The circuit
The 83\times312 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.
| wire | 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 |
|---|---|
| out 0 (133) | ·11··11·1·111···1·1··1··1·1·····11···1··1·····11····1··111·111·11···1········1···11··11·1··111·1····1··1··1·1111·1····1··11·1·1··1····11111·1···1··1···11··111··11·1·1·1·111···1·1·1··1··1·····11···1·1···11·1·1·11··111·1··1·······1······11··1111·111·1··1··1····1··11·1·1··1···1··11·11·1··11111·1··11··1··11·11··1·· |
| out 1 (125) | ·1·1·1111···1·1·1··1·1··1·1·1·1111·1··1···1··1·1·····1··11·111111·········1·1······1··1····1···1·····1·111····1··1···1·111·····1·1···1··11·111···1·1·1·1·1·1··1·1·11·111···11··1··11··1··1·11·1111···1··11·1··1··11··11111·······1·1·········1··1···1···1···1·111········1····1··1·111····11····11·11·11·1·11·1·11·····1 |
| out 2 (127) | ··11·11···1···1···111···1···1·111··1··1·1·1··1·······1··1··1·11·····1·····1·11··11···1··1···11····1·11···11·1111··1··1111·1···11··1···1···111···11···1··11··111··111·1···1··1····11···1····11·11·1···11·11····1··1···1·11···1····1·11·····11···1··1··11··1·11···1··1··11·1·1···1·1111·1··11·1·1···111···11··1··11·1··1·1 |
| out 3 (135) | 1111·11··1·11·1···11·1··1··1··11·1·11···1·1··1····1·11··1··11·1·····1······1·1··1·1··1··1·····11··1·11··1·11·111·1··1·111··1·····1·····11111·1····11·1·····1·1111111·1··1·111····111··1···1·1·1·11·1··1·11··111··1···11·1···1···1·1·1·····1·1··1··1····111·11··1···1·1·1·1·1··1·1·111··1···1···11111··1···111····1···1·1 |
| out 4 (47) | ·····1···1······1···················11····1··1···········1·1·······1········1···1····1·······1········1··········11·····1··1············1···1······1·········1·····1····1······1····1··············11···11········1··1·····1·······1······1····1······1······1················11····1··1········1···1······1·········1·· |
| out 5 (141) | 1··1····11·1··1·1··1·1··1·1···111··1·1··1·1··111··1·11·11·····111··1·······1····11·········1111···11·1·1··111····1··11·111111·1···1···1111·11···1·11·1·11··11·11··1····11·1·1··1··11··1··1··1·11·1··1·1·11111111·1·1····11·1······1·······11········1111·11·1·1····1·11·······1·11·1111111··1·1111·11··11·111·11·11····1 |
| out 6 (55) | ·····1··111·····1·······1···········11····1··1···········1···1·····1··········1·1···111······1··········1········11·····1··1············1····1·····1··········1····1···111·····1······1············11···11········1····1···1··············1···111·····1········1··············11····1··1········1·····1····1···········1 |
| out 7 (125) | ·11··11·111·1····11··1··1·1······1···········111····1··111·111·11···1········1···11···1·1··11·······1··1··1·11·1·11··11··1111·1··1····11111·1···1··1···11··111··11·1·1·111·1·····1·1··1··1······1········111·1·1·11··111·1··1·······1······11···1·1·11·····1··1····1··11···1··11·11··11111·1··11111·1··11··1··11·11··1·· |
| out 8 (47) | ······11················1···········11····1··1···········1·1·······1········1·····11·······1············1········11·····1··1············1···1······1·········1·······11······1········1············11···11········1··1·····1·······1········11······1··········1··············11····1··1········1···1······1·········1·· |
| out 9 (125) | ·1·1·11··11·1·1····1······111·1111·1·11·1······1····11·1···11·111··1······1·········11·····1·111···1·1·1·11···1··11····1·1·1···1·11····1·1·11····1···1·1·1·1·11·1·11·1··11·11···1·1······1111·1111··111····1·111·····11·11·1·····1············11····1·111·1·1·1·1··1·····1····11···1·1·1··111··1·1·11··1·1··1·1·11···1·1 |
| out 10 (127) | ··11·111··1··11···11········1·11···1·11·1·1··11·····11··1··1·11·····1·····1·11··11·1·1······11······11··111·11·1·····1111·1·1·11······1···111···11···1··11··111··111·11··1··1····11········11·1··1··111·111··11··1···1·11···1····1·11·····11·1·1·····11····11··11··1··11···1·····1111·1·111···1···111···11··1··11·1··1·1 |
| out 11 (133) | ·11···1··11·1·····1·····1·11····11·11···1·1···11·······111·111·11···1········1··111·1·1·1··11··1···11··1····1111··1···1·111·1·1··11···11111·1···1··1···11··111··11···1··11·1·····1····1··11····111·1··1·1·11···1·11··111·1··1·······1·····111·1·1·1·11··1·11··1·······11·1·11··1··1·111·11·11·11111·1··11··1··11·11··1·· |
| out 12 (117) | ·1·1··1·1···1·1····1·1····1·1··1·1·1··1·1·1··1111···11·1·1··1·111·········1·1···1·····1····1·1·1·····1·1·1··1····1·····111··1·11·11····111·1·····1·1·1·1·1·1··1·1·1··1·1···11·····11·····1·1··1·11···11·1111·111··1···1·11·······1·1······1·····1···1·1·1···1·1·1·····1·······1····111··11111··111·1···1·1·11·1·11·····1 |
| out 13 (109) | ·11··1··11··1·····1·····1·11··1······1·······111····1··11···11·11··11·······11···1······1··11··1···11··1·····1·1·1···11··1111·1··1····11·11·····1······11··11···11·1···11··1·····1····1··11·1·······1····111·1·1·1····11·1·11······11······1······1·11··1·11··1········1··11··1··11··11111·1··11·11····11·····11·11····· |
| out 14 (133) | ·11···1··11·1·····1·····1·1··1··11········1··1·1····1··111·111·11···1········1··111·1·1·1··11··1···11··1··111111·11··11·1111··1··1····11111·1···1··1···11··111··11···1··11·1·····1····1··1·····11·······11·1·1·1·11··111·1··1·······1·····111·1·1·1·11··1·11··1····1·111·1·1··11·11·1111·1·1··11111·1··11··1··11·11··1·· |
| out 15 (125) | 1·1···1··111······1·····1·111·········1···1····1··1·1··111·1·1·11··11·····1111··1···11··1··1·11···1·1··11111·111·1··1·1·11·1···1······1···1······111···1·1·1·1·1·1···1··111······1····1··111·········1··1··111·1111··1·1·1·11····1111·····1···11··1·1·11·1·1··111··1·1·1·1·1··1·1·1·11·1··1···1···1····1·111··1·11···1·· |
| out 16 (119) | 1111·1·····11·1·1·11·1·····1··1111·1·········1····1·111·1···1·1····11······1·1··1·······1····111··1·11····11·1·1····1111···1·····1··1··1111111····1··1·······1111111······111··1·111······1·1·1111·······1··111··1····1·1··11·····1·1·····1·······1···1111·11······1·1·1···1····1111···1···1·1·111111·1···1·1········1·1 |
| out 17 (47) | ·······1··1·············1··1········1········11··········1·1·······1········1······1··1················11·1······1·········11···········1···1······1·········1········1··1···········11···1········1·····11·······1··1·····1·······1·········1··1·············11···1··········1········11·······1···1······1·········1·· |
| out 18 (149) | 1··1·1111··1··1·1··1·1··1·11··111··111··1·1····1··1·11·11····1111··11······11····111·1·····1111···11·1·1···11·······11·1111···1···1···111··111··1·1111·11··11111··11·111··1·1··1··11··1··11·1·11·1·11·1·1··11111·1·····111·11·····11·······111·1····1111·11·1·1······11·········11·1111··1··1·111··11·111·111·11·11··1·1 |
| out 19 (125) | ·1·1···1··1·1·1·1··1·1··11111··1·1·1111·1······1····11·1···11·111··1······1·····1·111······1···1·····1·1111·1·····1····1·1·1···1·11····1·1·11····1···1·1·1·1·11·1·1···1··1·11··1··11··1·1111··1·11·1111····1·111·····11·11·1·····1········1·111·····1···1···1·1111·1··1········1···1·1·1··111··1·1·11··1·1··1·1·11···1·1 |
| out 20 (125) | ·1·1····11··1·1·1··1·1··1·1····1·1·1·11·1·1···11····11·1·1··1·111·········1·1···1·1··11····1···1·····1·111··1····11····111·11··1·11····111·1·····1·1·1·1·1·1··1·1·1····11··11··1··11··1··1····1·11··111·1·11·111··1···1·11·······1·1······1·1··11···1···1···1·111···1·1·······11···111·11·111··111·1···1·1·11·1·11·····1 |
| out 21 (117) | ·11···1·1·1·1·····1··11·1·1······1··11··1·1··1·1·······11···11·11··11·······11··111··11·1··11··1·······1··1·11·1······1·1111··1··11···11·11·····1······11··11···11···1·1·1·1·····1·1··1··1······1··11·1·11·1···1·1····11·1·11······11·····111··11·1·11··1·····1····1··11···1······1·1111·1·11·11·11····11·····11·11····· |
| out 22 (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 23 (95) | 11·········11···············1····1···11······1····1······1·11····1·1······111····11··11·····1111··11····11111·1·····11····1···11·1····11·1·······11·····11··1··11·········11···············1····1···11···1··1·····1··11····1·····111·······11··11····111111····11··1·11··1······11····1··111··11·1·······11····11·1····· |
| out 24 (31) | ········11·····11···················11····1··1······································11····1··1···················11·····1··1···········································11······1···················11···11····································11···1··1·······················11····1··1································ |
| out 25 (111) | 1·1··1·1··11······1·····1·1·1········11·······11··1·1··1·····1······1·····11·1····111···1··1·11···1·1··111·1·111·11·1·1··1·11··1·······11·1·1··1·11····1·1·1···1·1·1··1··11······1····1··1·1········11····1111·1·······1····1····11·1·······111···1·1·11·1·1··111····1·1·1·1··111·1··1·11·1····11·1·1····11···1·11······ |
