·1··111··1111·11··1····1····1·1····1···11·1·1··1·····1··111·····1·1·····1111····1······11·· |
| out 32 (111) | 1·1·1···1···1···111111··1·············1··1··11···111111·1·11··11·11·······1·········1·1·1··1···1········111··········1·11·11111···1·1·111·111····1·······1·1·1····1··1···1111111··········1·111·11·11111·11·11··1·1·······1·······11·1··1·1······11·1············1···11·1111··1···11·11··11·1·11····1······· |
| out 33 (127) | 1111·11·1·1·1·····1111··1··1·111······1··1·······1·1·1··1····1111·····1111···11··1··1··11··1······1····1····1·1···111··1···11111·11····11··111··1··111···1111·1·1·1·11·····11111··1111····1·1···1·11·1·1···111·1·····1111····11·1·1·11··1····1··1·······1··1··111····1···111··11·11······11···11·1·1··1·11·· |
| out 34 (111) | ·1····1·1·1·1···11·1·······1··111····1······11··1·1·1·····11······1···1111····11·1······1··1······1··1·1111·1111··11·1··1·1··111····1·1·111··1··1····1····1·····1·1·11···11·1·····1·111··1···11··1··1····11·······1··1111·····111····1··1····1·1111·1···11·11·11·1····1·1··1··11···1·1····111····1·1·····1·· |
| out 35 (135) | 1·1·1···1···1···111111··1····1··1··1·11··1··11···1·111··1111·1111·1···1······1·1····1·1·1··1···1········111··1·1··1·11·11·11111··11···11·11111·····11····1·1·1····1··1···1111111···1··1·111·111·1··111·1111111·1··1··1·······1·1··11·1··1·1······11·1····1··1·1·11···11·1111·11··11··1···1·11·11·1····1·1··· |
| out 36 (111) | ···1·11·111·1·1····11····1····111··1·111·····1·····111·····1·11···1···1··111···1·1··1··1·········11····1··1··1····1···1···111····1····1···1111··1···11·11···1·1·1·1111·1····11···1··111·1111··1····111····111·····1··1··1·11···11·1·1·······11··1···11···1····1····1····111······1···1······1·11·1·1····1111 |
| out 37 (135) | ··1··11111···11·11·1····1··1·111·1···111····111··1···11···11···111·1··11111·11·1····1·111······1·1···1·1····1·1··1··111·1····1······1·1111··11··11··1··11··1··1·1111··11·11·1··1··1111·1·111·11·1····11··11··1·11··1·1111·1·11·1··1111····1·1··11·······1··1·1··11·1··1····1·······1·1···111···1·1·11···1·11 |
| out 38 (119) | 1·1·1·1··11···1·1111····1·····1·······11·1··11···111··1·1·1····1·1·1·····1·1·····1·····1···1···1·11··1··11···111····1·1111···111·11·1··11··1····11···1·111·1·1··1··11··1·1111··1····1·····11111·11·1··11·1···1··1··1····1··1····1···1···1·1·11·1·11······1·11···1··1·11····1··11·111·····11···1····11····111 |
| out 39 (87) | ··11·····11·····1··1·······1··11·······1·1··11·····1······11··11·······1·····11··1·11············11·····1·11·····11··1······111··11······11·11··11·····1···11······11····1··1·····1·11·····1111····1·····11·11········1······11·1·1·········11···1··1·1······11··1········11··1··11········11··1·1·11·····1· |
| out 40 (119) | ·111··111····1·····11···1····11111···11····1·1···111·······1·11111·1··1··1·11111······1····1···1·······111·······11111··1·111111······11···1·1··11········111···111···1·····11·1···11111·11···1·11·1······1111·11··1·1··1··11111···1····1·1·····111··········11111····1·1111··11·····1···1····1··1·11······· |
| out 41 (127) | 1·11·11·111·1·1·111·····1·1···111··1···1·1··1····111··1·1·1····11·····1··111···1·1····1·1········11·····11·1·1····1·11111····111·11·1··1·1···1··1···11·111·11·1·1·1111·1·111···1····111·1··111··11·1··11·1···1·1·····1··1·11···11··1·1······11···11···1··1····1·11·1·11····1··11·111·····1·1·····1·1····1111 |
