The circuit
The 83\times310 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 |
|---|---|
| out 0 (93) | ·····1···1·1····1···1·····1···1·1··1·····11··1··1···1····1····1·······1···1·1··11·····1·1·1··1·1·11·1····1··11···1··1···1·1···1·1·1··1·1·1·1·1·1··1····1·····1·1·····1··1···1····1·1··1·····1·1···1···1·····1·······1··1········1·11··1·1·······1·1···1···11·1··1·1····1···1·1···1··1·1··1···11·1·1···1·1···1·1·11···1 |
| out 1 (119) | 1·1····1111··1·111·11·········1111······11······11·1111···1···1·1····11···1·1····1···11···1·11······11···11··1·1·······11··1111·111··11111·······1111·······1·111·1·11111········1111······11·········1··1·11··111····11·1·····11·11·····1····1·1·····1··11·······11···11····1·1·····11···1111··111···1111··1·······11 |
| out 2 (109) | ··1····1111······1···1····11·····1·1·1111·11··1·1····1····1···1·····1·······1·11···111·11·1··1··11··11·1···11······1···1···11····11·1···1·11···1·11·1·······11111·····1··1··11······1·1·1111··11···1··1········1······11·····1·····1·11····11·1··11···1···1·11····11·1····111·····1··1····11··1··11··1···1···11··1··11 |
| out 3 (127) | 1··11···111·····1··11··1···1··1·1··1·11···1·111····1111···1···11·1··111········111·1··11·1·1·1···11··1····1·11·1···11··11·1·1·1··111··1···11·1··11·1·11·······111····1·11·1··1···1·1··1·11····1··111·······11··1·11···111·1··1·11·····1·11·1····11···1··1·1··1··1··1····1··1·1·1··1·111··1·1·1···111···1·····11·1·1·1· |
| out 4 (103) | ········11···1···1···1·1··11·111·1·1111·1111111111·1······1·····1··1···············11·1··1··1·1···111··1·11··1·1·1··1··11··1·········1···1··1·················11··1···1··11·11··111·1·1111·11·11·111·11··1·1··········1··1·1···············11···1····1···1······111··1·11····1·1·1··111···1···········1·····1··1······ |
| out 5 (125) | 1··1·1·1·1···1·1·1·1·11···1···1·1··1·11·111·11·1····1·1··11···1·11··11··1·····1·1·1111·1·11·1··11··1·1·111··1··········11·1111····1·111······1·····1·1·1····11·1··1·1·11·1··1····1·1··1·11·11·1··11··1······1····1··1·11·11··1·1·1···1··1·111·1··1···11··1·11····1·1·111···1·········11··1111·1···1··111········1····· |
| out 6 (119) | 1···1··1111·····11·11··1·1·1··1·1··1·11···1·111····1·11···1···11····111·1···1··11··1··11···1·1····1··1····1·11·1···11··11·1···1···11··1····1·1··1111··1·····1·111····1111·1··1···1·1··1·11····1··111·······1···1·1····111····1·111·1··1·1··1····11······1·1·····1··1····1··1·1·1··1·111··1···1····11···1······1·1·1·11 |
| out 7 (127) | 1·1111···1··1······11··1··11·11111··1··1·····11111·11·1··1····1111········1···11····1·······11·111111··11··1·1······1··11··11···111111111··1·······11111·······1·1·····11·1·11··11111··1··1·······11·11··1·11····1··1··1111·······1··11·····1··1·········11111··111··11···1··1······111···11····1111·11111····1······· |
| out 8 (109) | 1·11···1111····111·1··········1111······11······11·1111·······1······1····1······11··1····1111······11···11··1·1·······11··1111·111···111········11111······11111···1111·········1111······11·········1··1·11··1·1·····1·······1··1······11···1·······1·111·······11···11····1·1·····11···11111·111····111·········111 |
| out 9 (119) | ··1·11··1····1·11···11·1·····1···1·······111·1·11··11····11···1111··1·1·····1····11·1·111··1·1·1··111···1111···1···11··1·····11··111·1··1·1····11···1·11······1···1·11··111·····1···1·······1·11··1··11····11·······1·11111··1··1··1·····11·1···111·····1·11····111···11111····1··1·11······11···111··1··1···1···11··· |
| out 10 (127) | ····1··111···1·1·1·····1···1·11·1··11··11·1···111··1·1········1111········1·1·1·111·1···1··1·1··1··111·11·1111·1·1······1·1111··1·111··1·1···1·111····1·····1·11··1·1·1···1··1··11·1··11··11··1····1·11····1···1·······1111·······11·1··111·11····1·····1·1·1····111·11·1·11·1·1·1····1··1111···1·11·1··1···1···111·1· |
| out 11 (119) | 1···1··1··1··1··1··1···1··1··1·1·1···1··11·1···111···11·······111··1111·1···1··11···1··1·1···1···1·111···111·····1·1······11··1···11·11··1·111··1111··1·····1···1·1··1·1··1·1···1·1·11··1··11··1·····11··1·····1·1·····111·1·1·111·1··1·1···1····1···1····1··1···111···11·1······11······11··1····11··11····1·111·1·11 |
| out 12 (119) | ····1···111····1····11·1··1··1·111··111··1·11····1··11····1···11·····1··1·1·1·1·1·1·1·1·11··11··1·1·····11··11·····11··1··1··1··1·11·1·1··1··1·1·11···1·······111···1···111·1···1·111··111··1··1·1·······1··1··1·····1111······1·111·1··1·1·1···1·1··1···11·1···1·····11···1·1····1·11···1··1···1·11··1·1····1··11··11 |
| out 13 (125) | ··1····1111······1···1·······11111··1111·1··11·1·1··11··············1···1···1·11···111·11·1··1··1111·1·11111·1·1·1·11···1··1·····11·11··1·11···1·1··1·······11111·····1··1······11111··1111·1····11··1···1··1··1·············1···1·1·11····11·1··11···1···1·11··11·1·1111·1··1·1·11·1·1···1···1··11··11··11··11··1··1· |
| out 14 (119) | ··1111·1·1·····11····1·1···1·1··11·11··1·111···11··11····11···11····111·1·········11···11····1·1··111··1111··1·1····1··1·····11··111·1··11·····1··1·1111····1··1····11···11··1··1··11·11··1·1·11·····11····11·······1·111····1·111········11·····11·······11···1111··1111····1·1····11······11···111··1··1··1····1···1 |
| out 15 (109) | ·····1··11······1····1····1···1·1··111···11····11···1····1····1·······1···1·1··11··1·11·1·1111·1·11·1····1·1·1···1·111··1·1···1·1·1··1·1·1·1·1·1··1····1·····111·····1···1··1····1·1··111···1·1······11·····1·······1··1········1·11··1·1··1··1·1·1···1·1111·1··1·1····1··1··1···11·1·1··1···11·1·1···1·1···1·1·11···1 |
| out 16 (135) | 1·1111·111·······1·11··1·····1···1·1··1·11111······11·1··1····11·····1··1·1···11·1·11····1··11·111···1·1·11111·1·1··1······11···111111111111····1·111111····1·11······111·1·····1···1·1··1·11·11·1··1······11····1··1··11······1·11··11··1·11········1···11111·····1·1·11·11·1·1·1··1·····11····1111·11111··111···1··1 |
| out 17 (119) | 1·11·1···11··1·1···1·1·····1··1·11···111·1·11··11···111··1······11···1··1···1··11·111···11·····1·1·11···11·11···········1·1··1···1···11·1·11·1·1·11111·1·······11·1·1··1·1···1···1·11···111·1··1·1···11·····1··1·1··1····11····1·1·1··1·1·111·····1··1·····1·1···11···11··11·······1··1··1··1····1····11·1···11·11··11 |
| out 18 (117) | 1··1·1·11····1·1·1·1·······1·1·111··1······1··1·11·11·1··1···11·11··11········1·1·1··1·1·11··1·11·1·11··1·1·11·1·1··1·····1·11····1·1·1·1····1····11·1·1····111···1·1·11·····1··1·111··1·······1···1··1··1·11····1··1··1·11··1·1·····1··1·1···1··1···11···111···1·11··1·1··1·1·1·1··1····1·11·1···1··1·1·1······1····1 |
| out 19 (119) | ···11··1··1··1·1·····1·1·····1·1·1··1111·1·111···1·1·1········1111········1···1·1111····11·111··1·1····111··1·······1··1··1111··1·111··1·1···1·111···11·····1···1·1·1····11·····1·1·1··1111·1··1·11······1·1···1·······1111·······1··1··1111······1··1··111·1·1·1····111···1········11···1111···1·11·1··1···1···111·1· |
| out 20 (135) | 1·1·11·1·1·········1···1··11·11111··1··1·····11111·1111··11···11·1···1····1·1·11·1··1······111·111111··11··1·1······1··11··11··111111·1111·1····1··11·11····1··1·······1··1·11··11111··1··1·······11·11··1·11··1·1··1·111·1····1··11·11··1··1···········111111··111··11···1··1······111···11····1111·1·111··1·1···1··· |