| out 26 (63) | ·····111·1····················1···1·11··1·1··1······1····1·1·······1········1···1·11·1······················1··1·11··1··1··1······1·····1···1······1·········1·····1·11·1···················1······11·1·11···1····1··1·····1·······1······1·11·1······················1····1··11·1··1··1····1···1···1······1·········1·· |
| out 27 (141) | 1··1·1111··1··1·1··1·1··1·11··111··1····1····1·1··1·11·11··1·1·11··········11····111·1·····1111···11·1·1···11····11·11·1·111··1···1···111··1·11·1·1··1·11··11111··11·111··1·1··1··11··1··11·1·11·1····1··1·11111·1···1·1·1········11·······111·1····1111·11·1·1······11·······1111·1·111·1··1·111··1··111·1·1·11·11··1·1 |
| out 28 (31) | ·····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······························· |
| out 29 (117) | ·1·1·1·1·11·1·1····1···1··1·1·1111·1111········1·····1·1···11·111··1······1·······1111·····1·1·1···1···1·1····1···1··1·1·1·1···1·1·····1·1·11····1···1·1·1·1·11·1·11··1·11·11·····1······1·11·1111·111·····1··11·····11·11·1·····1··········1111····1·1·1·1···1·1········1·····1·1·1·1·1··11···1·1·11··1·1··1·1·11···1·1 |
| out 30 (117) | ·11··1··11··1·····1·····1·1······1···········111····1··1·1·111·11··11·······11···1······1··11··1···11··1··1·11·1·11··11··1111·1··1····1·111·1···11·····11··11···11·1···11··1·····1····1··1······1········111·1·1··1··111·1111······11······1······1·11··1·11··1····1··11···1··11·11··11111·1··1·111·1··111····11·11····· |
| out 31 (117) | ·1·1·11··11·1·1·1··1·1··1·1·1··1·1·1·1··1······1····11·1···11·111··1······1·········11·····1···1·····1·111··1····111···1·1·1···1·11····1·1·11····1···1·1·1·1·11·1·11·1··11·11··1··11··1··1·1··1·11··1·1····1·111·····11·11·1·····1············11····1···1···1·111·····1·······11···1·1·1··111··1·1·11··1·1··1·1·11···1·1 |
| out 32 (141) | 1··1·11··111··1·1··1·1··1·11··111··1····1····1·1··1·11·11···1·111··········11····11·1·1····1111···11·1·1···11····11·11·1·111··1···1···111··11···1·1··1·11··11111··11·1··111·1··1··11··1··11·1·11·1····1··1·11111·1····1·11········11·······11·1·1···1111·11·1·1······11·······1111·1·111·1··1·111··111·11·1·1·11·11··1·1 |
| out 33 (117) | ·1·1·1···11···1····1····1·111·11·1·1··1······1·1····11·1·1··1·111·········1·1·····1·11·1···1·1·1···1·1·1111······1···1·1·1·····1·11····111·1·····1·1·1·1·1·1··1·1·11····11··1·····1···1··1111·1·11···1···1·1·111··1···1·11·······1·1········1·11····1·1·1·1·1·111··1··········1··1·1·1····111··111·1···1·1·11·1·11·····1 |
| out 34 (117) | ·1·1·1111···1·1·1··1·1··1·1·1··1·1·11·1·1······1····11·1···11·111··1······1········1··1····1···1·····1·111··1···1······1·1·1···1·11····1·1·11····1···1·1·1·1·11·1·11·111···11··1··11··1··1·1··1·1111·11····1·111·····11·11·1·····1···········1··1···1···1···1·111·····1······1·····1·1·1··111··1·1·11··1·1··1·1·11···1·1 |
| out 35 (95) | 11·········11···············1···11····1·1·········1······1··1·············111····11··11·····1111··11····11111·····1·1·····11··11·1····11·1··1···1111····1···1··11·········11···············1···11····11·····1·····1···1·······1··111·······11··11····111111····11··1·11········11·····11·111··11·1··1···1111···1··1····· |
| out 36 (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 37 (109) | ·1·1·1····1·1·1····1·1····1·1··1·1·1··1·1···11·1····11·1·1··1·111·········1·1·····1·1······1·1·1·····1·1·1··1····1·····1·11····1·11····111·1·····1·1·1·1·1·1··1·1·11·····1·11·····11·····1·1··1·11···11··1·1·111··1···1·11·······1·1········1·1·····1·1·1···1·1·1·····1·······1····1·11···111··111·1···1·1·11·1·11·····1 |
| out 38 (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 39 (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 40 (117) | ·1·1·1·111··1·1····1·1····1·1··1·1·1··1·1·11···1····11·1·1··1·111·········1·1·····11·11····1·1·1·····1·1·1··1····1·····11··1···1·11····111·1·····1·1·1·1·1·1··1·1·11··111··11·····11·····1·1··1·11···11·1··1·111··1···1·11·······1·1········11·11···1·1·1···1·1·1·····1·······1····11··1··111··111·1···1·1·11·1·11·····1 |
| out 41 (127) | ··11·1·1··1···1···1·····1···1·111··1111······11·····11··11···11····11·····1··1··1111·1··1···11···1··11···11·1111·1····11··1·1·11······1·1·11····11·1·1··11··1·1··111··1··1··1····1····1····11·11·1·111···11··11··11····11··11····1··1·····1111·1··1··11····11···1··1··11·1·1··1···11··1·111···1·1·11····11·11··11·1····1 |
| out 42 (47) | 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········1··1·····1·······1·1·········1······1···1··············1·····1·1·····1········1···1······1·········1·· |
| out 43 (125) | ·11····111··1···1·1·······1···1·11········1··1·1·····1·11···11·11··11·······11··11·1····1··111·1···11··11·1··111·11··11·1111··1··111··11·11·····1······11··11···11····111··1···1·1·······1··1··11·······11·1··11·1····11·1·11······11·····11·1····1·111·1·11··11···1···1·1·1··11·11·1111·1·11·11·11····11·····11·11····· |
| out 44 (135) | ··11·1·1111···1·1·11·1······1·11···11·1·1·····1·····11·····1··1·····1·1···1··1··11111···1···1······111··111·11·1·11··111··111·11······11··1111··11···11·11··1·1··111··1111··1··1·111·······11·1··1·1·11···1··11······1··1···1····1··1·····11111···1··1····111··11··1··11···1··11·111··11111···11··111·1·11··11·11·1····1 |
| out 45 (125) | ·11···1··11·1·····1·····1·11·····1···1···1···111·······111·111·11···1········1··111·1·1·1··11··1···11··1····11·1·1···1···1111·1··11···11111·1···1··1···11··111··11···1··11·1·····1····1··11·····1···1····111···1·11··111·1··1·······1·····111·1·1·1·11··1·11··1·······11···1··1··1···11111·11·11111·1··11··1··11·11··1·· |
| out 46 (125) | ·111·111·11·1·1····1····1·1·1·11·1·1·11·1·1····1·····1·1···11·111··1······1········111·····1·1·1···1·1·111·······11····111·1···1·1·····1·1·11····1···1·1·1·1·11·1111·11·11·11·····1···1··1·11·1·11··111·1··1··11·····11·11·1·····1·····1·····111····1·1·1·1·1·111·············11···111·1··11···1·1·11··1·1··1·1·11···1·1 |
| out 47 (133) | 1··1··1·1··1··1····1·1····1···111··1·1··1·1··111··1·11·11··1··111···············111··1·····11·1···11·1·11·111····1··11·111111·1···1···111··1····1·1··1·11··11·11··1··1·1··1·1·····11·····1··1·11·1··1·1·11111111·1···1··11················111··1····11·1·11·1·11···1·11·······1·11·1111111··1·111··1···11·1·1·11·11·1··1 |
| out 48 (119) | ·111·1····1···1···11········1·11···1·11···1··········1··1··1·11·····1·····1·11··111··1··1···11······11··111·11·1······111·11··11··1···1···111···11···1··11··111·1111·····1··1····11········11·1··1··11··1·····1··1···1·11···1····1·11·1···111··1··1··11····11··11··1··11···1······111·11·11·1·1···111···11··1··11·1··1·1 |
| out 49 (47) | ·····1··11·················1·········1····1···1··········1·1·······1········1···11··11····················1·······1·····1···1···········1···1······1·········1·····11··11·················1·········1···1·1·······1··1·····1·······1······11··11···················1···········1····1···1·······1···1······1·········1·· |
| out 50 (109) | ·11···111···1·····1·····1·1···1··1··11··1······1·······11···11·11··11·······11··1111·1··1··11··1···11··1··1····1······1··11···1··11···11·11·····1······11··11···11···111···1·····1····1··1··11··1··11·1····1···1·1····11·1·11······11·····1111·1··1·11··1·11··1····1·······1······1··11··1·11·11·11····11·····11·11····· |
| out 51 (117) | ·11··11·1···1···1·1·······1·····11···1··1·····11····1··1···111·11··11········1···11··1··1··111·1···11··11·1·1111·1····1··11·1·1··1····1··11·1···1······1···111··11·1·1·1···1···1·1·······1·····11···1·1···11·1·1·····111·1·111······1······11··1··1·111·1·11··11···1··11·1·1··1···1··11·11·1··1··11·1··11·····1··11··1·· |
| out 52 (133) | ·11··11·1···1···1·1·······11··1·11···1·11····111····1··111·111·11···1········1···11··1··1··111·1···11··11····111·1··1·1··1111·1··1····11111·1···1··1···11··111··11·1·1·1···1···1·1·······11·1··11···1·1··111·1·1·11··111·1··1·······1······11··1··1·111·1·11··11·······1·1·1··1·1·1··11111·1··11111·1··11··1··11·11··1·· |
| out 53 (149) | 1··1·1111··1··1·1··1·1··1·1···111··1·1··1·1··111··1·11·11··1·1111··1·······1·····111·1·····1111···11·1·1··111····1··11·111111·1···1···111····1··1·11·1·11··11·11··11·111··1·1··1··11··1··1··1·11·1··1·1·11111111·1··11·111·1······1········111·1····1111·11·1·1····1·11·······1·11·1111111··1·111·····111·111·11·11····1 |
| out 54 (133) | ·111··1·111·1···1·1··1··1·1·····11···1·······1·1·······111·111·11···1········1··111···1·1··111·1····1··1··1·1111·1···11··111··1··11···11111·1···1··1···11··111··111··1·111·1···1·1·1··1··1·····11···1····1·1···1·11··111·1··1·······1···1·111···1·1·111·1··1··1····1··11·1·1··1··11··111·1·11·11111·1··11··1··11·11··1·· |