| out 42 (135) | ··1·1111·1··111·11·1·1··1··1··11·1···111····11···1···11···11···111····11111·11·1····1·1·1··1·····1···1······111··1··111·1·1··1······1·1111·111··11··1··1···1·11·11·1·111·11·1·11··1·11·1·111·11·1····11··11··1·11····1111·1·11·1·111·1··1···1··1········11·1·1··11·1··1·1··1·······1·1···111··11·1·11···1·1· |
| out 43 (111) | 1···11·11·1··1····1········1·1··11····1··1···1····11··1·1··1····1·····111·1111·1·1··1·1·1··1······1····111··111··1··1··1··1···111·1···1··1·111······11···1···11··11·1·1····1······11··11··1·1·1··1·1··11··1····1·····111··1111·11·11·1··1····1··111·····11·1·1··1····1··1·····11··1··1·····1··11·1······11·· |
| out 44 (87) | ······1·1···1·1··11····11··1····1··1·1·······1···11···1·1··1··1·1·····11·1·1·11·····1·1··············1····11·1···1····111···1··1····1··1··1·1········1··1·······1·1··1·1··11···1··1···1·11····1·11····11··1·1··1·····11·1··1·11···11···········1····1·1··1···1·····1·11···1····1···1·····1··1··1·········1·1 |
| out 45 (119) | ···1·111·11·11···111·1·····1·1·111·1··11·····1·····111··1··1··111111··11·1·11····1··1111·········11····11··1··1···11···11···1111····1···1···········1··1····1·1·11·1111···111·1···11·1111·11··1····111·1··1·11·11·11·11·1··11···1·111·······11··11····1····1··11·····11···11··11···1······1·············1·1· |
| out 46 (135) | 1·11111··11···1·111··1··1····11111·1···1·1··1····11···1·111····111·1··1··1·1···1·1····111··1···1·11····111······1·1·11111····11··11····1···1·1··11··11·111·1111·1··11··1·111··11···111111··111··11····1111···1·11··1·1··1··1···11··111··1·1·11··111···········1·11·1·11····1··1··11······1····1··1·11···1111 |
| out 47 (111) | ···1111··11···1····111········111··1·111··1··1·····111·····1·11·1·1···1··111·····1··1······1···1·11·······1··1····1···11··111····1····1·1·1111··1····1·11···111·1··11··1····111·····111·1111··1····111····111··1··1··1··1·11····1·1·····1·1·11······1····1····1····1·1··111······1···1····1·1·11·1·1·····111 |
| out 48 (111) | 111··11·111·······111···1··1··1····1·1···1·······1···11·11···1111······111····11·1··1·111··11··1··1·········11·····1·1·1···111····1·1··11··11···1····1···111··1·1·111······111·1··1·1···11··1···1····1111··111·1······111·····111·1111··1·1··1··········11·····1·1···1···111······11·····11···11···1·····1·· |
| out 49 (103) | ·11·1111····11······1···1····11·11···········1····11··1····1·111·········111111········11············1·111····1··111······111111·1····1111······1···1·····11·11·11···11······1·1···11·11······1··1·1··1···1111··········1·11111·····11·········1111········1·111········11111·11·1···1···111·······1····1··· |
| out 50 (119) | ·11····1·1··11····11·········11111·1··11····1·····11·1··111···11···1····1·111·11····1··1·······1·1·1···1·111111·····11·1··1·11······1·1·1·1··1··11··11·1··11·····1·1·11····11······111111·11·1···1·1·1·111··11·····1···1··111·11··1·1·····1·1···1·1·1·1·11·1····11···1··1·11·······1·1····1·1····1·11···111· |
| out 51 (119) | ··11···1··1·11··11··1···1··1·1··11··········1····1·11·····11·111111···111··111·1·1····1·1······1··1··1····1·111··1··11··1··111······1··1111··1···1··11·····11····1··111··11··1·1··11··11·····1··1··11····11111·11·1··111···111·11··1·1····1··1·1····1···11·1·1··11····1··111·······11····1111····1··1···11·· |
| out 52 (127) | 11··11·1111··11·111111·······1···1·1···1·1··11·····1····1·11·11·11·1·····1··1·1··1·····11········11··········1···1·111111·111··1··1·1·1·11·1···1···111·1111··11··1111·11·111111····1···11··1111····1···1·1111··11··1····1···1·1·1···11······11···········1···1·111·1·11·111····1··11·1····11··1·······1·1111 |