| out 21 (125) | 11·1·1·111···1·1···1·1····1···1·1··1·11·111·11·1···11·1··1····1··1·111··1·1···1·1·1·11·1··1·11·11··1·1·111··1··········11·1·11····1·1·1··1··11·····1·1·1····1111··1·1··1·1··1····1·1··1·11·11·1··11··1·····11····1··1··1··11·1·1·11··1··1·1·1·1··1····1··1111····1·1·111···1·········11··1·11·1···1··1·1····1··11····· |
| out 22 (93) | ··11······1··········1··1·11·1··1··11···1·11·11·1····1····1···1·····1·········11·1···1·1111··1···1··1···1····1·········1···11····11·1···1·11···1·11·11·······1··1········1··11··1··1··11···1··11··11··1········1······11·····1·······11··1····1··11··11···1··1····1···1······1·······1····11··1··11··1···1···11··1··11 |
| out 23 (117) | 1··1·1·11····1·1·1·1······1···1·1··1·11·111·11·1···1··1··11···11·1··11··1·····1·1·1··1·1·11··1·11··1·1·111··1··········11·1··1····1·111··1···1·····1·1·1····111···1·1·11····1····1·1··1·11·11·1··11··1·····1·····1··1·111·1··1·1·1···1··1·1···1··1···11···111····1·1·111···1·········11··1··1·1···1··111···11···1····· |
| out 24 (127) | 1·11·1···11··1·1···1·1····1····1···111·11·1······1·1111··11······1·1·1··1···1··11·111···11·····1·1···1··1·11·1·1·1·11··1··11·1···1····1·111111·1·11111·1·······11·1·1··1·1··1·1···1···111·11··1··········1·11··1·1··1·1···11···1·1·1··1·1·111·····1··1·····1·1·····1··1·1·1··1·1·11·11···11·1····1·····1·1··111111··11 |
| out 25 (127) | 1···1····11·····11·1···1···1·11·1··11111··1·1·1····1111··11···11·1·1111·1···1··111····11·····1···11·······111··1····1··11·1·1·1···11··1···1111··1111··1········11····111··1··1··11·1··11111···1··1·1·······11··1·1··1·111·11·1·111·1··1·11······11········1··1··1·······1·11···1····111··1·1·1····111··1·····1111·1·11 |
| out 26 (125) | 1··111·1·11··1···1·111·1··11·1··1·····1··1··1·1·1···111··1·····1·1·11·····1·1·······11111·1·1··1···11··1·11·1··1·1·1···1···1····1··1··11·11·1··1·111·111····11·11·1···11111·11·11··1·····1··1····1·1··1·····1··1·1··1···1·11·1····11········1·1·111···1··1·1·····11··1·11··1···1·11··1····1···1·1··1···11···11·1·1··11 |
| out 27 (117) | 1·1·1···11···1··11·1·1·1··1···1······1111··111··1···1·1····1···1·1·1·11·······1·1··1·1··111·····1·1·1···1·1111·1····1···1·1···1··1·11···1···11·11·111·1······111··1··111·11·1····1······1111···1·11···1·····1····1······1·11···11····1··1··1··1···1··11·····1···1·1···1·1·11·1·1····1·1··1···11··1·1·1···1·····1111··1 |
| out 28 (125) | 1···11··111··1·····11··1·····111·1·11···1·11·1·1·1··111··1·····11··111··1·1·····11·11111111····1··11·1·1·····1·····11···1··1····1··1··11····1··111·1··11···1·1111·1····11·1·····111·1·11···1··11··1··1···1··1··1·1··1···11·1·1·1·11·····11·11·1·111··11····1····11·1·1·······1····1·1·1···1···1·1··1···11······1·11·1· |
| out 29 (119) | ····1··1··1····1·1··1··1···1··1·1··1····1·1··1111··1·1········11·····1··1·1·1·111111··1·1····1··1··11··11·1·1··1·1·1····1·1111··1·111··1··1··1·1·11···1··1··1···1···1·1·1·1··1···1·1··1····1··1···11·11····1···1·······11······1·111·11·1111····1·1·······1·1····11··11·1··1···1·11···1··1111···1·11·1··1····1··11··11 |
| out 30 (117) | 1·1···1·1·1····11··1·1········1111······11······11·1·11···1···1··1·1·11·1·1·1·····1·11···111·1······11···11··1·1·······11··1·11·111··1111·1·1····1·11·····1··11·1···11·1·1·······1111······11·········1··1·1···1·1····11··11···11111···1··1·1·1······11·1·1·······11···11····1·1·····11···1·111·111···1111···1·1····1· |
| out 31 (125) | ····11·1·11··1·111··1··1··11··1······1·111···111···111···1·····1·····11·1·····11·111·11···11···11111···1111·1··1····1······1111····111···111·····1····11····11·11·1·111·1·1·11···1······1·111·····11·1·····11··1····1···1······111···11··111··1·1·····1·1··111··11··11111··1···1····1·····11111····1·11·····111·····1· |
| out 32 (127) | 1··11···111·····1··11··1···1·11·1··11111··1·1·1·····111···1···11·11·111·1······111·1··11·1·1·1···11·······111··1····1··11·111·1···11··1···1··1··1111·11·······111····1·11·1··1··11·1··11111···1··1·1········1··1·1····111·1··1·111····1·11·1····11···1··1·1··1··1·······1·11···1····111··111·1····11···1·····1··1·1·11 |
| out 33 (109) | ·····1··11······1····1····1···1·1··1·····11··1··1········1····1·11····1···1·1··11··1·11·1·1111·1·11·1····1··11···1··1···111·1·1·1·1··1·1··11·1·1··1····1·····111·····1···1··1····1·1··1·····1·1···1···1···1·········1··1·11·····1·11··1·1··1··1·1·1···1·1111·1··1·1····1···1·1···1··1·1·11·1·11·1·1···1·1····11·11···1 |
| out 34 (127) | ··1·······1·····1···1·····1··1·1·1·11111··1·1··111··11···11·····11··111·1·1···1·11··1·11·1··1··11··111·11·111··1···1······111·1·11··11·11····1··111·1···········1····1··1···1···1·1·1·11111···1··1···11··1··1··1····1·1··11··1·1111·11··11··1···11···1···1·11····111·11·1·11···1··1······111·1··11···11·11······1·1·11 |
| out 35 (125) | 1··111·11·1··1····1111·1·····111·1·11···1·11·1·1·1·1111··11····111··1·····1·1······1·11111··1··1··11·1·1·····1·····11···1·······1··1·111··1····1·111·111····111·1·1····1111·····111·1·11···1··11··1··1···1·11··1·1··1·1·111··1····11·······1··1·111··1···1·1····11·1·1·······1····1·1·1·······1·1··1··111····1···1··11 |
| out 36 (109) | ··1·····1·1··1·······1····11····1··1···11·11··1·1··1·1····1···1····11···1···1·11·1·1·111111··1··11··11··1··1·······1···1····1·1··11·1···1·111··1·1··1········11·1·1······1··11·····1··1···11··11···1··1····1··11······11···1·1···1·1·11··1·1··1·111··11···1·11····11··1···1·······1··1·····1·11··11··1···1···111·1··1· |
| out 37 (95) | ·······1·1···1···1········11·11111·11·1·11111·1111·1······1·····1··1·············1··1·1··1········111····11·11·1·1·11··1···1·········1···1··1···············1··1··1···1·····11··11111·11·1·11·11·1·1·11·11·1··········1··1·1·············1··1···1····1··········111····11··1·1·1·11·11····1···········1·····1··1······ |
| out 38 (111) | 1··11·····1·····1······1···1·11·1··11111··1·1·1····1·11···1···11····111·1······111··1·11·1···1···11·······111··1····1··11·1···1···11··1····1·1··1111·11·········1····1····1··1··11·1··11111···1··1·1·······1···1·1····111····1·111····1·11··1···11···1·1··1··1··1·······1·11···1····111··1···1····11···1······1·1·1·11 |
| out 39 (119) | ····1··11·1··1·1·1··11·1···1·11·1··1·1··1·1···111··1·1········11·····1··1·1·1·1·111·····1···11··1··111·11·1······1······1·1111··1·111··1··1··1·1·11···1·····1·1·1·1·1·1·111··1··11·1··1·1··1·11····1·11····1···1·······11······1·111·1··111·······1······11·1····111·11·1········1····1··1111···1·11·1··1····1··11··11 |
| out 40 (125) | 1···11·1111··1·····1·1·1·····111·1·11···1·11·1·1·1··111··11····11··11·····1········1111111111··1··11·1·1·····1·····11···1··1····1····111····1··1·111··11····11111·1····1·11·····111·1·11···1··11··1··1···1··1··1·1·11·1·11·1·1····1········11·1·111··11·11·1····11·1·1·······1····1·1·1···1···1·1·····111······1·1··11 |
| out 41 (55) | ···1···111···1······1········1······1··1·····1··············1····1·1····1···1····1·11·1····1·········1·····1·1·····1···················1··1·1·····1··1······1·11··1·····1·······1······1··1·······1·······················11·····1·1·····1·11···1·······1··········1······1··1····1·····················1····1·1·····1 |