| out 55 (117) | ·1·1·1111···1·1·1··1·1··1·1·1·11·1·11·1·1····1·1·····1·11··111111·······1·1········1··1····1···1·····1·111·············1·1·····1·1·······1·111···1·1·1·1·111·11·1·11·111···11··1··11··1··1·11·1·11·1·11··1·1··11·1···11111·····1·1···········1··1···1···1···1·111··················1·1····11·····1·11·11·1·11·1·11···1·1 |
| out 56 (125) | 1··1·1····11··1····1·1····11··111··1····1····1·1··1·11·111····111·1········1·····1··111····11·1···11·1·11··11····11·11·1·111··1···1···11···11···1····1·11··11·11··11·····11·1·····11·····11·1·11·1····1··1·11111·11·····11········1········1··111···11·1·11·1·11·····11·······1111·1·111·1··1·11···11··11···1·11·11····1 |
| out 57 (47) | ······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··1·······1···1·····1················1··1······1········1·········1·····1·1·····1·······1····1······1······1····· |
| out 58 (125) | 1·1···1··111······1·····1·111···1····11·1·1··1·1··1·1··11··1·1·11··11······1·1··1···11··1··1·11···1·1··11111·1·1·11·111·11·····1········1·1······111···1·1·1···1·1···1··111······1····1··111···1····111·11·111·1·1···1·1·1·11·····1·1·····1···11··1·1·11·1·1··111··1·1·1···1··11111·11····1·····1·1····1·111··1·11·1···· |
| out 59 (125) | ·1·1··11·11·1·1····1·1····111··1·1·1·11·1·1·········11·1···11·111··1······1·····1··111·····1·1·1·····1·1·11·1····11····111·1·1·1·11····1·1·11····1···1·1·1·1·11·1·1··11·11·11·····11·····111··1·11··111·1····111·····11·11·1·····1········1··111····1·1·1···1·1·1··1··1·······11···111·1··111··1·1·11··1·1··1·1·11···1·1 |
| out 60 (117) | ·11···1··11·1·····1·····1·1······1······1·1··1·1···11··11···11·11··11·······11··111·1·1·1··11··1···11··1··1·11·1·11···1·1111··1·······11·11·····1······11··11···11···1··11·1·····1····1··1······1·····1·11·1·1·1·1····11·1·11······11·····111·1·1·1·11··1·11··1····1··11···1··11··1·1111·1····11·11····11·····11·11····· |
| out 61 (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 62 (125) | 1··1··1·1··1··1····1·1····1···11···111··1······1··1··1·1·1···1111··1···1···11···111··1·····11·1···11·1·11·111·1·····11·1·11···1·······1····111··1·11·1··1··11111··1··1·1··1·1·····11·····1··1·1··1·11·1····11·11··1····111·1······11······111··1····11·1·11·1·11···1·11··1······11·1·11··1····1····11·111·111··1·11··1·1 |
| out 63 (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 64 (47) | ····1·11··1················1·········1····1···1··········1·1·······1········1··1··11··1···················1·······1·····1···1···········1···1······1·········1·······11··1················1·········1···1·1·······1··1·····1·······1·····1··11··1··················1···········1····1···1·······1···1······1·········1·· |
| out 65 (31) | ·····11·1·1··············································111·1··················1·1·1·1·················································1·1·11·····················1·1·1·1········································1··1·1··················1·1·1·1···············································1·1·1·1················· |
| out 66 (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 67 (149) | 1··1·1111··1··1·1··1·1··1·1···111··11···1·····11··1·11·111·1·1111··1·······111···111·1·····1111···11·1·1··111·····1·11·1·11·1·1···1···11···1·1··1·11·1·11··11111··11·111··1·1··1··11··1··1··1·11·1·1··1···111111·11··1·111·1······111······111·1····1111·11·1·1····1·11········111·1·11·11··1·11···1··111·111·11·11··111 |
| out 68 (47) | ······1··1······1·······1···········11····1··1···········1···1·······1······1·····1··1·······1··········1········11·····1··1············1····1·······1·······1·······1··1······1······1············11···11········1····1···········1········1··1······1········1··············11····1··1········1·····1·····1········1·· |
| out 69 (47) | ·······························11···11··1·1··1······1····1·1·······1········1·································1··11··1··1··1······1·····1···1······1·········1································11···11·1·11···1····1··1·····1·······1····································11····11·1··1··1····1···1···1······1·········1·· |
| check 70 (134) | ······1·1·111·1·1·11·1·····1··111····11·1·1··11···1··1··11·1····1··········1·1·111··1·1·1····111···1··111111·11·11···1···11·1····11····1·1111···11····1111···11······1·1·1111··1·111······1·1·11····111·111·1·1··11··1············1·1····111··1·1·1···111·1··1111··1·1·1·1···11··1···11·1··11··1·1111··111···1111····1·1 |
| check 71 (128) | 1··1··1·····1······1····1·1····111··1·1·1·1············1···11··1···1····1·1··1··1111··1·1··11·1····11·1·1111··1111··11·1111·1··1·11···1·1··111···111·1·11····1·1··1··1·····1······1···1··1····111··1·11·1······1·····11··1·1···1·1··1·····1111··1·1·11·1··11·1·11··1·1···1·1·11·11·1111·1·111·1·1··11·1··1111·11·····1·· |
| check 72 (126) | ·11··11·111·1···1··1······1···1·11··11····1··11···1·11·11··11··11·······1·111····11···1·1·1···1···1··11··11··111····1··1·······1··1···11·11·11··1·1··11··1···11·11·1·1·111·1···1··1······1··1··11··11···111·1111·1···11··1·····1·111·······11···1·11···1·1··11··1··1···1·1·1····1··1······1·1·11·11·1·111·1·11··1····1·1 |
| check 73 (118) | ·11····111··1···1·1······1··1·11···1··1·1····1····1··1·11···11·11··11·······11··11·1····1··111·1···11··11··11·1·1···11·11···1··1······11·11·····1······11··11···11····111··1···1·1······1··11·1··1···11··1··1·11·1····11·1·11······11·····11·1····1·111·1·11··11·····11··1···1··11·11···1·1···11·11····11·····11·11····· |
| check 74 (110) | ·····1··111·····1·······1···········11··1·1···1·····1··1····1·1·1···1···1·1111··1···111······1··········1········11··1··1···1·····1·1·11111111··1111·11111·11·1····1···111·····1······1············11·1·1·1··1·1······1·1···1··1·1111·····1···111·····1········1··············11·1··1···1···111111111·1111111111111····1 |
| check 75 (128) | ······1·1·1···1····11··11··1·11·1···11·11·111··11·1·11·11··1··1·1111·1·1·1····1···1·1·1··1·······11··1··1·111·1··11·11··111··11·1·11·1·1····1·111·11·1·1····1·11··1111··111··11·1····1···1··1·1··1····111····1··111·1······1·1··1·1··1··1·111··111··11·1······1···1···1·1···1····1·11·······1·111··1·······1···1·1··1··· |
| check 76 (166) | ·11··1···11···1··111·1·11·11····11··1·1···11··1··1·1·1···1·11111····11·1····111··1··1·1111·11····1··11·1····1111··11·11·1·1·1111··11·11·111·1·111··1·1··1··11·1··11··1·11··1·1·1·1···111··111·11·1····111111···1·11111·1·1111·1·11··1·1·1·111·····1··11·1·11····1·1·1··111111·11··11111111·11·111·1111·111····111·11·1·· |
| check 77 (166) | 1·1···111111·11····1··111·1·1·1·1·1··1···11·1··1111··1·1··1···1111·1·1···111111·1··1·1···1·1·11·111··1·111·111···1111···1111··1···11···11···111·111111·1·1·11111··1·1·11··1···11·1·····1·11·1111·1···1·111·111·111··1··1·111111···11···11·1111··1·1·11·1·1·1··1····1111·1··11·1·1·1111····1···1·1·111··1··11··11·1·1·11· |
| check 78 (150) | ·1·11111··1··1··111··1····1·11·1·1·111··1·111··1··111··1·11·1111·1·1··11··1·1·11···11··111·1····11···1·1·1·11·····11···11·11···11·11···11111·1·111···11··1·1····1·1·1·1··1111··11·111111·1·111··111··11··1·1··11···11·111·11·11··11·1·····11111··1··1··11···11·1·······11····11····1·1····11···1······1·····1·11·1··1111 |
| check 79 (112) | ·····1··11··111·1···1·11···1······1·1·1···1···111111·1·····1··1·11······11··1·1·1···11·111···1····1·11····1····1·1·1····1···111111·1········1·111·········1·111····1··1··11····1···11111··1····1111·1···1····1········11·11·····111·1·····1··1··11····1···1··1111··1·····11·11·1····1·······1········111·1·······1·11·1· |
| check 80 (158) | 1·1··1·····1···1·1·11·11··111·1·1···1111·11111··11·1·1·1·····1·11·11·1111111111···1·1·1·1·11·11111···1·1·11111·1··1·····1·1··11·1111···11·1·1····1·1111··1111111·1·1······1··11111·11111·1111··1···11111··1111·1·······1·1··111·1···········1·1·1·1··1···111·1·1···1·111···1···11111·1·11·1····11·1·1··1·11···11···11·1· |
| check 81 (144) | ··11·11··1····1···11·1··1···11·1··111··11111111111111···1··1·11·····1·····1·11··11····1·1···11·····111···111·1···11111·111··11··11·1··1···111···11···1··11··111··111·1··1···1····111··1·111·11·11·1·11·1······1··1···1·11···1····1·11·····11····1·1··11···111···111·1·1·111111····1···11·11·1·1···111···11··1··11·1··1·1 |
| check 82 (152) | ··11····111···1···11·1··1···1·111··1··1·1·1··1·······1111111····1111·111111··11··11·1···1···11·····111···11·1111··1··1111·1···11··1·111·1··11111·1111·11111······11····111··1····111··1····11·11·1···11·11····1·1··11·11111·111·1·11·······11·1···1··11···111···1··1··11·1·1···1·1111·1··11·1··1·11··1·11···1····1111111 |
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 n312Noisy T states per run.