| out 53 (119) | 1·1·1·1··11···1·1111····1·····1·1·····1111··1····11···1·111····111·1··1··1·1·1···1·····1···1···1·11··1··11···11·····1··11····11··11····1···1·1··11·1·1·111·1·1··1··11··1·1111··1····1·1···1111··11····1111···1·11··1·1··1··1·1··1···1···1·1·11·1·11······1·1····1····11····1··1··11······1····1··1·11·1··111 |
| out 54 (119) | 1111111···1·······111···1··1··111··1··1··1·······1···11·11···111·1···11111····11·1··1···1······1··1·········1111···11··1···111····1·1··1·1·111··1····1···111111·1···1······111·1··1·111·1·1·1···1····1111··111··1···11111·····111·1··1····1··1··········11·11··11····1···111······11·····1·1··1111·1·····1·· |
| out 55 (111) | 1111111···1·······111···1··1·111···1··1··1·······1·1·1·11····1111······111···11··1··1···1······1··1·········1·1····11··1···111·1·1·····11··11···1··111···111111·1···1······111·1··1111··1·1·1···1··1·1·1···111·1······111····11·1·1··1····1··1··········1··1···11····1···111···1·1·······11···11···1··1·11·· |
| 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 (119) | 1··1·1·1·11··11·111·11·······1··11·1·111·1··11··········1·11·11·11··········1·1··1··1·1·1··1·····1···1·······1·1·1·1··111·111·····1·1·1·11·········111·111··1·1··1·11·111111·11····1··111111111········1·1111··11···········1·1·1·11·1··1···1··1·········1··11·1···1·11·111·······11·1····11··········1·1111 |
| out 58 (111) | 111···1·1·1·1·····1·1···1··1··1····1·····1·······1···1··11··11111······1111···11·1··1·11···1······1··1······11·····111·1···111···11·1·111··11···11···1···111····1·1·11·····1·1·1··1·1···1···1···1····1·11··111·1······111·1···111·111···1····1·1········11·····111···1···111·····111·1···11···11···11····1·· |
| out 59 (103) | 1·1·····11····11··1·····1··1·1··1··1·1·1·1···1···1··1···1··1···1··1···111·11·111····1···1··············1··1·111····11·11··1··1·1··1···11··1··1·····1···111·1······11···1···1···1··11··1·11·11·1·1···1··1··1··1····1··111··11·111··1··1··········1···1···11·1···11··1·1··1··1···1··1··1···1··1····1····1···11 |
| out 60 (119) | 1··1·111··1·111··1····1·1····1···1·1·11··1·······1·1·11·······1·11······111·1·11·1····111··1······1··1·1··111·1·····1·1·1·1·1·1··11·1·111·11·1······1···11··1·1·11··1111··1····1···1···1111·1···1··1·11·····1··11······11·1·1·111··111··1····1·11···1·1·1··1····1··1··1·1·1···1··111·1···11·1·1··1······1··1 |
| out 61 (111) | 1·1·············11111···1······11··11····1··11···11·111·1·11·1111·1·················1·111··············1111···11··11···11·111111··1·1·11·1111············1·1·············11111·1·····11·1···111·11··1111·11111·1··1···············1111··········111·1······11·11·····11·1111··11··11·1···1·11·11············ |
| out 62 (103) | 1111111···1·······111···1··1··1····1·1···1·······1···11·11···111·1·····111·······1··1···1······1··1·········11·····1·1·1···111····1·1··1·1·11···1···11···111111·1···1······111·1··1·1···11··1···1····1111··111··1·····111·······1·1··1····1··1··········11·····1·1···1···111······11·····1·1··11···1···111·· |
| out 63 (127) | 11·11··1111··11·111·1········1···1·1·1···1··11·····1····1·11·11·11·1······1·1·1··1····11·········11··1·1·····1···1·1·1111·111··1··1·1·1·11·1·····1·111·1111·11···1111·11·111·1·····1···111··111····1···1·1111··11··1······1·1·1·1··11·······11·11········1···1·1·111·11·111····1··11·1····11··1·····1·1·1111 |
| out 64 (111) | ·1·1·1···1····1·11··1······1····1··1··11····1·····11·11···1··11····1··111··1··1·····1··11··1·····1···1··11··1·1····1·11·1··11·11····1··111··11···1··1··11·1·1·1····1···1·11··1····1···1·1·11·1···1·1·11··1·11·1····1·111···1··1···1·11··1···1··1·11·····1··1···1·1·1··1··11···11···1·····111···1·1··1···1·11 |