| out 42 (125) | ···111·1111··1·····11··1·····111·1·11···1·11·1·1·1··111··1·····1·1·11····11·1······11111111····1··11·1·1·····1·····11···1··1····1··1··11·11·1··1·11··111····11111·1····11·1·····111·1·11···1··11··1··1···1··1··1·1··1···1·11·1····11·······11·1·111··11····1····11·1·1·······1····1·1·1···1···1·1··1···11···11·1·1··11 |
| out 43 (117) | 1··1·1··11·····1···1·······1·1·11···11·····1·11·1··11·1··1····1··1·111··1·····1·111·1111··1··1·11·1·11····1··1·1·1·11·····1·11····1·1·1··1··11·····1·1·1·····111····1··1·····1··1·11···11······1··11··1····11····1··1··1··11·1·1·1···1··111·1·1·11····1···111···1·11····1····1·1·11·1··1·1·11·1···1··1·1····1··11····· |
| out 44 (31) | ·······1·1···1···1··································1··············1····1········1··1·1··1··································11··············1·····1·········1··1··1···1·····································11·············1·····1·······1··1···1····1·····································11··················1·····1 |
| out 45 (133) | ··11·1·1·1···1··11···1·····1···111···1111··11111·1··1····1····1·11···11·1·11···111···1··111111·1·1·1·1·1··1111·1···1···1··1···1·1·1··1·1··11·1·11···11·1····11·1··1··11··1···1····111···1111···1·111·1···1··1·······1··1·11····1111···1·11····1···1··11·1111·1···1·1·1··1·11·1·1··1··1···1···11·1·1···1·1····11·111··· |
| out 46 (109) | 1··111····1········111·1··11·········11··1··1·1·1··1·111·11····1·1··1···1·1·1····1···1·1111·1··1····11···11····1·1·1···1····1······1·111·11····1·1·1·111·····1··1······1111·11··········11··1····1·1··1····1···1·1··1·1·1·1··1···111·····1····1··11··11··1·1······11···11······1·11··1·····1··1····1··111···11···1··1· |
| out 47 (119) | 1·11·1·1··1····1·1·1·1····1··1·1·1·11··11·1······1·111···1·······1···1······1··11111··1·1······1·11·······1111·1·1·11··1··11·1···1···11·1111·1·1·1·111·1····1···1···1·11·1··1···1·1·1·11··11··1··········1·11··1····1·····1····1···1··1·1111····1·1········1·1··1·······1·11·1·1·11·11···11·1··1·1····11·1··111·11··1· |
| out 48 (119) | 1·1111··1····1·····11··1··11··1111············1111··1·1·11····111·······1·1···11···1··1·····11·1111111·11··········11··11···1···11·111111·11······111111······1···1····11·1·11···1111··············1·11··1··1····1··1··111·······11··11····1····1········11111··1111·11···········1·111····1····11·1·11111···11······1 |
| out 49 (125) | ··1·····111··················11111··1111·1··11·1·1···1····1···1·····1·······1··1·1·111·1111·11··1111·1·11111·1·1·1·11···1··11····11·1···1·11···1·11·1···1····1111···············11111··1111·1····11··1···1·····1······11·····1·····1··1··1·11·1··11··11··11·11··11·1·1111·1··1·1·11·1·1···11··1··11··1···1···11··1··11 |
| out 50 (31) | ····1···1····1······1········1······1··1·····1·······························1·····1··1····1·········1·····1·1·····1··································1·······1···1·····1·······1······1··1·······1········································1····1·······1··········1······1··1····1··································· |
| out 51 (117) | ···1·1·1·····1··1···11····1···1····1·1·1·11··1··1··11····11···1··1·1·11·1·1····111··11··1·1·11·1·11·1··1·1··········1···1·11··1·1·1····1·11111·11····1·1····11····1··1··11··1····1····1·1·1·1·1·1·1···1····11·······1·11··11···1111···1·11··1·1···1···1··111·1··1·1··1·1············1·1··11··11·1·1·····1···1111111··· |
| out 52 (133) | 1··111·1·11··1···1·111·1·····111·1·11···1·11·1·1·1···11··11····111·11·····1·1·······11111·1·1··1··11·1·1·····1·····11···1··11···1··1·111··1·11·1·111·111····11·11·1···11111·····111·1·11···1··11··1··1···1·····1·1··1·1·111111····11········1·1·111···1··1·1····11·1·1·······1····1·1·1···11··1·1··1··111····1·111··11 |
| out 53 (127) | 1·1··1··111··1·1·1·111····1····1···1·1·11·1·11···1·1111··11······1·1·1··1······11·1·1···1··1···1·11··1··1·1··1·1·11·1··1··11·1···1····1·111111·1·1111··1······111·1·1·1111··1·····1···1·1·11··1··11······1·11··1·1··1·1···11···1·1····1·1·1·1·····1·····1··1·1··1··1··1·1····1·1·1··11···11·1····1·····1·1··111111··11 |
| out 54 (127) | ···11··1111··1···1··1··1···1·11·1··11··11·1···111····1····1···11·1·1······1···1·111·1···1····1··1··111·11·1111·1·1······1·1·11··1·1111·1····11·111···11·····1·111·1···1·1·1··1··11·1··11··11··1····1·11········1······111·11······1··1··111·1·····11······1·1····111·11·1·11·1·1·1····1··1·11···1·11·11·1······1111·1· |
| out 55 (119) | 1···1··1··1··1···1·111·1··1··1·111··1···11·1···111···11·······11·1·11·1·····1··11···1··1···111···1·111·1·1··1····1·1······11··1···11·11···1111···1·1··1·····1···1·1···11111·1···1·111··1···11··1·····11··1·····1·1·····11·11·1··1··1··1·1···1····1··1···111··1···111·1·1···1·····11······11··1····11··11·····1111···1· |
| out 56 (111) | 1··1···········11··1·1····11··111··1····1111··1··1····1···1·········1·1···1·1·11·1111··11··11···11·····1·111···1···1····1··1111·1···1·11··11···11··1·1··············11·1·1··11···111··1····11·11···1·····1·······1····1······1··1·11·11··1111····11·····11··11·······1·11·1···11··1···1···1111··1····1·11····11··11··· |
| out 57 (109) | ···1·1···1······11··11····1···1·1··1·····11··1··1········11···1··1··1·1···1····11····11·111·11·1·11·1····1··11···1··1···1·1·1·1·1·1····1·111·111··1··1·1·····1·1·····11·11··1····1·1··1·····1·1···1···1·············1·11··1··1··1·1···1·1·····1·1·1··11··111·1··1·1····1···1·1···1··1·1··1·1·11·1·1·····1···111·11···1 |
| out 58 (125) | 1····1···1·····1·1·11······1···111·····1···1·11·11·11·1··1····1··1··1·······1·1·11111111·111·1·11·1·1···1·111··1·1·11·····1·11····1·1·1··1···1·11·11···1·····1·1····1·111····1····111·····1····1··11··1··1·11····1··1··1··1··11····1·1··11111·1·11···11·1·111···1·1···1·1·11···1·11·1····1·11·1···1··1·1····1···111··1 |
| out 59 (109) | ··1·1··1·······1·1··1··1··1··11··1·····1··11···1···1······1····1····11··1·1····11·11·111·11·1····1·1···11·111··111·1···11·1··1··11·1···11··1·1······1·1·····11······1·1·1·1·1···11··1·····1···11·····1·····1··········1·1····1·1·11···1·1·11··1·11···11··1···1···1···11·1·11···1·11··11··1··1·1·11·1····11····1·1····· |
| out 60 (125) | ····11·1·11····111···1·1··11·1······1··111···111···111···1·····1·····11·1·····11·111·1·1··1·1··11111·1·11111···1····1······1111····111···111·····1····11····11·11··1111··11·11··1······1··111·····11·1·····11··1····1···1······111···11··111··1··1····1··1·111··11·1·1111·1····1····1·····11111····1·11·····111·····1· |
| out 61 (127) | 1·11·1···11····1·1·1······1··1·1·1·11··11·1······1·1111··11······1·1·1··1···1··11·111·1·1···1····11·······1111·1·1·11··1··11·1···1····1·111111·1·11111·1·······11···1·11···11···1·1·1·11··11··1··········1·11··1·1··1·1···11···1·1·1··1·1·111···1·1······1···1··1·······1·11·1·1·11·11···11·1····1·····1·1··111111··11 |
| out 62 (125) | 1····1···1·····1·1·11······1···11·1·11·1···1·11·11·11·1··1····1··1·111··1···1·1·11111111·111·1·11·1·1····11····1·1·11·····1·11····1·1·1··1··11·····1···1·····1·1····1·111····1····11···11·1····1··11··1··1·11····1··1··1··11·1·1·1·1·1··11111·1·11···11·1·111···1·1····11······1·11·1····1·11·1···1··1·1····1··11····· |