outputs k70
distance d3Exact, proved and witnessed here.
error coefficient A_{3}601Faults 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 r13
V_{\mathrm{ex}}70T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3604Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3604Overhead 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 width70Rank of the output rows modulo the check rows.
Output gate
70 T0 CS0 CCZon 70 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}
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 (output wires per term, separated by +)
This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.
Clifford correction
With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 78 single-wire gates and 1081 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{Z} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{S} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{Z} on output 13, \mathrm{Z} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23 and 1135 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 1159 correction gates
\mathrm{Z} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{Z} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{S} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{Z} on output 13, \mathrm{Z} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} 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{Z} on output 27, \mathrm{S} on output 28, \mathrm{Z} on output 29, \mathrm{Z} on output 30, \mathrm{Z} on output 31, \mathrm{Z} on output 32, \mathrm{Z} on output 33, \mathrm{Z} on output 34, \mathrm{S} on output 35, \mathrm{S} on output 36, \mathrm{Z} on output 37, \mathrm{S} on output 38, \mathrm{S} on output 39, \mathrm{Z} on output 40, \mathrm{S} on output 41, \mathrm{S} on output 42, \mathrm{Z} on output 43, \mathrm{S} on output 44, \mathrm{Z} on output 45, \mathrm{Z} on output 46, \mathrm{Z} on output 47, \mathrm{S} on output 48, \mathrm{S} on output 49, \mathrm{Z} on output 50, \mathrm{Z} on output 51, \mathrm{Z} on output 52, \mathrm{Z} on output 53, \mathrm{Z} on output 54, \mathrm{Z} on output 55, \mathrm{Z} on output 56, \mathrm{S} 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{S} on output 63, \mathrm{S} on output 64, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{Z} on output 67, \mathrm{S} on output 68, \mathrm{S} on output 69, \mathrm{S} on check 70, \mathrm{S} on check 72, \mathrm{S} on check 73, \mathrm{S} on check 74, \mathrm{S} on check 76, \mathrm{S} on check 77, \mathrm{S} on check 78, \mathrm{S} on check 80, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 5, \mathrm{CZ} on output 0, output 7, \mathrm{CZ} on output 0, output 9, \mathrm{CZ} on output 0, output 11, \mathrm{CZ} on output 0, output 12, \mathrm{CZ} on output 0, output 13, \mathrm{CZ} on output 0, output 14, \mathrm{CZ} on output 0, output 15, \mathrm{CZ} on output 0, output 18, \mathrm{CZ} on output 0, output 19, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 21, \mathrm{CZ} on output 0, output 27, \mathrm{CZ} on output 0, output 29, \mathrm{CZ} on output 0, output 30, \mathrm{CZ} on output 0, output 31, \mathrm{CZ} on output 0, output 32, \mathrm{CZ} on output 0, output 33, \mathrm{CZ} on output 0, output 34, \mathrm{CZ} on output 0, output 37, \mathrm{CZ} on output 0, output 40, \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 47, \mathrm{CZ} on output 0, output 50, \mathrm{CZ} on output 0, output 51, \mathrm{CZ} on output 0, output 52, \mathrm{CZ} on output 0, output 53, \mathrm{CZ} on output 0, output 54, \mathrm{CZ} on output 0, output 55, \mathrm{CZ} on output 0, output 56, \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 67, \mathrm{CZ} on output 0, check 70, \mathrm{CZ} on output 0, check 72, \mathrm{CZ} on output 0, check 73, \mathrm{CZ} on output 0, check 74, \mathrm{CZ} on output 0, check 76, \mathrm{CZ} on output 0, check 77, \mathrm{CZ} on output 0, check 78, \mathrm{CZ} on output 0, check 80, \mathrm{CZ} on output 1, output 5, \mathrm{CZ} on output 1, output 7, \mathrm{CZ} on output 1, output 9, \mathrm{CZ} on output 1, output 11, \mathrm{CZ} on output 1, output 12, \mathrm{CZ} on output 1, output 13, \mathrm{CZ} on output 1, output 14, \mathrm{CZ} on output 1, output 15, \mathrm{CZ} on output 1, output 18, \mathrm{CZ} on output 1, output 19, \mathrm{CZ} on output 1, output 20, \mathrm{CZ} on output 1, output 21, \mathrm{CZ} on output 1, output 27, \mathrm{CZ} on output 1, output 29, \mathrm{CZ} on output 1, output 30, \mathrm{CZ} on output 1, output 31, \mathrm{CZ} on output 1, output 32, \mathrm{CZ} on output 1, output 33, \mathrm{CZ} on output 1, output 34, \mathrm{CZ} on output 1, output 37, \mathrm{CZ} on output 1, output 40, \mathrm{CZ} on output 1, output 43, \mathrm{CZ} on output 1, output 45, \mathrm{CZ} on output 1, output 46, \mathrm{CZ} on output 1, output 47, \mathrm{CZ} on output 1, output 50, \mathrm{CZ} on output 1, output 51, \mathrm{CZ} on output 1, output 52, \mathrm{CZ} on output 1, output 53, \mathrm{CZ} on output 1, output 54, \mathrm{CZ} on output 1, output 55, \mathrm{CZ} on output 1, output 56, \mathrm{CZ} on output 1, output 58, \mathrm{CZ} on output 1, output 59, \mathrm{CZ} on output 1, output 60, \mathrm{CZ} on output 1, output 62, \mathrm{CZ} on output 1, output 67, \mathrm{CZ} on output 1, check 70, \mathrm{CZ} on output 1, check 72, \mathrm{CZ} on output 1, check 73, \mathrm{CZ} on output 1, check 74, \mathrm{CZ} on output 1, check 76, \mathrm{CZ} on output 1, check 77, \mathrm{CZ} on output 1, check 78, \mathrm{CZ} on output 1, check 80, \mathrm{CZ} on output 5, output 7, \mathrm{CZ} on output 5, output 9, \mathrm{CZ} on output 5, output 11, \mathrm{CZ} on output 5, output 12, \mathrm{CZ} on output 5, output 13, \mathrm{CZ} on output 5, output 14, \mathrm{CZ} on output 5, output 15, \mathrm{CZ} on output 5, output 18, \mathrm{CZ} on output 5, output 19, \mathrm{CZ} on output 5, output 20, \mathrm{CZ} on output 5, output 21, \mathrm{CZ} on output 5, output 27, \mathrm{CZ} on output 5, output 29, \mathrm{CZ} on output 5, output 30, \mathrm{CZ} on output 5, output 31, \mathrm{CZ} on output 5, output 32, \mathrm{CZ} on output 5, output 33, \mathrm{CZ} on output 5, output 34, \mathrm{CZ} on output 5, output 37, \mathrm{CZ} on output 5, output 40, \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 47, \mathrm{CZ} on output 5, output 50, \mathrm{CZ} on output 5, output 51, \mathrm{CZ} on output 5, output 52, \mathrm{CZ} on output 5, output 53, \mathrm{CZ} on output 5, output 54, \mathrm{CZ} on output 5, output 55, \mathrm{CZ} on output 5, output 56, \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 67, \mathrm{CZ} on output 5, check 70, \mathrm{CZ} on output 5, check 72, \mathrm{CZ} on output 5, check 73, \mathrm{CZ} on output 5, check 74, \mathrm{CZ} on output 5, check 76, \mathrm{CZ} on output 5, check 77, \mathrm{CZ} on output 5, check 78, \mathrm{CZ} on output 5, check 80, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, output 11, \mathrm{CZ} on output 7, output 12, \mathrm{CZ} on output 7, output 13, \mathrm{CZ} on output 7, output 14, \mathrm{CZ} on output 7, output 15, \mathrm{CZ} on output 7, output 18, \mathrm{CZ} on output 7, output 19, \mathrm{CZ} on output 7, output 20, \mathrm{CZ} on output 7, output 21, \mathrm{CZ} on output 7, output 27, \mathrm{CZ} on output 7, output 29, \mathrm{CZ} on output 7, output 30, \mathrm{CZ} on output 7, output 31, \mathrm{CZ} on output 7, output 32, \mathrm{CZ} on output 7, output 33, \mathrm{CZ} on output 7, output 34, \mathrm{CZ} on output 7, output 37, \mathrm{CZ} on output 7, output 40, \mathrm{CZ} on output 7, output 43, \mathrm{CZ} on output 7, output 45, \mathrm{CZ} on output 7, output 46, \mathrm{CZ} on output 7, output 47, \mathrm{CZ} on output 7, output 50, \mathrm{CZ} on output 7, output 