| out 65 (111) | ·1··1···11··1·1·11·11······1····1··1·111····1·····11·1···11··11·11·····11··1··11·1··1·1········1·1······11··1·1····1111·1··11·11·1·········11····1····111·1··1····11·1·1·11·11····1···1·1111·1···1·1·1··11·11··11·····11···1··111·11······1·1····11·····1··1···111·1··1··11···11·1············11····1·····11 |
| out 66 (119) | ·1·111····1·1·1·1·1··1··1·····111··1········1····1·11···1·1···1··111··1·1··1·····1··1··1·1·1···1··1··1··1··11·1··111·111··1·1·11·1····11···11···1··11···1·1·1111····11·1·1·1··11····111·1····1··1··11··1·1··1···1·11·1·1···1····1·1·1·1·1·1··1·1·1····1·1··1·111·1·1·1··1·1···11·1···1···1····11···1··1·1··1 |
| out 67 (111) | ·111··111····1·····11···1······1·1·1·········1···111··1··1·1·111······1··111111·······1····1···1·······111···1·1·1·1······111111·1··1·1111···1··1···1·····111···111···1·····11·1·····1·11·····1·11·1··1·1·1111·······1··1·11111····1····1·1·····111······11·11·1········1111··11·1·1·1···111·····1·1····1··· |
| check 68 (128) | 1·1···1111··1·1·1·1··1··1·····1····1·11·····1····1·11····1·1·1·1·1·1·111·11·1·11····1··1·1·1···1··1··1··1··11··1·1111·11··1·1·11·11·····111··1······11·1·1·1····1111·1·1·1·1··11····1···111··1··1··11···1·11·1··1··1111·1·1·1·11··1·1·1·1·1··1·1·1····1·1···11111··1·1··1·1···11·11·······111····1······111· |
| check 69 (120) | ··111·11··1·1····1·1····1····1·111·1········11····1·1·1··1····1·11·1·111··11········1··11··1··11·1·····11·111··1·····111···1·1····1···111·1··1··11·111·1···111··11··11····1·1··1···1·1111····11··1··1·1·1···1··11··1111···11······1·11··111·1···11··1·1·1···1····1·1·1···1·1······1··1···11·1····1·11·1·111· |
| check 70 (112) | ·111··111····1·····11···11·1···11····111·1··1······111··111·····1·1··1·11······1·1····1····1···1·······111·11·11······111········11·····1·1111······11·11·111···111···1·····11·1·11··11··11111·····111·111·····1··1·1·11·······11··1····1·1·····111···1·1··11······1·11··········11·······1·1·11·1······1111 |
| check 71 (164) | 1···111··11··1111···1·111···1·11·111·11·1·1·1··1·1··1··1·11···1·1·11···111·111·1·111··11··111···111·1111·1·1··111·111·····1···1··1111·1111·111111·1····11····1···11·11···1·11··11·11·1··111111·11111···111·1····11·1·····1·1···111·111·1··11·1··11··1·11111111111·1111··111··1·111·1·111·1··1111·11···1····· |
| check 72 (140) | ·1··11··111·1·····1·1·111···1··1···11111···11·1··1·1·11·1··111·····1··111····1·111······1·11·1···1·1·····111·1···11··1·11111··1··1···111·11···11·1····11·····1··1·11····1111·1111·1111·····1··1·111·111111·1···11111·1··11···11···1·····1·1·111·11····111·1··1·11····1·1·1···1·111·11····11··1····111··1111· |
| check 73 (148) | ·11·1···1···111···1·1···1···1·1··11··1·····11··111·11···1·····1·111···111·1111·11···11111····1·11·11·1111··1···11··111111·1··111·1···1111···1·1·111··11·1·1··11··11·11·111111···1·1·111···1····1·······111·1·11111···1·········11·111··1··1···1·11·11·111··1·1·1···1·1·1111·1·1·11·1·1111·1·11·1··11·11····1 |
| check 74 (140) | ····111···1·1·1·11·1·11·1·111·····1·1···1·1··111·111··1···111·1·11·11··1·1·1·11··1··1·111··1·1·····11··1111·11·1··111···1·1········11111·111·1·······11·1···11··1·1··1··1·11······1·1·1···1··11··1111··1··1···11··11·11111····11·11·1······1·1·1··111·1··11··11·11·1·111··1·1·1·11·1···1····1111··11·11·11·· |