| out 63 (109) | ···1·1···1······11··11····1··11·11·1···1·11··1······1····1····1·······1···1····11····11·111·11·1·11·11··11··1····1··1·1·1·1···1·1·1··1·1·1·1·1·1··1··1·1·····1·1·····11·11··1···11·11·1···1·1·1···1·········1·······1··1········1·1···1·1·····1·1·1··11··111·1··1·11··11···1·····1··1·1··1···11·1·1···1·1···1·1·11···1 |
| out 64 (117) | 1··1·1·11····1·1·1·1·······1···1·1··1········11·11··1·1··11···1·11··11··1·····1·1·1··1·1·11··1·11·1·1··11·1·11·1·1·11·····1111····1·111······1·····1·1·1····111···1·1·11·····1····1·1··1··········11··1··1··1····1··1·11·11··1·1·1···1··1·1···1··1···11···111···1·1··11·1··1·1·1111·1····1111·1···1··111········1····· |
| out 65 (111) | ····1···111····1····11·1··1···········1··1·11····1·1·1········1111········1·1·1·1·1·1·1·11··11··1·1··111·1·1·1·····11··1··1111··1·111··1·1···1·111····1·······111···1···111·1············1··1··1·1·······1·1···1·······1111·······11·1··1·1·1···1·1··1···11·1···1··1·1·1··1··1····1·11···1111···1·11·1··1···1···111·1· |
| out 66 (119) | ····1··11·1··1·1·1··11·1···1·11·1··11··11·1···111·1··1········11··········1·1·1·111·····1···11··1··111·11·1111·1·1······1···11··1·111··1··1··1·111····1·····1·1·1·1·1·1·111··1··11·1··11··11··1····1·11········1·······11·········11·1··111·······1······11·1····111·11·1·11·1·1·1····1····11···1·11·1··1····1··111·1· |
| out 67 (127) | 1·1111··1····1·····11··1··11·11111··1··1·····11111····1··1····1111·····11·1···11···1··1·····11·111111··11··1·1······1··11·······111111111··1·····1111111······1···1····11·1·11··11111··1··1·······11·11··1·······1··1··1111······11··11····1····1········11111··111··11···1··1······111·········1111·11111····1·····11 |
| out 68 (119) | ····1···111····1····11·1··1·1··1····111··1·11····1·1·1········11·····1··1·1·1·1·1·1·1·1·11··11··1·1·11·1·1··11·····11··1··1111··1·111··1··1··1·1·11···1·······111···1···111·1·····1····111··1··1·1·······1·1···1·······11······1·111·1··1·1·1···1·1··1···11·1···1·11·1·1···1·1····1·11···1111···1·11·1··1····1··11··11 |
| out 69 (117) | 1···11··1·1······1·1·1·1··11····1···111··1··111·1··1111··11····1····11··1·1······1·1·1·11·111··1····11·1·111···1·1··············1··1·111·1·····111·1··11·····11·1·····11·11·11·····1···111··1····111··11···11··1·1··1·1·1····1·1·11······1·1··1··11···1·11·1······11·1·11·1····1·1············1·1··1··111···1····11·1· |
| out 70 (135) | 1·1111···1····1····1·1·1··11·11111··1··1·····11111·11·1··1····11·····1··1·1···11····1···1··1·1·111111··11··1·1······1··11··11···111111111111····1·111111·······1·······1·11·11··11111··1··1·······11·11··1·11····1··1··11······1·11··11·····1·····1·····1·1111··111··11···1··1······111···11····1111·11111··111···1··1 |
| out 71 (117) | 1··1·1··11·····1···1·······1···1····11···1·1·11·11··1·1··11···1·11··11··1·····1·111·1111··1··1·11·1·1··1··1··111·1·11·····1111····1·111······1·····1·1·1·····111····1··1·····1····1····11···1··1··11··1··1··1····1··1·11·11··1·1·1···1··111·1·1·11····1···111···1·1··1··1····1·1·11·1····1111·1···1··111········1····· |
| check 72 (110) | 1··1·11···1····1····11·1···1···1···11111···1·1·1···1······1···1······11·1·····1·····1·11··1······11·1···11·11··1·1·····11·1··1··11·1··1··11·1··11111·1·1··1··1··1···1···111··1····1···11111····1··1··1·····1··········11·······111···1······1···11····1······1··1·1···11··11···1·1···11··1··1·1·11·1···1····11·1·11·11 |
| check 73 (112) | 1···1··1··1·11·1·1··11·····1·11·11·1·11·11·1···111···11·········1··1·1··1···1··11···1·1·111····11·1·····1·1·1····1·1······11··1···11·1·11·1····1···1··1·····1···111·1·1·11···1··11·11·1·11·11··1·····11··1·····1·1·······1·1···1·1·1··1·1···1···1·1··11····11···1·····1·1··1·····11······11··1····11··1·11···1···1···· |
| check 74 (120) | 1·1····1111··1·111·11·····11····1··1·111··111·11···11····11····1·1·111··1·1·1····1···11···1·11····11···1···1·1···1·11····11········11····1·1·1·11·111·······1·111·1·11111···11·····1··1·111···11·1·1·1·····11·······1·1·1·11·1·1·111·····1····1·1·····1··11·····11···1····1··1···11·1···11·········1·1······1·1·111··1 |
| check 75 (152) | ··1111··1··1·····11111111·11111·1···11·1······11·1111·1·11·1··11····11··111···11···1·1···11····1·111··11···111·····11·111·111···11·111·11111··1·1·111·1·1··11·····111·1·11111·1·111··1·······1·11···111·····11··1····1··111·1·····111·1·11······11·1·1·1··1·11·1·11·····1······11111·111···11·1111111·11111···1·1····· |
| check 76 (160) | 111··1····11·111··11·11··11··1··11·1·1·11·1·1··1·111111111··1·····11····1·1····11·11·1···11··1·1··1···11··1··1·1·11111·1···1·1··111··11111··11·1111111···1·1·1·11···11·111·111·1··11·111111··111···1···1···1··1111····11·1·11·1·1··11······11···1·1·11··1····1·111·1·11···1·111·11111··1·111111··1··1··1·11···11··111· |
| check 77 (136) | ··11·····1·1·11··11··11·1111·11··111··111·11·11·11··11··1·1··1····1·1··1···11·······111·111·11··11111·11··111·11·11·11·11···1··1··1··1··1··1··1··1······11··11·11·11········11111·1·111·1·1111111111111·1··1····1·1··1·1··1···1··1···11··11·11··11················1·11·1··1·1········1·1··1···1··1···1····1··1···1···1 |
| check 78 (158) | ··111···1111·1···11·11·111··111·1····111·11····111············1···1·1··1·····111·1·11·111··1·11···111111·11··1·1111·1·1·1··11··1·11·11··1·1····1··1·11·111···1····1·11··11·1······11··11··1·1··111···1·11····1111··11111111··1·111··1····1···11·1111111·1·1111··11··11·1111111·11···11·1··1111···1111····1·11·1··1111· |
| check 79 (152) | ··11·1··1·11····1····11111·1··1···1·1··111·1·1111····1·111·······1···111··1·1·1·11·11111·1·1·111·11··1··1···11···1·111111·11··1··11·1··111···11·1···11·1··1111·1·····1·11··1·1···1·1111·11111··1····1··111·····1·111·11···11111··111·1·1··1··1··11···1·1·1··1···1··1·1·1111·11···1·1···1·11··1·11··11·1·11··1··1·1·111 |
| check 80 (152) | ···11···1·1···11·11·1·1·111····1·1····1···11·1·111·1·1·····11111··1·11·11·1···1·1·1···1···1···1··11··1·111·1·11·1·1·1111··1111··1·111·1·1·11·111··1··11·······1·1111·1·1·1111·····1·1····11111··11·11··11··1···1·········1111·1·1·1··1··1·1····1·11111·111111···1··1·111··1···111111··11·1111···1·11·1··1·111··1··111· |
| check 81 (150) | 1···11·1111··1·····1·1·1····1·1·1·11·1··11·11···11·1111··11····1····11··1·1········1111111111··1··111·1·11·1111·1·1·111·1·······1··1·111·1·····111·1··11····11111·1····1·11·11111·1·11·1·11··11·1·1111·11··11··1·1··1·1·1····1·1·11········11·1·111··11·11·1··11···111··11··1·111111·1·1······1·1··1··111···1····11·1· |
| check 82 (144) | 1··11···111·····1··11··1···1··1·1··1·11···1·111···111·111··111111·1···111······111·1··11·1·1·1···11··1····1·11·1···11··11···1·111··1·1·111···11···11·11·······111····1·11·1··1···1·1··1·11····1··111······1··1111·11111···111111······1·11·1····11···1··1·1··1··1··1····1··1·1·1··1·111·111·1·11·11·11·1··11·111·1111· |
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 n310Noisy T states per run.
outputs k72
distance d3Exact, proved and witnessed here.
error coefficient A_{3}2,254Faults 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 N83
checks r11
V_{\mathrm{ex}}72T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3289Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3289Overhead 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 width72Rank of the output rows modulo the check rows.