51, \mathrm{CZ} on output 7, output 52, \mathrm{CZ} on output 7, output 53, \mathrm{CZ} on output 7, output 54, \mathrm{CZ} on output 7, output 55, \mathrm{CZ} on output 7, output 56, \mathrm{CZ} on output 7, output 58, \mathrm{CZ} on output 7, output 59, \mathrm{CZ} on output 7, output 60, \mathrm{CZ} on output 7, output 62, \mathrm{CZ} on output 7, output 67, \mathrm{CZ} on output 7, check 70, \mathrm{CZ} on output 7, check 72, \mathrm{CZ} on output 7, check 73, \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 7, check 78, \mathrm{CZ} on output 7, check 80, \mathrm{CZ} on output 9, output 11, \mathrm{CZ} on output 9, output 12, \mathrm{CZ} on output 9, output 13, \mathrm{CZ} on output 9, output 14, \mathrm{CZ} on output 9, output 15, \mathrm{CZ} on output 9, output 18, \mathrm{CZ} on output 9, output 19, \mathrm{CZ} on output 9, output 20, \mathrm{CZ} on output 9, output 21, \mathrm{CZ} on output 9, output 27, \mathrm{CZ} on output 9, output 29, \mathrm{CZ} on output 9, output 30, \mathrm{CZ} on output 9, output 31, \mathrm{CZ} on output 9, output 32, \mathrm{CZ} on output 9, output 33, \mathrm{CZ} on output 9, output 34, \mathrm{CZ} on output 9, output 37, \mathrm{CZ} on output 9, output 40, \mathrm{CZ} on output 9, output 43, \mathrm{CZ} on output 9, output 45, \mathrm{CZ} on output 9, output 46, \mathrm{CZ} on output 9, output 47, \mathrm{CZ} on output 9, output 50, \mathrm{CZ} on output 9, output 51, \mathrm{CZ} on output 9, output 52, \mathrm{CZ} on output 9, output 53, \mathrm{CZ} on output 9, output 54, \mathrm{CZ} on output 9, output 55, \mathrm{CZ} on output 9, output 56, \mathrm{CZ} on output 9, output 58, \mathrm{CZ} on output 9, output 59, \mathrm{CZ} on output 9, output 60, \mathrm{CZ} on output 9, output 62, \mathrm{CZ} on output 9, output 67, \mathrm{CZ} on output 9, check 70, \mathrm{CZ} on output 9, check 72, \mathrm{CZ} on output 9, check 73, \mathrm{CZ} on output 9, check 74, \mathrm{CZ} on output 9, check 76, \mathrm{CZ} on output 9, check 77, \mathrm{CZ} on output 9, check 78, \mathrm{CZ} on output 9, check 80, \mathrm{CZ} on output 11, output 12, \mathrm{CZ} on output 11, output 13, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 15, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 19, \mathrm{CZ} on output 11, output 20, \mathrm{CZ} on output 11, output 21, \mathrm{CZ} on output 11, output 27, \mathrm{CZ} on output 11, output 29, \mathrm{CZ} on output 11, output 30, \mathrm{CZ} on output 11, output 31, \mathrm{CZ} on output 11, output 32, \mathrm{CZ} on output 11, output 33, \mathrm{CZ} on output 11, output 34, \mathrm{CZ} on output 11, output 37, \mathrm{CZ} on output 11, output 40, \mathrm{CZ} on output 11, output 43, \mathrm{CZ} on output 11, output 45, \mathrm{CZ} on output 11, output 46, \mathrm{CZ} on output 11, output 47, \mathrm{CZ} on output 11, output 50, \mathrm{CZ} on output 11, output 51, \mathrm{CZ} on output 11, output 52, \mathrm{CZ} on output 11, output 53, \mathrm{CZ} on output 11, output 54, \mathrm{CZ} on output 11, output 55, \mathrm{CZ} on output 11, output 56, \mathrm{CZ} on output 11, output 58, \mathrm{CZ} on output 11, output 59, \mathrm{CZ} on output 11, output 60, \mathrm{CZ} on output 11, output 62, \mathrm{CZ} on output 11, output 67, \mathrm{CZ} on output 11, check 70, \mathrm{CZ} on output 11, check 72, \mathrm{CZ} on output 11, check 73, \mathrm{CZ} on output 11, check 74, \mathrm{CZ} on output 11, check 76, \mathrm{CZ} on output 11, check 77, \mathrm{CZ} on output 11, check 78, \mathrm{CZ} on output 11, check 80, \mathrm{CZ} on output 12, output 13, \mathrm{CZ} on output 12, output 14, \mathrm{CZ} on output 12, output 15, \mathrm{CZ} on output 12, output 18, \mathrm{CZ} on output 12, output 19, \mathrm{CZ} on output 12, output 20, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, output 27, \mathrm{CZ} on output 12, output 29, \mathrm{CZ} on output 12, output 30, \mathrm{CZ} on output 12, output 31, \mathrm{CZ} on output 12, output 32, \mathrm{CZ} on output 12, output 33, \mathrm{CZ} on output 12, output 34, \mathrm{CZ} on output 12, output 37, \mathrm{CZ} on output 12, output 40, \mathrm{CZ} on output 12, output 43, \mathrm{CZ} on output 12, output 45, \mathrm{CZ} on output 12, output 46, \mathrm{CZ} on output 12, output 47, \mathrm{CZ} on output 12, output 50, \mathrm{CZ} on output 12, output 51, \mathrm{CZ} on output 12, output 52, \mathrm{CZ} on output 12, output 53, \mathrm{CZ} on output 12, output 54, \mathrm{CZ} on output 12, output 55, \mathrm{CZ} on output 12, output 56, \mathrm{CZ} on output 12, output 58, \mathrm{CZ} on output 12, output 59, \mathrm{CZ} on output 12, output 60, \mathrm{CZ} on output 12, output 62, \mathrm{CZ} on output 12, output 67, \mathrm{CZ} on output 12, check 70, \mathrm{CZ} on output 12, check 72, \mathrm{CZ} on output 12, check 73, \mathrm{CZ} on output 12, check 74, \mathrm{CZ} on output 12, check 76, \mathrm{CZ} on output 12, check 77, \mathrm{CZ} on output 12, check 78, \mathrm{CZ} on output 12, check 80, \mathrm{CZ} on output 13, output 14, \mathrm{CZ} on output 13, output 15, \mathrm{CZ} on output 13, output 18, \mathrm{CZ} on output 13, output 19, \mathrm{CZ} on output 13, output 20, \mathrm{CZ} on output 13, output 21, \mathrm{CZ} on output 13, output 27, \mathrm{CZ} on output 13, output 29, \mathrm{CZ} on output 13, output 30, \mathrm{CZ} on output 13, output 31, \mathrm{CZ} on output 13, output 32, \mathrm{CZ} on output 13, output 33, \mathrm{CZ} on output 13, output 34, \mathrm{CZ} on output 13, output 37, \mathrm{CZ} on output 13, output 40, \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 47, \mathrm{CZ} on output 13, output 50, \mathrm{CZ} on output 13, output 51, \mathrm{CZ} on output 13, output 52, \mathrm{CZ} on output 13, output 53, \mathrm{CZ} on output 13, output 54, \mathrm{CZ} on output 13, output 55, \mathrm{CZ} on output 13, output 56, \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 67, \mathrm{CZ} on output 13, check 70, \mathrm{CZ} on output 13, check 72, \mathrm{CZ} on output 13, check 73, \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 13, check 78, \mathrm{CZ} on output 13, check 80, \mathrm{CZ} on output 14, output 15, \mathrm{CZ} on output 14, output 18, \mathrm{CZ} on output 14, output 19, \mathrm{CZ} on output 14, output 20, \mathrm{CZ} on output 14, output 21, \mathrm{CZ} on output 14, output 27, \mathrm{CZ} on output 14, output 29, \mathrm{CZ} on output 14, output 30, \mathrm{CZ} on output 14, output 31, \mathrm{CZ} on output 14, output 32, \mathrm{CZ} on output 14, output 33, \mathrm{CZ} on output 14, output 34, \mathrm{CZ} on output 14, output 37, \mathrm{CZ} on output 14, output 40, \mathrm{CZ} on output 14, output 43, \mathrm{CZ} on output 14, output 45, \mathrm{CZ} on output 14, output 46, \mathrm{CZ} on output 14, output 47, \mathrm{CZ} on output 14, output 50, \mathrm{CZ} on output 14, output 51, \mathrm{CZ} on output 14, output 52, \mathrm{CZ} on output 14, output 53, \mathrm{CZ} on output 14, output 54, \mathrm{CZ} on output 14, output 55, \mathrm{CZ} on output 14, output 56, \mathrm{CZ} on output 14, output 58, \mathrm{CZ} on output 14, output 59, \mathrm{CZ} on output 14, output 60, \mathrm{CZ} on output 14, output 62, \mathrm{CZ} on output 14, output 67, \mathrm{CZ} on output 14, check 70, \mathrm{CZ} on output 14, check 72, \mathrm{CZ} on output 14, check 73, \mathrm{CZ} on output 14, check 74, \mathrm{CZ} on output 14, check 76, \mathrm{CZ} on output 14, check 77, \mathrm{CZ} on output 14, check 78, \mathrm{CZ} on output 14, check 80, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 19, \mathrm{CZ} on output 15, output 20, \mathrm{CZ} on output 15, output 21, \mathrm{CZ} on output 15, output 27, \mathrm{CZ} on output 15, output 29, \mathrm{CZ} on output 15, output 30, \mathrm{CZ} on output 15, output 