| check 75 (148) | ··1·1··1·1···1·1111··1·11·11·1··111··11···111·1··1··111·111·1111111·····1··111·1··1····11···11···11·1111·111111········1··1111·111·1··11111···1··1··1111···1··1··1··1·1·11···1·····1111111·1·1·1·1····1··1··111·1··1·111·1111·111·············11···11··1111··11··11···1···1111·111·1··1····1111··1·1··1111·· |
| check 76 (160) | ·1·1·1··1·····1·1·1··111·····11·1··1···1··11··111···1·1··1·1·11·111····1··111··11·1····1··1·11·1·111111·111···1···1·111111·1·1·11···1·1·11111·111·1·1·1·1·1·1·1111·11··1··1·11·11··11·1·1··111111111·1··1·111··11·1·11·111···11·11··1·111·1·111·1··1·······1··1·11·11··11·1·111·11·1·1····111·11111·1111·11· |
| check 77 (156) | 1··11·11·1·1··111·····11···1·11··1···111·1········1·1··1··1·111·111·1···1······1111···111··1··111··1111···1·1····1··1111···11·11···1·11···1·1·111·11111·11··11··11·1·11·1·1111111·111··1·1111····1··1··11·1··11··1·1111·1111111··1·111··1··1111·1111····1····1··11·1·1···11···11··111·111111·11·111·11·1··1· |
| check 78 (160) | 111·1···11··1·1···1·····1·1111··11111·111111··1111··1111··111··1··111·1·11·1111·111····11······1·1·····1··11·11·11···1··11··1··111·1·1·1··111111·111111·1111·1····11·1·1···1···1·1··11···1···111·111···11··11·1111··1·1··11····1·1··11····1·1···1···11·11·1·1·111·1111·111·1111·1·1111111·11·1··1·11·1·1··1· |
The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.
Figures of merit
inputs n300Noisy T states per run.
outputs k68
distance d3Exact, proved and witnessed here.
error coefficient A_{3}1,952Faults 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 N79
checks r11
V_{\mathrm{ex}}68T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3510Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3510Overhead 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 width68Rank of the output rows modulo the check rows.
Output gate
68 T0 CS0 CCZon 68 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}
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 (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 74 single-wire gates and 256 \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 306 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 330 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{Z} on check 71, \mathrm{Z} on check 72, \mathrm{Z} on check 73, \mathrm{Z} on check 74, \mathrm{Z} on check 75, \mathrm{Z} on check 77, \mathrm{CZ} on output 0, check 71, \mathrm{CZ} on output 0, check 72, \mathrm{CZ} on output 1, check 71, \mathrm{CZ} on output 1, check 73, \mathrm{CZ} on output 2, check 72, \mathrm{CZ} on output 2, check 73, \mathrm{CZ} on output 2, check 76, \mathrm{CZ} on output 2, check 77, \mathrm{CZ} on output 3, check 71, \mathrm{CZ} on output 3, check 72, \mathrm{CZ} on output 3, check 74, \mathrm{CZ} on output 3, check 75, \mathrm{CZ} on output 3, check 76, \mathrm{CZ} on output 3, check 77, \mathrm{CZ} on output 4, check 71, \mathrm{CZ} on output 4, check 73, \mathrm{CZ} on output 4, check 74, \mathrm{CZ} on output 4, check 75, \mathrm{CZ} on output 4, check 76, \mathrm{CZ} on output 4, check 77, \mathrm{CZ} on output 6, check 71, \mathrm{CZ} on output 6, check 72, \mathrm{CZ} on output 6, check 76, \mathrm{CZ} on output 6, check 77, \mathrm{CZ} on output 7, check 71, \mathrm{CZ} on output 7, check 74, \mathrm{CZ} on output 7, check 76, \mathrm{CZ} on output 7, check 77, \mathrm{CZ} on output 8, check 73, \mathrm{CZ} on output 8, check 75, \mathrm{CZ} on output 9, check 74, \mathrm{CZ} on output 