Output gate
72 T0 CS0 CCZon 72 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}
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 (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 75 single-wire gates and 703 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{Z} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{Z} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23 and 754 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 778 correction gates
\mathrm{Z} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{Z} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{Z} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{Z} on output 26, \mathrm{Z} on output 27, \mathrm{Z} on output 28, \mathrm{S} on output 29, \mathrm{Z} on output 30, \mathrm{Z} on output 31, \mathrm{S} on output 32, \mathrm{Z} on output 33, \mathrm{S} on output 34, \mathrm{Z} on output 35, \mathrm{Z} on output 36, \mathrm{S} on output 37, \mathrm{S} on output 38, \mathrm{S} on output 39, \mathrm{Z} on output 40, \mathrm{S} on output 41, \mathrm{Z} on output 42, \mathrm{Z} on output 43, \mathrm{S} on output 44, \mathrm{Z} on output 45, \mathrm{Z} on output 46, \mathrm{S} on output 47, \mathrm{S} on output 48, \mathrm{Z} on output 49, \mathrm{S} on output 50, \mathrm{Z} on output 51, \mathrm{Z} on output 52, \mathrm{S} on output 53, \mathrm{S} on output 54, \mathrm{S} on output 55, \mathrm{S} on output 56, \mathrm{Z} on output 57, \mathrm{Z} on output 58, \mathrm{Z} on output 59, \mathrm{Z} on output 60, \mathrm{S} on output 61, \mathrm{Z} on output 62, \mathrm{Z} on output 63, \mathrm{Z} on output 64, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{Z} on output 69, \mathrm{S} on output 70, \mathrm{Z} on output 71, \mathrm{S} on check 72, \mathrm{S} on check 78, \mathrm{S} on check 81, \mathrm{CZ} on output 0, output 2, \mathrm{CZ} on output 0, output 5, \mathrm{CZ} on output 0, output 8, \mathrm{CZ} on output 0, output 13, \mathrm{CZ} on output 0, output 15, \mathrm{CZ} on output 0, output 18, \mathrm{CZ} on output 0, output 21, \mathrm{CZ} on output 0, output 22, \mathrm{CZ} on output 0, output 23, \mathrm{CZ} on output 0, output 26, \mathrm{CZ} on output 0, output 27, \mathrm{CZ} on output 0, output 28, \mathrm{CZ} on output 0, output 30, \mathrm{CZ} on output 0, output 31, \mathrm{CZ} on output 0, output 33, \mathrm{CZ} on output 0, output 35, \mathrm{CZ} on output 0, output 36, \mathrm{CZ} on output 0, output 40, \mathrm{CZ} on output 0, output 42, \mathrm{CZ} on output 0, output 43, \mathrm{CZ} on output 0, output 45, \mathrm{CZ} on output 0, output 46, \mathrm{CZ} on output 0, output 49, \mathrm{CZ} on output 0, output 51, \mathrm{CZ} on output 0, output 52, \mathrm{CZ} on output 0, output 57, \mathrm{CZ} on output 0, output 58, \mathrm{CZ} on output 0, output 59, \mathrm{CZ} on output 0, output 60, \mathrm{CZ} on output 0, output 62, \mathrm{CZ} on output 0, output 63, \mathrm{CZ} on output 0, output 64, \mathrm{CZ} on output 0, output 69, \mathrm{CZ} on output 0, output 71, \mathrm{CZ} on output 0, check 72, \mathrm{CZ} on output 0, check 78, \mathrm{CZ} on output 0, check 81, \mathrm{CZ} on output 2, output 5, \mathrm{CZ} on output 2, output 8, \mathrm{CZ} on output 2, output 13, \mathrm{CZ} on output 2, output 15, \mathrm{CZ} on output 2, output 18, \mathrm{CZ} on output 2, output 21, \mathrm{CZ} on output 2, output 22, \mathrm{CZ} on output 2, output 23, \mathrm{CZ} on output 2, output 26, \mathrm{CZ} on output 2, output 27, \mathrm{CZ} on output 2, output 28, \mathrm{CZ} on output 2, output 30, \mathrm{CZ} on output 2, output 31, \mathrm{CZ} on output 2, output 33, \mathrm{CZ} on output 2, output 35, \mathrm{CZ} on output 2, output 36, \mathrm{CZ} on output 2, output 40, \mathrm{CZ} on output 2, output 42, \mathrm{CZ} on output 2, output 43, \mathrm{CZ} on output 2, output 45, \mathrm{CZ} on output 2, output 46, \mathrm{CZ} on output 2, output 49, \mathrm{CZ} on output 2, output 51, \mathrm{CZ} on output 2, output 52, \mathrm{CZ} on output 2, output 57, \mathrm{CZ} on output 2, output 58, \mathrm{CZ} on output 2, output 59, \mathrm{CZ} on output 2, output 60, \mathrm{CZ} on output 2, output 62, \mathrm{CZ} on output 2, output 63, \mathrm{CZ} on output 2, output 64, \mathrm{CZ} on output 2, output 69, \mathrm{CZ} on output 2, output 71, \mathrm{CZ} on output 2, check 72, \mathrm{CZ} on output 2, check 78, \mathrm{CZ} on output 2, check 81, \mathrm{CZ} on output 5, output 8, \mathrm{CZ} on output 5, output 13, \mathrm{CZ} on output 5, output 15, \mathrm{CZ} on output 5, output 18, \mathrm{CZ} on output 5, output 21, \mathrm{CZ} on output 5, output 22, \mathrm{CZ} on output 5, output 23, \mathrm{CZ} on output 5, output 26, \mathrm{CZ} on output 5, output 27, \mathrm{CZ} on output 5, output 28, \mathrm{CZ} on output 5, output 30, \mathrm{CZ} on output 5, output 31, \mathrm{CZ} on output 5, output 33, \mathrm{CZ} on output 5, output 35, \mathrm{CZ} on output 5, output 36, \mathrm{CZ} on output 5, output 40, \mathrm{CZ} on output 5, output 42, \mathrm{CZ} on output 5, output 43, \mathrm{CZ} on output 5, output 45, \mathrm{CZ} on output 5, output 46, \mathrm{CZ} on output 5, output 49, \mathrm{CZ} on output 5, output 51, \mathrm{CZ} on output 5, output 52, \mathrm{CZ} on output 5, output 57, \mathrm{CZ} on output 5, output 58, \mathrm{CZ} on output 5, output 59, \mathrm{CZ} on output 5, output 60, \mathrm{CZ} on output 5, output 62, \mathrm{CZ} on output 5, output 63, \mathrm{CZ} on output 5, output 64, \mathrm{CZ} on output 5, output 69, \mathrm{CZ} on output 5, output 71, \mathrm{CZ} on output 5, check 72, \mathrm{CZ} on output 5, check 78, \mathrm{CZ} on output 5, check 81, \mathrm{CZ} on output 8, output 13, \mathrm{CZ} on output 8, output 15, \mathrm{CZ} on output 8, output 18, \mathrm{CZ} on output 8, output 21, \mathrm{CZ} on output 8, output 22, \mathrm{CZ} on output 8, output 23, \mathrm{CZ} on output 8, output 26, \mathrm{CZ} on output 8, output 27, \mathrm{CZ} on output 8, output 28, \mathrm{CZ} on output 8, output 30, \mathrm{CZ} on output 8, output 31, \mathrm{CZ} on output 8, output 33, \mathrm{CZ} on output 8, output 35, \mathrm{CZ} on output 8, output 36, \mathrm{CZ} on output 8, output 40, \mathrm{CZ} on output 8, output 42, \mathrm{CZ} on output 8, output 43, \mathrm{CZ} on output 8, output 45, \mathrm{CZ} on output 8, output 46, \mathrm{CZ} on output 8, output 49, \mathrm{CZ} on output 8, output 51, \mathrm{CZ} on output 8, output 52, \mathrm{CZ} on output 8, output 57, \mathrm{CZ} on output 8, output 58, \mathrm{CZ} on output 8, output 59, \mathrm{CZ} on output 8, output 60, \mathrm{CZ} on output 8, output 62, \mathrm{CZ} on output 8, output 63, \mathrm{CZ} on output 8, output 64, \mathrm{CZ} on output 8, output 69, \mathrm{CZ} on output 8, output 71, \mathrm{CZ} on output 8, check 72, \mathrm{CZ} on output 8, check 78, \mathrm{CZ} on output 8, check 81, \mathrm{CZ} on output 13, output 15, \mathrm{CZ} on output 13, output 18, \mathrm{CZ} on output 13, output 21, \mathrm{CZ} on output 13, output 22, \mathrm{CZ} on output 13, output 23, \mathrm{CZ} on output 13, output 26, \mathrm{CZ} on output 13, output 27, \mathrm{CZ} on output 13, output 28, \mathrm{CZ} on output 13, output 30, \mathrm{CZ} on output 13, output 31, \mathrm{CZ} on output 13, output 33, \mathrm{CZ} on output 13, output 35, \mathrm{CZ} on output 13, output 36, \mathrm{CZ} on output 13, output 40, \mathrm{CZ} on output 13, output 42, \mathrm{CZ} on output 13, output 43, \mathrm{CZ} on output 13, output 45, \mathrm{CZ} on