31, \mathrm{CZ} on output 15, output 32, \mathrm{CZ} on output 15, output 33, \mathrm{CZ} on output 15, output 34, \mathrm{CZ} on output 15, output 37, \mathrm{CZ} on output 15, output 40, \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 47, \mathrm{CZ} on output 15, output 50, \mathrm{CZ} on output 15, output 51, \mathrm{CZ} on output 15, output 52, \mathrm{CZ} on output 15, output 53, \mathrm{CZ} on output 15, output 54, \mathrm{CZ} on output 15, output 55, \mathrm{CZ} on output 15, output 56, \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 67, \mathrm{CZ} on output 15, check 70, \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 76, \mathrm{CZ} on output 15, check 77, \mathrm{CZ} on output 15, check 78, \mathrm{CZ} on output 15, check 80, \mathrm{CZ} on output 18, output 19, \mathrm{CZ} on output 18, output 20, \mathrm{CZ} on output 18, output 21, \mathrm{CZ} on output 18, output 27, \mathrm{CZ} on output 18, output 29, \mathrm{CZ} on output 18, output 30, \mathrm{CZ} on output 18, output 31, \mathrm{CZ} on output 18, output 32, \mathrm{CZ} on output 18, output 33, \mathrm{CZ} on output 18, output 34, \mathrm{CZ} on output 18, output 37, \mathrm{CZ} on output 18, output 40, \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 47, \mathrm{CZ} on output 18, output 50, \mathrm{CZ} on output 18, output 51, \mathrm{CZ} on output 18, output 52, \mathrm{CZ} on output 18, output 53, \mathrm{CZ} on output 18, output 54, \mathrm{CZ} on output 18, output 55, \mathrm{CZ} on output 18, output 56, \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 67, \mathrm{CZ} on output 18, check 70, \mathrm{CZ} on output 18, check 72, \mathrm{CZ} on output 18, check 73, \mathrm{CZ} on output 18, check 74, \mathrm{CZ} on output 18, check 76, \mathrm{CZ} on output 18, check 77, \mathrm{CZ} on output 18, check 78, \mathrm{CZ} on output 18, check 80, \mathrm{CZ} on output 19, output 20, \mathrm{CZ} on output 19, output 21, \mathrm{CZ} on output 19, output 27, \mathrm{CZ} on output 19, output 29, \mathrm{CZ} on output 19, output 30, \mathrm{CZ} on output 19, output 31, \mathrm{CZ} on output 19, output 32, \mathrm{CZ} on output 19, output 33, \mathrm{CZ} on output 19, output 34, \mathrm{CZ} on output 19, output 37, \mathrm{CZ} on output 19, output 40, \mathrm{CZ} on output 19, output 43, \mathrm{CZ} on output 19, output 45, \mathrm{CZ} on output 19, output 46, \mathrm{CZ} on output 19, output 47, \mathrm{CZ} on output 19, output 50, \mathrm{CZ} on output 19, output 51, \mathrm{CZ} on output 19, output 52, \mathrm{CZ} on output 19, output 53, \mathrm{CZ} on output 19, output 54, \mathrm{CZ} on output 19, output 55, \mathrm{CZ} on output 19, output 56, \mathrm{CZ} on output 19, output 58, \mathrm{CZ} on output 19, output 59, \mathrm{CZ} on output 19, output 60, \mathrm{CZ} on output 19, output 62, \mathrm{CZ} on output 19, output 67, \mathrm{CZ} on output 19, check 70, \mathrm{CZ} on output 19, check 72, \mathrm{CZ} on output 19, check 73, \mathrm{CZ} on output 19, check 74, \mathrm{CZ} on output 19, check 76, \mathrm{CZ} on output 19, check 77, \mathrm{CZ} on output 19, check 78, \mathrm{CZ} on output 19, check 80, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 27, \mathrm{CZ} on output 20, output 29, \mathrm{CZ} on output 20, output 30, \mathrm{CZ} on output 20, output 31, \mathrm{CZ} on output 20, output 32, \mathrm{CZ} on output 20, output 33, \mathrm{CZ} on output 20, output 34, \mathrm{CZ} on output 20, output 37, \mathrm{CZ} on output 20, output 40, \mathrm{CZ} on output 20, output 43, \mathrm{CZ} on output 20, output 45, \mathrm{CZ} on output 20, output 46, \mathrm{CZ} on output 20, output 47, \mathrm{CZ} on output 20, output 50, \mathrm{CZ} on output 20, output 51, \mathrm{CZ} on output 20, output 52, \mathrm{CZ} on output 20, output 53, \mathrm{CZ} on output 20, output 54, \mathrm{CZ} on output 20, output 55, \mathrm{CZ} on output 20, output 56, \mathrm{CZ} on output 20, output 58, \mathrm{CZ} on output 20, output 59, \mathrm{CZ} on output 20, output 60, \mathrm{CZ} on output 20, output 62, \mathrm{CZ} on output 20, output 67, \mathrm{CZ} on output 20, check 70, \mathrm{CZ} on output 20, check 72, \mathrm{CZ} on output 20, check 73, \mathrm{CZ} on output 20, check 74, \mathrm{CZ} on output 20, check 76, \mathrm{CZ} on output 20, check 77, \mathrm{CZ} on output 20, check 78, \mathrm{CZ} on output 20, check 80, \mathrm{CZ} on output 21, output 27, \mathrm{CZ} on output 21, output 29, \mathrm{CZ} on output 21, output 30, \mathrm{CZ} on output 21, output 31, \mathrm{CZ} on output 21, output 32, \mathrm{CZ} on output 21, output 33, \mathrm{CZ} on output 21, output 34, \mathrm{CZ} on output 21, output 37, \mathrm{CZ} on output 21, output 40, \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 47, \mathrm{CZ} on output 21, output 50, \mathrm{CZ} on output 21, output 51, \mathrm{CZ} on output 21, output 52, \mathrm{CZ} on output 21, output 53, \mathrm{CZ} on output 21, output 54, \mathrm{CZ} on output 21, output 55, \mathrm{CZ} on output 21, output 56, \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 67, \mathrm{CZ} on output 21, check 70, \mathrm{CZ} on output 21, check 72, \mathrm{CZ} on output 21, check 73, \mathrm{CZ} on output 21, check 74, \mathrm{CZ} on output 21, check 76, \mathrm{CZ} on output 21, check 77, \mathrm{CZ} on output 21, check 78, \mathrm{CZ} on output 21, check 80, \mathrm{CZ} on output 27, output 29, \mathrm{CZ} on output 27, output 30, \mathrm{CZ} on output 27, output 31, \mathrm{CZ} on output 27, output 32, \mathrm{CZ} on output 27, output 33, \mathrm{CZ} on output 27, output 34, \mathrm{CZ} on output 27, output 37, \mathrm{CZ} on output 27, output 40, \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 47, \mathrm{CZ} on output 27, output 50, \mathrm{CZ} on output 27, output 51, \mathrm{CZ} on output 27, output 52, \mathrm{CZ} on output 27, output 53, \mathrm{CZ} on output 27, output 54, \mathrm{CZ} on output 27, output 55, \mathrm{CZ} on output 27, output 56, \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 67, \mathrm{CZ} on output 27, check 70, \mathrm{CZ} on output 27, check 72, \mathrm{CZ} on output 27, check 73, \mathrm{CZ} on output 27, check 74, \mathrm{CZ} on output 27, check 76, \mathrm{CZ} on output 27, check 77, \mathrm{CZ} on output 27, check 78, \mathrm{CZ} on output 27, check 80, \mathrm{CZ} on output 29, output 30, \mathrm{CZ} on output 29, output 31, \mathrm{CZ} on output 29, output 32, \mathrm{CZ} on output 29, output 33, \mathrm{CZ} on output 29, output 34, \mathrm{CZ} on output 29, output 37, \mathrm{CZ} on output 29, output 40, \mathrm{CZ} on output 29, output 43, \mathrm{CZ} on output 29, output 45, \mathrm{CZ} on output 29, output 46, \mathrm{CZ} on output 29, output 47, \mathrm{CZ} on output 29, output 50, \mathrm{CZ} on output 29, output 51, \mathrm{CZ} on output 29, output 52, \mathrm{CZ} on output 29, output 53, \mathrm{CZ} on output 29, output 54, \mathrm{CZ} on output 29, output 55, \mathrm{CZ} on output 29, output 56, \mathrm{CZ} on output 29, output 58, \mathrm{CZ} on output 29, output 59, \mathrm{CZ} on output 29, output 60, \mathrm{CZ} on output 29, output 62, \mathrm{CZ} on output 29, output 67, \mathrm{CZ} on output 29, check 70, \mathrm{CZ} on output 29, check 72, \mathrm{CZ} on output 29, check 73, \mathrm{CZ} on output 29, check 74, \mathrm{CZ} on output 29, check 76, \mathrm{CZ} on output 29, check 77, \mathrm{CZ} on output 29, check 78, \mathrm{CZ} on output 29, check 80, \mathrm{CZ} on output 30, output 31, \mathrm{CZ} on output 30, output 32, \mathrm{CZ} on output 30, output 33, \mathrm{CZ} on output 30, output 34, \mathrm{CZ} on output 30, output 37, \mathrm{CZ} on output 30, output 40, \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 47, \mathrm{CZ} on output 30, output 50, \mathrm{CZ} on