9, check 75, \mathrm{CZ} on output 9, check 76, \mathrm{CZ} on output 9, check 77, \mathrm{CZ} on output 10, check 71, \mathrm{CZ} on output 10, check 73, \mathrm{CZ} on output 10, check 74, \mathrm{CZ} on output 10, check 75, \mathrm{CZ} on output 11, check 74, \mathrm{CZ} on output 11, check 75, \mathrm{CZ} on output 12, check 71, \mathrm{CZ} on output 12, check 73, \mathrm{CZ} on output 13, check 71, \mathrm{CZ} on output 13, check 74, \mathrm{CZ} on output 13, check 76, \mathrm{CZ} on output 13, check 77, \mathrm{CZ} on output 15, check 72, \mathrm{CZ} on output 15, check 73, \mathrm{CZ} on output 15, check 74, \mathrm{CZ} on output 15, check 75, \mathrm{CZ} on output 16, check 72, \mathrm{CZ} on output 16, check 73, \mathrm{CZ} on output 17, check 74, \mathrm{CZ} on output 17, check 75, \mathrm{CZ} on output 18, check 72, \mathrm{CZ} on output 18, check 75, \mathrm{CZ} on output 19, check 71, \mathrm{CZ} on output 19, check 73, \mathrm{CZ} on output 19, check 76, \mathrm{CZ} on output 19, check 77, \mathrm{CZ} on output 20, check 74, \mathrm{CZ} on output 20, check 75, \mathrm{CZ} on output 21, check 71, \mathrm{CZ} on output 21, check 73, \mathrm{CZ} on output 21, check 74, \mathrm{CZ} on output 21, check 75, \mathrm{CZ} on output 21, check 76, \mathrm{CZ} on output 21, check 77, \mathrm{CZ} on output 22, check 71, \mathrm{CZ} on output 22, check 72, \mathrm{CZ} on output 23, check 74, \mathrm{CZ} on output 23, check 75, \mathrm{CZ} on output 24, check 73, \mathrm{CZ} on output 24, check 75, \mathrm{CZ} on output 25, check 74, \mathrm{CZ} on output 25, check 75, \mathrm{CZ} on output 25, check 76, \mathrm{CZ} on output 25, check 77, \mathrm{CZ} on output 26, check 74, \mathrm{CZ} on output 26, check 75, \mathrm{CZ} on output 27, check 71, \mathrm{CZ} on output 27, check 73, \mathrm{CZ} on output 27, check 74, \mathrm{CZ} on output 27, check 75, \mathrm{CZ} on output 27, check 76, \mathrm{CZ} on output 27, check 77, \mathrm{CZ} on output 28, check 73, \mathrm{CZ} on output 28, check 74, \mathrm{CZ} on output 29, check 71, \mathrm{CZ} on output 29, check 73, \mathrm{CZ} on output 29, check 74, \mathrm{CZ} on output 29, check 75, \mathrm{CZ} on output 30, check 71, \mathrm{CZ} on output 30, check 73, \mathrm{CZ} on output 30, check 74, \mathrm{CZ} on output 30, check 75, \mathrm{CZ} on output 30, check 76, \mathrm{CZ} on output 30, check 77, \mathrm{CZ} on output 31, check 71, \mathrm{CZ} on output 31, check 72, \mathrm{CZ} on output 31, check 74, \mathrm{CZ} on output 31, check 75, \mathrm{CZ} on output 32, check 76, \mathrm{CZ} on output 32, check 77, \mathrm{CZ} on output 33, check 71, \mathrm{CZ} on output 33, check 73, \mathrm{CZ} on output 33, check 74, \mathrm{CZ} on output 33, check 75, \mathrm{CZ} on output 33, check 76, \mathrm{CZ} on output 33, check 77, \mathrm{CZ} on output 34, check 71, \mathrm{CZ} on output 34, check 73, \mathrm{CZ} on output 34, check 74, \mathrm{CZ} on output 34, check 75, \mathrm{CZ} on output 35, check 76, \mathrm{CZ} on output 35, check 77, \mathrm{CZ} on output 36, check 71, \mathrm{CZ} on output 36, check 73, \mathrm{CZ} on output 37, check 72, \mathrm{CZ} on output 37, check 73, \mathrm{CZ} on output 37, check 74, \mathrm{CZ} on output 37, check 75, \mathrm{CZ} on output 38, check 71, \mathrm{CZ} on output 38, check 73, \mathrm{CZ} on output 38, check 76, \mathrm{CZ} on output 38, check 77, \mathrm{CZ} on