output 13, output 46, \mathrm{CZ} on output 13, output 49, \mathrm{CZ} on output 13, output 51, \mathrm{CZ} on output 13, output 52, \mathrm{CZ} on output 13, output 57, \mathrm{CZ} on output 13, output 58, \mathrm{CZ} on output 13, output 59, \mathrm{CZ} on output 13, output 60, \mathrm{CZ} on output 13, output 62, \mathrm{CZ} on output 13, output 63, \mathrm{CZ} on output 13, output 64, \mathrm{CZ} on output 13, output 69, \mathrm{CZ} on output 13, output 71, \mathrm{CZ} on output 13, check 72, \mathrm{CZ} on output 13, check 78, \mathrm{CZ} on output 13, check 81, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 21, \mathrm{CZ} on output 15, output 22, \mathrm{CZ} on output 15, output 23, \mathrm{CZ} on output 15, output 26, \mathrm{CZ} on output 15, output 27, \mathrm{CZ} on output 15, output 28, \mathrm{CZ} on output 15, output 30, \mathrm{CZ} on output 15, output 31, \mathrm{CZ} on output 15, output 33, \mathrm{CZ} on output 15, output 35, \mathrm{CZ} on output 15, output 36, \mathrm{CZ} on output 15, output 40, \mathrm{CZ} on output 15, output 42, \mathrm{CZ} on output 15, output 43, \mathrm{CZ} on output 15, output 45, \mathrm{CZ} on output 15, output 46, \mathrm{CZ} on output 15, output 49, \mathrm{CZ} on output 15, output 51, \mathrm{CZ} on output 15, output 52, \mathrm{CZ} on output 15, output 57, \mathrm{CZ} on output 15, output 58, \mathrm{CZ} on output 15, output 59, \mathrm{CZ} on output 15, output 60, \mathrm{CZ} on output 15, output 62, \mathrm{CZ} on output 15, output 63, \mathrm{CZ} on output 15, output 64, \mathrm{CZ} on output 15, output 69, \mathrm{CZ} on output 15, output 71, \mathrm{CZ} on output 15, check 72, \mathrm{CZ} on output 15, check 78, \mathrm{CZ} on output 15, check 81, \mathrm{CZ} on output 18, output 21, \mathrm{CZ} on output 18, output 22, \mathrm{CZ} on output 18, output 23, \mathrm{CZ} on output 18, output 26, \mathrm{CZ} on output 18, output 27, \mathrm{CZ} on output 18, output 28, \mathrm{CZ} on output 18, output 30, \mathrm{CZ} on output 18, output 31, \mathrm{CZ} on output 18, output 33, \mathrm{CZ} on output 18, output 35, \mathrm{CZ} on output 18, output 36, \mathrm{CZ} on output 18, output 40, \mathrm{CZ} on output 18, output 42, \mathrm{CZ} on output 18, output 43, \mathrm{CZ} on output 18, output 45, \mathrm{CZ} on output 18, output 46, \mathrm{CZ} on output 18, output 49, \mathrm{CZ} on output 18, output 51, \mathrm{CZ} on output 18, output 52, \mathrm{CZ} on output 18, output 57, \mathrm{CZ} on output 18, output 58, \mathrm{CZ} on output 18, output 59, \mathrm{CZ} on output 18, output 60, \mathrm{CZ} on output 18, output 62, \mathrm{CZ} on output 18, output 63, \mathrm{CZ} on output 18, output 64, \mathrm{CZ} on output 18, output 69, \mathrm{CZ} on output 18, output 71, \mathrm{CZ} on output 18, check 72, \mathrm{CZ} on output 18, check 78, \mathrm{CZ} on output 18, check 81, \mathrm{CZ} on output 21, output 22, \mathrm{CZ} on output 21, output 23, \mathrm{CZ} on output 21, output 26, \mathrm{CZ} on output 21, output 27, \mathrm{CZ} on output 21, output 28, \mathrm{CZ} on output 21, output 30, \mathrm{CZ} on output 21, output 31, \mathrm{CZ} on output 21, output 33, \mathrm{CZ} on output 21, output 35, \mathrm{CZ} on output 21, output 36, \mathrm{CZ} on output 21, output 40, \mathrm{CZ} on output 21, output 42, \mathrm{CZ} on output 21, output 43, \mathrm{CZ} on output 21, output 45, \mathrm{CZ} on output 21, output 46, \mathrm{CZ} on output 21, output 49, \mathrm{CZ} on output 21, output 51, \mathrm{CZ} on output 21, output 52, \mathrm{CZ} on output 21, output 57, \mathrm{CZ} on output 21, output 58, \mathrm{CZ} on output 21, output 59, \mathrm{CZ} on output 21, output 60, \mathrm{CZ} on output 21, output 62, \mathrm{CZ} on output 21, output 63, \mathrm{CZ} on output 21, output 64, \mathrm{CZ} on output 21, output 69, \mathrm{CZ} on output 21, output 71, \mathrm{CZ} on output 21, check 72, \mathrm{CZ} on output 21, check 78, \mathrm{CZ} on output 21, check 81, \mathrm{CZ} on output 22, output 23, \mathrm{CZ} on output 22, output 26, \mathrm{CZ} on output 22, output 27, \mathrm{CZ} on output 22, output 28, \mathrm{CZ} on output 22, output 30, \mathrm{CZ} on output 22, output 31, \mathrm{CZ} on output 22, output 33, \mathrm{CZ} on output 22, output 35, \mathrm{CZ} on output 22, output 36, \mathrm{CZ} on output 22, output 40, \mathrm{CZ} on output 22, output 42, \mathrm{CZ} on output 22, output 43, \mathrm{CZ} on output 22, output 45, \mathrm{CZ} on output 22, output 46, \mathrm{CZ} on output 22, output 49, \mathrm{CZ} on output 22, output 51, \mathrm{CZ} on output 22, output 52, \mathrm{CZ} on output 22, output 57, \mathrm{CZ} on output 22, output 58, \mathrm{CZ} on output 22, output 59, \mathrm{CZ} on output 22, output 60, \mathrm{CZ} on output 22, output 62, \mathrm{CZ} on output 22, output 63, \mathrm{CZ} on output 22, output 64, \mathrm{CZ} on output 22, output 69, \mathrm{CZ} on output 22, output 71, \mathrm{CZ} on output 22, check 72, \mathrm{CZ} on output 22, check 78, \mathrm{CZ} on output 22, check 81, \mathrm{CZ} on output 23, output 26, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 28, \mathrm{CZ} on output 23, output 30, \mathrm{CZ} on output 23, output 31, \mathrm{CZ} on output 23, output 33, \mathrm{CZ} on output 23, output 35, \mathrm{CZ} on output 23, output 36, \mathrm{CZ} on output 23, output 40, \mathrm{CZ} on output 23, output 42, \mathrm{CZ} on output 23, output 43, \mathrm{CZ} on output 23, output 45, \mathrm{CZ} on output 23, output 46, \mathrm{CZ} on output 23, output 49, \mathrm{CZ} on output 23, output 51, \mathrm{CZ} on output 23, output 52, \mathrm{CZ} on output 23, output 57, \mathrm{CZ} on output 23, output 58, \mathrm{CZ} on output 23, output 59, \mathrm{CZ} on output 23, output 60, \mathrm{CZ} on output 23, output 62, \mathrm{CZ} on output 23, output 63, \mathrm{CZ} on output 23, output 64, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, output 71, \mathrm{CZ} on output 23, check 72, \mathrm{CZ} on output 23, check 78, \mathrm{CZ} on output 23, check 81, \mathrm{CZ} on output 26, output 27, \mathrm{CZ} on output 26, output 28, \mathrm{CZ} on output 26, output 30, \mathrm{CZ} on output 26, output 31, \mathrm{CZ} on output 26, output 33, \mathrm{CZ} on output 26, output 35, \mathrm{CZ} on output 26, output 36, \mathrm{CZ} on output 26, output 40, \mathrm{CZ} on output 26, output 42, \mathrm{CZ} on output 26, output 43, \mathrm{CZ} on output 26, output 45, \mathrm{CZ} on output 26, output 46, \mathrm{CZ} on output 26, output 49, \mathrm{CZ} on output 26, output 51, \mathrm{CZ} on output 26, output 52, \mathrm{CZ} on output 26, output 57, \mathrm{CZ} on output 26, output 58, \mathrm{CZ} on output 26, output 59, \mathrm{CZ} on output 26, output 60, \mathrm{CZ} on output 26, output 62, \mathrm{CZ} on output 26, output 63, \mathrm{CZ} on output 26, output 64, \mathrm{CZ} on output 26, output 69, \mathrm{CZ} on output 26, output 71, \mathrm{CZ} on output 26, check 72, \mathrm{CZ} on output 26, check 78, \mathrm{CZ} on output 26, check 81, \mathrm{CZ} on output 27, output 28, \mathrm{CZ} on output 27, output 30, \mathrm{CZ} on output 27, output 31, \mathrm{CZ} on output 27, output 33, \mathrm{CZ} on output 27, output 35, \mathrm{CZ} on output 27, output 36, \mathrm{CZ} on output 27, output 40, \mathrm{CZ} on output 27, output 42, \mathrm{CZ} on output 27, output 43, \mathrm{CZ} on output 27, output 45, \mathrm{CZ} on output 27, output 46, \mathrm{CZ} on output 27, output 49, \mathrm{CZ} on output 27, output 