output 30, output 51, \mathrm{CZ} on output 30, output 52, \mathrm{CZ} on output 30, output 53, \mathrm{CZ} on output 30, output 54, \mathrm{CZ} on output 30, output 55, \mathrm{CZ} on output 30, output 56, \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 67, \mathrm{CZ} on output 30, check 70, \mathrm{CZ} on output 30, check 72, \mathrm{CZ} on output 30, check 73, \mathrm{CZ} on output 30, check 74, \mathrm{CZ} on output 30, check 76, \mathrm{CZ} on output 30, check 77, \mathrm{CZ} on output 30, check 78, \mathrm{CZ} on output 30, check 80, \mathrm{CZ} on output 31, output 32, \mathrm{CZ} on output 31, output 33, \mathrm{CZ} on output 31, output 34, \mathrm{CZ} on output 31, output 37, \mathrm{CZ} on output 31, output 40, \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 47, \mathrm{CZ} on output 31, output 50, \mathrm{CZ} on output 31, output 51, \mathrm{CZ} on output 31, output 52, \mathrm{CZ} on output 31, output 53, \mathrm{CZ} on output 31, output 54, \mathrm{CZ} on output 31, output 55, \mathrm{CZ} on output 31, output 56, \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 67, \mathrm{CZ} on output 31, check 70, \mathrm{CZ} on output 31, check 72, \mathrm{CZ} on output 31, check 73, \mathrm{CZ} on output 31, check 74, \mathrm{CZ} on output 31, check 76, \mathrm{CZ} on output 31, check 77, \mathrm{CZ} on output 31, check 78, \mathrm{CZ} on output 31, check 80, \mathrm{CZ} on output 32, output 33, \mathrm{CZ} on output 32, output 34, \mathrm{CZ} on output 32, output 37, \mathrm{CZ} on output 32, output 40, \mathrm{CZ} on output 32, output 43, \mathrm{CZ} on output 32, output 45, \mathrm{CZ} on output 32, output 46, \mathrm{CZ} on output 32, output 47, \mathrm{CZ} on output 32, output 50, \mathrm{CZ} on output 32, output 51, \mathrm{CZ} on output 32, output 52, \mathrm{CZ} on output 32, output 53, \mathrm{CZ} on output 32, output 54, \mathrm{CZ} on output 32, output 55, \mathrm{CZ} on output 32, output 56, \mathrm{CZ} on output 32, output 58, \mathrm{CZ} on output 32, output 59, \mathrm{CZ} on output 32, output 60, \mathrm{CZ} on output 32, output 62, \mathrm{CZ} on output 32, output 67, \mathrm{CZ} on output 32, check 70, \mathrm{CZ} on output 32, check 72, \mathrm{CZ} on output 32, check 73, \mathrm{CZ} on output 32, check 74, \mathrm{CZ} on output 32, check 76, \mathrm{CZ} on output 32, check 77, \mathrm{CZ} on output 32, check 78, \mathrm{CZ} on output 32, check 80, \mathrm{CZ} on output 33, output 34, \mathrm{CZ} on output 33, output 37, \mathrm{CZ} on output 33, output 40, \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 47, \mathrm{CZ} on output 33, output 50, \mathrm{CZ} on output 33, output 51, \mathrm{CZ} on output 33, output 52, \mathrm{CZ} on output 33, output 53, \mathrm{CZ} on output 33, output 54, \mathrm{CZ} on output 33, output 55, \mathrm{CZ} on output 33, output 56, \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 67, \mathrm{CZ} on output 33, check 70, \mathrm{CZ} on output 33, check 72, \mathrm{CZ} on output 33, check 73, \mathrm{CZ} on output 33, check 74, \mathrm{CZ} on output 33, check 76, \mathrm{CZ} on output 33, check 77, \mathrm{CZ} on output 33, check 78, \mathrm{CZ} on output 33, check 80, \mathrm{CZ} on output 34, output 37, \mathrm{CZ} on output 34, output 40, \mathrm{CZ} on output 34, output 43, \mathrm{CZ} on output 34, output 45, \mathrm{CZ} on output 34, output 46, \mathrm{CZ} on output 34, output 47, \mathrm{CZ} on output 34, output 50, \mathrm{CZ} on output 34, output 51, \mathrm{CZ} on output 34, output 52, \mathrm{CZ} on output 34, output 53, \mathrm{CZ} on output 34, output 54, \mathrm{CZ} on output 34, output 55, \mathrm{CZ} on output 34, output 56, \mathrm{CZ} on output 34, output 58, \mathrm{CZ} on output 34, output 59, \mathrm{CZ} on output 34, output 60, \mathrm{CZ} on output 34, output 62, \mathrm{CZ} on output 34, output 67, \mathrm{CZ} on output 34, check 70, \mathrm{CZ} on output 34, check 72, \mathrm{CZ} on output 34, check 73, \mathrm{CZ} on output 34, check 74, \mathrm{CZ} on output 34, check 76, \mathrm{CZ} on output 34, check 77, \mathrm{CZ} on output 34, check 78, \mathrm{CZ} on output 34, check 80, \mathrm{CZ} on output 37, output 40, \mathrm{CZ} on output 37, output 43, \mathrm{CZ} on output 37, output 45, \mathrm{CZ} on output 37, output 46, \mathrm{CZ} on output 37, output 47, \mathrm{CZ} on output 37, output 50, \mathrm{CZ} on output 37, output 51, \mathrm{CZ} on output 37, output 52, \mathrm{CZ} on output 37, output 53, \mathrm{CZ} on output 37, output 54, \mathrm{CZ} on output 37, output 55, \mathrm{CZ} on output 37, output 56, \mathrm{CZ} on output 37, output 58, \mathrm{CZ} on output 37, output 59, \mathrm{CZ} on output 37, output 60, \mathrm{CZ} on output 37, output 62, \mathrm{CZ} on output 37, output 67, \mathrm{CZ} on output 37, check 70, \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 76, \mathrm{CZ} on output 37, check 77, \mathrm{CZ} on output 37, check 78, \mathrm{CZ} on output 37, check 80, \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 47, \mathrm{CZ} on output 40, output 50, \mathrm{CZ} on output 40, output 51, \mathrm{CZ} on output 40, output 52, \mathrm{CZ} on output 40, output 53, \mathrm{CZ} on output 40, output 54, \mathrm{CZ} on output 40, output 55, \mathrm{CZ} on output 40, output 56, \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 67, \mathrm{CZ} on output 40, check 70, \mathrm{CZ} on output 40, check 72, \mathrm{CZ} on output 40, check 73, \mathrm{CZ} on output 40, check 74, \mathrm{CZ} on output 40, check 76, \mathrm{CZ} on output 40, check 77, \mathrm{CZ} on output 40, check 78, \mathrm{CZ} on output 40, check 80, \mathrm{CZ} on output 43, output 45, \mathrm{CZ} on output 43, output 46, \mathrm{CZ} on output 43, output 47, \mathrm{CZ} on output 43, output 50, \mathrm{CZ} on output 43, output 51, \mathrm{CZ} on output 43, output 52, \mathrm{CZ} on output 43, output 53, \mathrm{CZ} on output 43, output 54, \mathrm{CZ} on output 43, output 55, \mathrm{CZ} on output 43, output 56, \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 67, \mathrm{CZ} on output 43, check 70, \mathrm{CZ} on output 43, check 72, \mathrm{CZ} on output 43, check 73, \mathrm{CZ} on output 43, check 74, \mathrm{CZ} on output 43, check 76, \mathrm{CZ} on output 43, check 77, \mathrm{CZ} on output 43, check 78, \mathrm{CZ} on output 43, check 80, \mathrm{CZ} on output 45, output 46, \mathrm{CZ} on output 45, output 47, \mathrm{CZ} on output 45, output 50, \mathrm{CZ} on output 45, output 51, \mathrm{CZ} on output 45, output 52, \mathrm{CZ} on output 45, output 53, \mathrm{CZ} on output 45, output 54, \mathrm{CZ} on output 45, output 55, \mathrm{CZ} on output 45, output 56, \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 67, \mathrm{CZ} on output 45, check 70, \mathrm{CZ} on output 45, check 72, \mathrm{CZ} on output 45, check 73, \mathrm{CZ} on output 45, check 74, \mathrm{CZ} on output 45, check 76, \mathrm{CZ} on output 45, check 77, \mathrm{CZ} on output 45, check 78, \mathrm{CZ} on output 45, check 80, \mathrm{CZ} on output 46, output 47, \mathrm{CZ} on output 46, output 50, \mathrm{CZ} on output 46, output 51, \mathrm{CZ} on output 46, output 52, \mathrm{CZ} on output 46, output 53, \mathrm{CZ} on output 46, output 54, \mathrm{CZ} on output 46, output 55, \mathrm{CZ} on output 46, output 56, \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 67, \mathrm{CZ} on output 46, check 70, \mathrm{CZ} on output 46, check 72, \mathrm{CZ} on output 46, check 73, \mathrm{CZ} on output 46, check 74, \mathrm{CZ} on output 46, check 76, \mathrm{CZ} on output 46, check 77, \mathrm{CZ} on output 46, check 78, \mathrm{CZ} on output 46, check 80, \mathrm{CZ} on output 47, output 50, \mathrm{CZ} on output 47, output 51, \mathrm{CZ} on output 47, output 52, \mathrm{CZ} on