output 39, check 71, \mathrm{CZ} on output 39, check 72, \mathrm{CZ} on output 39, check 73, \mathrm{CZ} on output 39, check 74, \mathrm{CZ} on output 39, check 76, \mathrm{CZ} on output 39, check 77, \mathrm{CZ} on output 40, check 72, \mathrm{CZ} on output 40, check 73, \mathrm{CZ} on output 41, check 71, \mathrm{CZ} on output 41, check 73, \mathrm{CZ} on output 41, check 76, \mathrm{CZ} on output 41, check 77, \mathrm{CZ} on output 42, check 72, \mathrm{CZ} on output 42, check 73, \mathrm{CZ} on output 42, check 74, \mathrm{CZ} on output 42, check 75, \mathrm{CZ} on output 43, check 71, \mathrm{CZ} on output 43, check 72, \mathrm{CZ} on output 43, check 74, \mathrm{CZ} on output 43, check 75, \mathrm{CZ} on output 43, check 76, \mathrm{CZ} on output 43, check 77, \mathrm{CZ} on output 44, check 72, \mathrm{CZ} on output 44, check 74, \mathrm{CZ} on output 45, check 71, \mathrm{CZ} on output 45, check 74, \mathrm{CZ} on output 46, check 71, \mathrm{CZ} on output 46, check 73, \mathrm{CZ} on output 46, check 76, \mathrm{CZ} on output 46, check 77, \mathrm{CZ} on output 47, check 71, \mathrm{CZ} on output 47, check 73, \mathrm{CZ} on output 48, check 71, \mathrm{CZ} on output 48, check 73, \mathrm{CZ} on output 48, check 74, \mathrm{CZ} on output 48, check 75, \mathrm{CZ} on output 48, check 76, \mathrm{CZ} on output 48, check 77, \mathrm{CZ} on output 49, check 72, \mathrm{CZ} on output 49, check 73, \mathrm{CZ} on output 50, check 73, \mathrm{CZ} on output 50, check 75, \mathrm{CZ} on output 51, check 71, \mathrm{CZ} on output 51, check 72, \mathrm{CZ} on output 51, check 74, \mathrm{CZ} on output 51, check 75, \mathrm{CZ} on output 52, check 71, \mathrm{CZ} on output 52, check 72, \mathrm{CZ} on output 52, check 76, \mathrm{CZ} on output 52, check 77, \mathrm{CZ} on output 53, check 71, \mathrm{CZ} on output 53, check 73, \mathrm{CZ} on output 53, check 76, \mathrm{CZ} on output 53, check 77, \mathrm{CZ} on output 54, check 71, \mathrm{CZ} on output 54, check 73, \mathrm{CZ} on output 54, check 74, \mathrm{CZ} on output 54, check 75, \mathrm{CZ} on output 54, check 76, \mathrm{CZ} on output 54, check 77, \mathrm{CZ} on output 55, check 71, \mathrm{CZ} on output 55, check 73, \mathrm{CZ} on output 55, check 74, \mathrm{CZ} on output 55, check 75, \mathrm{CZ} on output 55, check 76, \mathrm{CZ} on output 55, check 77, \mathrm{CZ} on output 57, check 71, \mathrm{CZ} on output 57, check 72, \mathrm{CZ} on output 57, check 76, \mathrm{CZ} on output 57, check 77, \mathrm{CZ} on output 58, check 71, \mathrm{CZ} on output 58, check 73, \mathrm{CZ} on output 58, check 74, \mathrm{CZ} on output 58, check 75, \mathrm{CZ} on output 58, check 76, \mathrm{CZ} on output 58, check 77, \mathrm{CZ} on output 59, check 74, \mathrm{CZ} on output 59, check 75, \mathrm{CZ} on output 59, check 76, \mathrm{CZ} on output 59, check 77, \mathrm{CZ} on output 60, check 71, \mathrm{CZ} on output 60, check 75, \mathrm{CZ} on output 60, check 76, \mathrm{CZ} on output 60, check 77, \mathrm{CZ} on output 61, check 76, \mathrm{CZ} on output 61, check 77, \mathrm{CZ} on output 62, check 71, \mathrm{CZ} on output 62, check 73, \mathrm{CZ} on output 62, check 74, \mathrm{CZ} on output 62, check 75, \mathrm{CZ} on output 62, check 76, \mathrm{CZ} on output 62, check 77, \mathrm{CZ} on output 63, check 71, \mathrm{CZ} on output 63, check 72, \mathrm{CZ} on output 63, check 