51, \mathrm{CZ} on output 27, output 52, \mathrm{CZ} on output 27, output 57, \mathrm{CZ} on output 27, output 58, \mathrm{CZ} on output 27, output 59, \mathrm{CZ} on output 27, output 60, \mathrm{CZ} on output 27, output 62, \mathrm{CZ} on output 27, output 63, \mathrm{CZ} on output 27, output 64, \mathrm{CZ} on output 27, output 69, \mathrm{CZ} on output 27, output 71, \mathrm{CZ} on output 27, check 72, \mathrm{CZ} on output 27, check 78, \mathrm{CZ} on output 27, check 81, \mathrm{CZ} on output 28, output 30, \mathrm{CZ} on output 28, output 31, \mathrm{CZ} on output 28, output 33, \mathrm{CZ} on output 28, output 35, \mathrm{CZ} on output 28, output 36, \mathrm{CZ} on output 28, output 40, \mathrm{CZ} on output 28, output 42, \mathrm{CZ} on output 28, output 43, \mathrm{CZ} on output 28, output 45, \mathrm{CZ} on output 28, output 46, \mathrm{CZ} on output 28, output 49, \mathrm{CZ} on output 28, output 51, \mathrm{CZ} on output 28, output 52, \mathrm{CZ} on output 28, output 57, \mathrm{CZ} on output 28, output 58, \mathrm{CZ} on output 28, output 59, \mathrm{CZ} on output 28, output 60, \mathrm{CZ} on output 28, output 62, \mathrm{CZ} on output 28, output 63, \mathrm{CZ} on output 28, output 64, \mathrm{CZ} on output 28, output 69, \mathrm{CZ} on output 28, output 71, \mathrm{CZ} on output 28, check 72, \mathrm{CZ} on output 28, check 78, \mathrm{CZ} on output 28, check 81, \mathrm{CZ} on output 30, output 31, \mathrm{CZ} on output 30, output 33, \mathrm{CZ} on output 30, output 35, \mathrm{CZ} on output 30, output 36, \mathrm{CZ} on output 30, output 40, \mathrm{CZ} on output 30, output 42, \mathrm{CZ} on output 30, output 43, \mathrm{CZ} on output 30, output 45, \mathrm{CZ} on output 30, output 46, \mathrm{CZ} on output 30, output 49, \mathrm{CZ} on output 30, output 51, \mathrm{CZ} on output 30, output 52, \mathrm{CZ} on output 30, output 57, \mathrm{CZ} on output 30, output 58, \mathrm{CZ} on output 30, output 59, \mathrm{CZ} on output 30, output 60, \mathrm{CZ} on output 30, output 62, \mathrm{CZ} on output 30, output 63, \mathrm{CZ} on output 30, output 64, \mathrm{CZ} on output 30, output 69, \mathrm{CZ} on output 30, output 71, \mathrm{CZ} on output 30, check 72, \mathrm{CZ} on output 30, check 78, \mathrm{CZ} on output 30, check 81, \mathrm{CZ} on output 31, output 33, \mathrm{CZ} on output 31, output 35, \mathrm{CZ} on output 31, output 36, \mathrm{CZ} on output 31, output 40, \mathrm{CZ} on output 31, output 42, \mathrm{CZ} on output 31, output 43, \mathrm{CZ} on output 31, output 45, \mathrm{CZ} on output 31, output 46, \mathrm{CZ} on output 31, output 49, \mathrm{CZ} on output 31, output 51, \mathrm{CZ} on output 31, output 52, \mathrm{CZ} on output 31, output 57, \mathrm{CZ} on output 31, output 58, \mathrm{CZ} on output 31, output 59, \mathrm{CZ} on output 31, output 60, \mathrm{CZ} on output 31, output 62, \mathrm{CZ} on output 31, output 63, \mathrm{CZ} on output 31, output 64, \mathrm{CZ} on output 31, output 69, \mathrm{CZ} on output 31, output 71, \mathrm{CZ} on output 31, check 72, \mathrm{CZ} on output 31, check 78, \mathrm{CZ} on output 31, check 81, \mathrm{CZ} on output 33, output 35, \mathrm{CZ} on output 33, output 36, \mathrm{CZ} on output 33, output 40, \mathrm{CZ} on output 33, output 42, \mathrm{CZ} on output 33, output 43, \mathrm{CZ} on output 33, output 45, \mathrm{CZ} on output 33, output 46, \mathrm{CZ} on output 33, output 49, \mathrm{CZ} on output 33, output 51, \mathrm{CZ} on output 33, output 52, \mathrm{CZ} on output 33, output 57, \mathrm{CZ} on output 33, output 58, \mathrm{CZ} on output 33, output 59, \mathrm{CZ} on output 33, output 60, \mathrm{CZ} on output 33, output 62, \mathrm{CZ} on output 33, output 63, \mathrm{CZ} on output 33, output 64, \mathrm{CZ} on output 33, output 69, \mathrm{CZ} on output 33, output 71, \mathrm{CZ} on output 33, check 72, \mathrm{CZ} on output 33, check 78, \mathrm{CZ} on output 33, check 81, \mathrm{CZ} on output 35, output 36, \mathrm{CZ} on output 35, output 40, \mathrm{CZ} on output 35, output 42, \mathrm{CZ} on output 35, output 43, \mathrm{CZ} on output 35, output 45, \mathrm{CZ} on output 35, output 46, \mathrm{CZ} on output 35, output 49, \mathrm{CZ} on output 35, output 51, \mathrm{CZ} on output 35, output 52, \mathrm{CZ} on output 35, output 57, \mathrm{CZ} on output 35, output 58, \mathrm{CZ} on output 35, output 59, \mathrm{CZ} on output 35, output 60, \mathrm{CZ} on output 35, output 62, \mathrm{CZ} on output 35, output 63, \mathrm{CZ} on output 35, output 64, \mathrm{CZ} on output 35, output 69, \mathrm{CZ} on output 35, output 71, \mathrm{CZ} on output 35, check 72, \mathrm{CZ} on output 35, check 78, \mathrm{CZ} on output 35, check 81, \mathrm{CZ} on output 36, output 40, \mathrm{CZ} on output 36, output 42, \mathrm{CZ} on output 36, output 43, \mathrm{CZ} on output 36, output 45, \mathrm{CZ} on output 36, output 46, \mathrm{CZ} on output 36, output 49, \mathrm{CZ} on output 36, output 51, \mathrm{CZ} on output 36, output 52, \mathrm{CZ} on output 36, output 57, \mathrm{CZ} on output 36, output 58, \mathrm{CZ} on output 36, output 59, \mathrm{CZ} on output 36, output 60, \mathrm{CZ} on output 36, output 62, \mathrm{CZ} on output 36, output 63, \mathrm{CZ} on output 36, output 64, \mathrm{CZ} on output 36, output 69, \mathrm{CZ} on output 36, output 71, \mathrm{CZ} on output 36, check 72, \mathrm{CZ} on output 36, check 78, \mathrm{CZ} on output 36, check 81, \mathrm{CZ} on output 40, output 42, \mathrm{CZ} on output 40, output 43, \mathrm{CZ} on output 40, output 45, \mathrm{CZ} on output 40, output 46, \mathrm{CZ} on output 40, output 49, \mathrm{CZ} on output 40, output 51, \mathrm{CZ} on output 40, output 52, \mathrm{CZ} on output 40, output 57, \mathrm{CZ} on output 40, output 58, \mathrm{CZ} on output 40, output 59, \mathrm{CZ} on output 40, output 60, \mathrm{CZ} on output 40, output 62, \mathrm{CZ} on output 40, output 63, \mathrm{CZ} on output 40, output 64, \mathrm{CZ} on output 40, output 69, \mathrm{CZ} on output 40, output 71, \mathrm{CZ} on output 40, check 72, \mathrm{CZ} on output 40, check 78, \mathrm{CZ} on output 40, check 81, \mathrm{CZ} on output 42, output 43, \mathrm{CZ} on output 42, output 45, \mathrm{CZ} on output 42, output 46, \mathrm{CZ} on output 42, output 49, \mathrm{CZ} on output 42, output 51, \mathrm{CZ} on output 42, output 52, \mathrm{CZ} on output 42, output 57, \mathrm{CZ} on output 42, output 58, \mathrm{CZ} on output 42, output 59, \mathrm{CZ} on output 42, output 60, \mathrm{CZ} on output 42, output 62, \mathrm{CZ} on output 42, output 63, \mathrm{CZ} on output 42, output 64, \mathrm{CZ} on output 42, output 69, \mathrm{CZ} on output 42, output 71, \mathrm{CZ} on output 42, check 72, \mathrm{CZ} on output 42, check 78, \mathrm{CZ} on output 42, check 81, \mathrm{CZ} on output 43, output 45, \mathrm{CZ} on output 43, output 46, \mathrm{CZ} on output 43, output 49, \mathrm{CZ} on output 43, output 51, \mathrm{CZ} on output 43, output 52, \mathrm{CZ} on output 43, output 57, \mathrm{CZ} on output 43, output 58, \mathrm{CZ} on output 43, output 59, \mathrm{CZ} on output 43, output 60, \mathrm{CZ} on output 43, output 62, \mathrm{CZ} on output 43, output 63, \mathrm{CZ} on output 43, output 64, \mathrm{CZ} on output 43, output 69, \mathrm{CZ} on output 43, output 71, \mathrm{CZ} on output 43, check 72, \mathrm{CZ} on output 43, check 78, \mathrm{CZ} on output 43, check 81, \mathrm{CZ} on output 45, output 46, \mathrm{CZ} on output 45, output 49, \mathrm{CZ} on output 45, output 