76, \mathrm{CZ} on output 63, check 77, \mathrm{CZ} on output 64, check 74, \mathrm{CZ} on output 64, check 75, \mathrm{CZ} on output 65, check 74, \mathrm{CZ} on output 65, check 75, \mathrm{CZ} on output 66, check 71, \mathrm{CZ} on output 66, check 72, \mathrm{CZ} on output 66, check 73, \mathrm{CZ} on output 66, check 75, \mathrm{CZ} on output 67, check 72, \mathrm{CZ} on output 67, check 73, \mathrm{CZ} on check 68, check 72, \mathrm{CZ} on check 68, check 73, \mathrm{CZ} on check 68, check 75, \mathrm{CZ} on check 68, check 76, \mathrm{CZ} on check 69, check 75, \mathrm{CZ} on check 69, check 76, \mathrm{CZ} on check 70, check 72, \mathrm{CZ} on check 70, check 73, \mathrm{CZ} on check 71, check 72, \mathrm{CZ} on check 71, check 76, \mathrm{CZ} on check 72, check 73, \mathrm{CZ} on check 72, check 74, \mathrm{CZ} on check 72, check 77, \mathrm{CZ} on check 73, check 75, \mathrm{CZ} on check 73, check 76, \mathrm{CZ} on check 73, check 77, \mathrm{CZ} on check 74, check 75, \mathrm{CZ} on check 74, check 77, \mathrm{CZ} on check 74, check 78, \mathrm{CZ} on check 75, check 77, \mathrm{CZ} on check 75, check 78, \mathrm{CZ} on check 76, check 77, \mathrm{CZ} on check 76, check 78, \mathrm{CZ} on check 77, check 78
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 8, 10, 19, 26, 32, 33, 51, 55, 57, 71, 74, 77, 79, 80, 82, 87, 88, 90, 94, 95, 96, 99, 100, 102 and 76 more (listed below); \mathrm{T}^5 on rotations 3, 4, 5, 12, 14, 16, 18, 20, 25, 27, 30, 34, 36, 37, 38, 42, 43, 46, 49, 56, 59, 66, 70, 83 and 4 more (listed below); \mathrm{T}^\dagger on rotations 0, 1, 9, 15, 28, 29, 31, 35, 45, 48, 60, 73, 85, 86, 159, 165, 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 100 rotations at T³
8, 10, 19, 26, 32, 33, 51, 55, 57, 71, 74, 77, 79, 80, 82, 87, 88, 90, 94, 95, 96, 99, 100, 102, 103, 104, 105, 113, 115, 116, 117, 118, 119, 120, 122, 124, 128, 129, 131, 133, 136, 137, 139, 140, 141, 146, 150, 161, 168, 172, 175, 179, 181, 182, 185, 186, 187, 188, 189, 194, 195, 200, 205, 207, 208, 210, 211, 212, 213, 215, 219, 221, 223, 225, 226, 227, 228, 229, 232, 235, 238, 240, 244, 245, 247, 250, 254, 265, 268, 269, 272, 273, 276, 278, 279, 281, 284, 291, 292, 295
All 28 rotations at T⁵
3, 4, 5, 12, 14, 16, 18, 20, 25, 27, 30, 34, 36, 37, 38, 42, 43, 46, 49, 56, 59, 66, 70, 83, 107, 154, 156, 157
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/300.68.3.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-300.68.3.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 1,952 faults of weight 3 are undetectable and damaging, so A_{3}=1{,}952. 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 [0,15,63].
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_300_68_3.json",
"label": "restricted_light_300_68_3",
"N": 79,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=92), with searched graph punctures",
"provenance": "gamma frontier release record restricted_light_300_68_3 (source catalogue id restricted_light_300_68_3); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=92), with searched graph punctures; matrix 2bac793753a158f0...; the release states d=3 (exact), gamma=1.3510451182732883 (exact)",
"notes": "matrix gamma_frontier_release/matrices/2bac793753a158f0ba77370b176cc70e488caf7e8f684a7c0983ae766b29d56e.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/300.68.3.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[953].