51, \mathrm{CZ} on output 45, output 52, \mathrm{CZ} on output 45, output 57, \mathrm{CZ} on output 45, output 58, \mathrm{CZ} on output 45, output 59, \mathrm{CZ} on output 45, output 60, \mathrm{CZ} on output 45, output 62, \mathrm{CZ} on output 45, output 63, \mathrm{CZ} on output 45, output 64, \mathrm{CZ} on output 45, output 69, \mathrm{CZ} on output 45, output 71, \mathrm{CZ} on output 45, check 72, \mathrm{CZ} on output 45, check 78, \mathrm{CZ} on output 45, check 81, \mathrm{CZ} on output 46, output 49, \mathrm{CZ} on output 46, output 51, \mathrm{CZ} on output 46, output 52, \mathrm{CZ} on output 46, output 57, \mathrm{CZ} on output 46, output 58, \mathrm{CZ} on output 46, output 59, \mathrm{CZ} on output 46, output 60, \mathrm{CZ} on output 46, output 62, \mathrm{CZ} on output 46, output 63, \mathrm{CZ} on output 46, output 64, \mathrm{CZ} on output 46, output 69, \mathrm{CZ} on output 46, output 71, \mathrm{CZ} on output 46, check 72, \mathrm{CZ} on output 46, check 78, \mathrm{CZ} on output 46, check 81, \mathrm{CZ} on output 49, output 51, \mathrm{CZ} on output 49, output 52, \mathrm{CZ} on output 49, output 57, \mathrm{CZ} on output 49, output 58, \mathrm{CZ} on output 49, output 59, \mathrm{CZ} on output 49, output 60, \mathrm{CZ} on output 49, output 62, \mathrm{CZ} on output 49, output 63, \mathrm{CZ} on output 49, output 64, \mathrm{CZ} on output 49, output 69, \mathrm{CZ} on output 49, output 71, \mathrm{CZ} on output 49, check 72, \mathrm{CZ} on output 49, check 78, \mathrm{CZ} on output 49, check 81, \mathrm{CZ} on output 51, output 52, \mathrm{CZ} on output 51, output 57, \mathrm{CZ} on output 51, output 58, \mathrm{CZ} on output 51, output 59, \mathrm{CZ} on output 51, output 60, \mathrm{CZ} on output 51, output 62, \mathrm{CZ} on output 51, output 63, \mathrm{CZ} on output 51, output 64, \mathrm{CZ} on output 51, output 69, \mathrm{CZ} on output 51, output 71, \mathrm{CZ} on output 51, check 72, \mathrm{CZ} on output 51, check 78, \mathrm{CZ} on output 51, check 81, \mathrm{CZ} on output 52, output 57, \mathrm{CZ} on output 52, output 58, \mathrm{CZ} on output 52, output 59, \mathrm{CZ} on output 52, output 60, \mathrm{CZ} on output 52, output 62, \mathrm{CZ} on output 52, output 63, \mathrm{CZ} on output 52, output 64, \mathrm{CZ} on output 52, output 69, \mathrm{CZ} on output 52, output 71, \mathrm{CZ} on output 52, check 72, \mathrm{CZ} on output 52, check 78, \mathrm{CZ} on output 52, check 81, \mathrm{CZ} on output 57, output 58, \mathrm{CZ} on output 57, output 59, \mathrm{CZ} on output 57, output 60, \mathrm{CZ} on output 57, output 62, \mathrm{CZ} on output 57, output 63, \mathrm{CZ} on output 57, output 64, \mathrm{CZ} on output 57, output 69, \mathrm{CZ} on output 57, output 71, \mathrm{CZ} on output 57, check 72, \mathrm{CZ} on output 57, check 78, \mathrm{CZ} on output 57, check 81, \mathrm{CZ} on output 58, output 59, \mathrm{CZ} on output 58, output 60, \mathrm{CZ} on output 58, output 62, \mathrm{CZ} on output 58, output 63, \mathrm{CZ} on output 58, output 64, \mathrm{CZ} on output 58, output 69, \mathrm{CZ} on output 58, output 71, \mathrm{CZ} on output 58, check 72, \mathrm{CZ} on output 58, check 78, \mathrm{CZ} on output 58, check 81, \mathrm{CZ} on output 59, output 60, \mathrm{CZ} on output 59, output 62, \mathrm{CZ} on output 59, output 63, \mathrm{CZ} on output 59, output 64, \mathrm{CZ} on output 59, output 69, \mathrm{CZ} on output 59, output 71, \mathrm{CZ} on output 59, check 72, \mathrm{CZ} on output 59, check 78, \mathrm{CZ} on output 59, check 81, \mathrm{CZ} on output 60, output 62, \mathrm{CZ} on output 60, output 63, \mathrm{CZ} on output 60, output 64, \mathrm{CZ} on output 60, output 69, \mathrm{CZ} on output 60, output 71, \mathrm{CZ} on output 60, check 72, \mathrm{CZ} on output 60, check 78, \mathrm{CZ} on output 60, check 81, \mathrm{CZ} on output 62, output 63, \mathrm{CZ} on output 62, output 64, \mathrm{CZ} on output 62, output 69, \mathrm{CZ} on output 62, output 71, \mathrm{CZ} on output 62, check 72, \mathrm{CZ} on output 62, check 78, \mathrm{CZ} on output 62, check 81, \mathrm{CZ} on output 63, output 64, \mathrm{CZ} on output 63, output 69, \mathrm{CZ} on output 63, output 71, \mathrm{CZ} on output 63, check 72, \mathrm{CZ} on output 63, check 78, \mathrm{CZ} on output 63, check 81, \mathrm{CZ} on output 64, output 69, \mathrm{CZ} on output 64, output 71, \mathrm{CZ} on output 64, check 72, \mathrm{CZ} on output 64, check 78, \mathrm{CZ} on output 64, check 81, \mathrm{CZ} on output 69, output 71, \mathrm{CZ} on output 69, check 72, \mathrm{CZ} on output 69, check 78, \mathrm{CZ} on output 69, check 81, \mathrm{CZ} on output 71, check 72, \mathrm{CZ} on output 71, check 78, \mathrm{CZ} on output 71, check 81, \mathrm{CZ} on check 72, check 78, \mathrm{CZ} on check 72, check 81, \mathrm{CZ} on check 78, check 81
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 7, 11, 17, 24, 27, 29, 30, 32, 33, 34, 35, 43, 44, 46, 47, 52, 56, 58, 61, 64, 65, 71, 83, 88 and 105 more (listed below); \mathrm{T}^5 on rotations 5, 10, 14, 15, 16, 18, 21, 23, 25, 39, 41, 48, 54, 57, 62, 63, 66, 74, 161; \mathrm{T}^\dagger on rotations 0, 1, 2, 3, 4, 9, 13, 20, 26, 28, 37, 38, 40, 45, 49, 50, 51, 53, 55, 59, 67, 98, 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 129 rotations at T³
7, 11, 17, 24, 27, 29, 30, 32, 33, 34, 35, 43, 44, 46, 47, 52, 56, 58, 61, 64, 65, 71, 83, 88, 90, 92, 93, 94, 97, 99, 100, 101, 103, 104, 105, 106, 108, 111, 113, 114, 115, 116, 117, 119, 120, 135, 139, 142, 144, 146, 149, 153, 154, 155, 157, 158, 159, 160, 163, 165, 166, 172, 174, 177, 178, 179, 182, 183, 184, 186, 187, 188, 189, 190, 191, 193, 195, 197, 198, 199, 201, 204, 206, 208, 209, 214, 215, 218, 219, 224, 225, 228, 229, 233, 239, 240, 243, 247, 248, 249, 251, 254, 256, 258, 260, 261, 263, 265, 266, 267, 269, 270, 271, 272, 275, 277, 279, 280, 282, 284, 289, 291, 292, 293, 299, 300, 304, 305, 306
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/310.72.3.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-310.72.3.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 2,254 faults of weight 3 are undetectable and damaging, so A_{3}=2{,}254. 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 [0,10,94].
A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.
Original source
S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535
Provenance
built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows
Found by: AI search (gamma frontier): from Wills parent codes
Discovery: AI search
1 recorded source
[
{
"regime": "AI search (gamma frontier): from Wills parent codes",
"file": "gamma_frontier_release/protocols/paired_column_contraction_310_72_3_07b415183008.json",
"label": "paired_column_contraction_310_72_3_07b415183008",
"N": 83,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=96), with searched graph punctures; 1 paired-column contraction",
"provenance": "gamma frontier release record paired_column_contraction_310_72_3_07b415183008 (source catalogue id paired_column_contraction_310_72_3_07b415183008); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=96), with searched graph punctures; 1 paired-column contraction; matrix 07b415183008901e...; the release states d=3 (exact), gamma=1.328863870832027 (exact)",
"notes": "matrix gamma_frontier_release/matrices/07b415183008901e44bd99889451f2a1d11aa7325d3b8d2d0ae92924e0ea56a3.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/310.72.3.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[963].