output 47, output 53, \mathrm{CZ} on output 47, output 54, \mathrm{CZ} on output 47, output 55, \mathrm{CZ} on output 47, output 56, \mathrm{CZ} on output 47, output 58, \mathrm{CZ} on output 47, output 59, \mathrm{CZ} on output 47, output 60, \mathrm{CZ} on output 47, output 62, \mathrm{CZ} on output 47, output 67, \mathrm{CZ} on output 47, check 70, \mathrm{CZ} on output 47, check 72, \mathrm{CZ} on output 47, check 73, \mathrm{CZ} on output 47, check 74, \mathrm{CZ} on output 47, check 76, \mathrm{CZ} on output 47, check 77, \mathrm{CZ} on output 47, check 78, \mathrm{CZ} on output 47, check 80, \mathrm{CZ} on output 50, output 51, \mathrm{CZ} on output 50, output 52, \mathrm{CZ} on output 50, output 53, \mathrm{CZ} on output 50, output 54, \mathrm{CZ} on output 50, output 55, \mathrm{CZ} on output 50, output 56, \mathrm{CZ} on output 50, output 58, \mathrm{CZ} on output 50, output 59, \mathrm{CZ} on output 50, output 60, \mathrm{CZ} on output 50, output 62, \mathrm{CZ} on output 50, output 67, \mathrm{CZ} on output 50, check 70, \mathrm{CZ} on output 50, check 72, \mathrm{CZ} on output 50, check 73, \mathrm{CZ} on output 50, check 74, \mathrm{CZ} on output 50, check 76, \mathrm{CZ} on output 50, check 77, \mathrm{CZ} on output 50, check 78, \mathrm{CZ} on output 50, check 80, \mathrm{CZ} on output 51, output 52, \mathrm{CZ} on output 51, output 53, \mathrm{CZ} on output 51, output 54, \mathrm{CZ} on output 51, output 55, \mathrm{CZ} on output 51, output 56, \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 67, \mathrm{CZ} on output 51, check 70, \mathrm{CZ} on output 51, check 72, \mathrm{CZ} on output 51, check 73, \mathrm{CZ} on output 51, check 74, \mathrm{CZ} on output 51, check 76, \mathrm{CZ} on output 51, check 77, \mathrm{CZ} on output 51, check 78, \mathrm{CZ} on output 51, check 80, \mathrm{CZ} on output 52, output 53, \mathrm{CZ} on output 52, output 54, \mathrm{CZ} on output 52, output 55, \mathrm{CZ} on output 52, output 56, \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 67, \mathrm{CZ} on output 52, check 70, \mathrm{CZ} on output 52, check 72, \mathrm{CZ} on output 52, check 73, \mathrm{CZ} on output 52, check 74, \mathrm{CZ} on output 52, check 76, \mathrm{CZ} on output 52, check 77, \mathrm{CZ} on output 52, check 78, \mathrm{CZ} on output 52, check 80, \mathrm{CZ} on output 53, output 54, \mathrm{CZ} on output 53, output 55, \mathrm{CZ} on output 53, output 56, \mathrm{CZ} on output 53, output 58, \mathrm{CZ} on output 53, output 59, \mathrm{CZ} on output 53, output 60, \mathrm{CZ} on output 53, output 62, \mathrm{CZ} on output 53, output 67, \mathrm{CZ} on output 53, check 70, \mathrm{CZ} on output 53, check 72, \mathrm{CZ} on output 53, check 73, \mathrm{CZ} on output 53, check 74, \mathrm{CZ} on output 53, check 76, \mathrm{CZ} on output 53, check 77, \mathrm{CZ} on output 53, check 78, \mathrm{CZ} on output 53, check 80, \mathrm{CZ} on output 54, output 55, \mathrm{CZ} on output 54, output 56, \mathrm{CZ} on output 54, output 58, \mathrm{CZ} on output 54, output 59, \mathrm{CZ} on output 54, output 60, \mathrm{CZ} on output 54, output 62, \mathrm{CZ} on output 54, output 67, \mathrm{CZ} on output 54, check 70, \mathrm{CZ} on output 54, check 72, \mathrm{CZ} on output 54, check 73, \mathrm{CZ} on output 54, check 74, \mathrm{CZ} on output 54, check 76, \mathrm{CZ} on output 54, check 77, \mathrm{CZ} on output 54, check 78, \mathrm{CZ} on output 54, check 80, \mathrm{CZ} on output 55, output 56, \mathrm{CZ} on output 55, output 58, \mathrm{CZ} on output 55, output 59, \mathrm{CZ} on output 55, output 60, \mathrm{CZ} on output 55, output 62, \mathrm{CZ} on output 55, output 67, \mathrm{CZ} on output 55, check 70, \mathrm{CZ} on output 55, check 72, \mathrm{CZ} on output 55, check 73, \mathrm{CZ} on output 55, check 74, \mathrm{CZ} on output 55, check 76, \mathrm{CZ} on output 55, check 77, \mathrm{CZ} on output 55, check 78, \mathrm{CZ} on output 55, check 80, \mathrm{CZ} on output 56, output 58, \mathrm{CZ} on output 56, output 59, \mathrm{CZ} on output 56, output 60, \mathrm{CZ} on output 56, output 62, \mathrm{CZ} on output 56, output 67, \mathrm{CZ} on output 56, check 70, \mathrm{CZ} on output 56, check 72, \mathrm{CZ} on output 56, check 73, \mathrm{CZ} on output 56, check 74, \mathrm{CZ} on output 56, check 76, \mathrm{CZ} on output 56, check 77, \mathrm{CZ} on output 56, check 78, \mathrm{CZ} on output 56, check 80, \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 67, \mathrm{CZ} on output 58, check 70, \mathrm{CZ} on output 58, check 72, \mathrm{CZ} on output 58, check 73, \mathrm{CZ} on output 58, check 74, \mathrm{CZ} on output 58, check 76, \mathrm{CZ} on output 58, check 77, \mathrm{CZ} on output 58, check 78, \mathrm{CZ} on output 58, check 80, \mathrm{CZ} on output 59, output 60, \mathrm{CZ} on output 59, output 62, \mathrm{CZ} on output 59, output 67, \mathrm{CZ} on output 59, check 70, \mathrm{CZ} on output 59, check 72, \mathrm{CZ} on output 59, check 73, \mathrm{CZ} on output 59, check 74, \mathrm{CZ} on output 59, check 76, \mathrm{CZ} on output 59, check 77, \mathrm{CZ} on output 59, check 78, \mathrm{CZ} on output 59, check 80, \mathrm{CZ} on output 60, output 62, \mathrm{CZ} on output 60, output 67, \mathrm{CZ} on output 60, check 70, \mathrm{CZ} on output 60, check 72, \mathrm{CZ} on output 60, check 73, \mathrm{CZ} on output 60, check 74, \mathrm{CZ} on output 60, check 76, \mathrm{CZ} on output 60, check 77, \mathrm{CZ} on output 60, check 78, \mathrm{CZ} on output 60, check 80, \mathrm{CZ} on output 62, output 67, \mathrm{CZ} on output 62, check 70, \mathrm{CZ} on output 62, check 72, \mathrm{CZ} on output 62, check 73, \mathrm{CZ} on output 62, check 74, \mathrm{CZ} on output 62, check 76, \mathrm{CZ} on output 62, check 77, \mathrm{CZ} on output 62, check 78, \mathrm{CZ} on output 62, check 80, \mathrm{CZ} on output 67, check 70, \mathrm{CZ} on output 67, check 72, \mathrm{CZ} on output 67, check 73, \mathrm{CZ} on output 67, check 74, \mathrm{CZ} on output 67, check 76, \mathrm{CZ} on output 67, check 77, \mathrm{CZ} on output 67, check 78, \mathrm{CZ} on output 67, check 80, \mathrm{CZ} on check 70, check 72, \mathrm{CZ} on check 70, check 73, \mathrm{CZ} on check 70, check 74, \mathrm{CZ} on check 70, check 76, \mathrm{CZ} on check 70, check 77, \mathrm{CZ} on check 70, check 78, \mathrm{CZ} on check 70, check 80, \mathrm{CZ} on check 72, check 73, \mathrm{CZ} on check 72, check 74, \mathrm{CZ} on check 72, check 76, \mathrm{CZ} on check 72, check 77, \mathrm{CZ} on check 72, check 78, \mathrm{CZ} on check 72, check 80, \mathrm{CZ} on check 73, check 74, \mathrm{CZ} on check 73, check 76, \mathrm{CZ} on check 73, check 77, \mathrm{CZ} on check 73, check 78, \mathrm{CZ} on check 73, check 80, \mathrm{CZ} on check 74, check 76, \mathrm{CZ} on check 74, check 77, \mathrm{CZ} on check 74, check 78, \mathrm{CZ} on check 74, check 80, \mathrm{CZ} on check 76, check 77, \mathrm{CZ} on check 76, check 78, \mathrm{CZ} on check 76, check 80, \mathrm{CZ} on check 77, check 78, \mathrm{CZ} on check 77, check 80, \mathrm{CZ} on check 78, check 80
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 2, 5, 7, 11, 24, 29, 34, 37, 39, 43, 47, 50, 58, 60, 66, 71, 81, 83, 86, 88, 90, 93, 95, 96 and 99 more (listed below); \mathrm{T}^5 on rotations 4, 12, 15, 25, 30, 31, 32, 35, 70, 79, 87; \mathrm{T}^\dagger on rotations 0, 1, 3, 10, 13, 19, 20, 22, 36, 40, 41, 42, 46, 49, 55, 56, 61, 64, 72, 80, 173, 184, 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 123 rotations at T³
2, 5, 7, 11, 24, 29, 34, 37, 39, 43, 47, 50, 58, 60, 66, 71, 81, 83, 86, 88, 90, 93, 95, 96, 99, 101, 106, 108, 110, 115, 116, 117, 118, 119, 120, 121, 124, 125, 127, 128, 133, 134, 135, 137, 138, 139, 141, 143, 145, 147, 148, 149, 150, 156, 157, 158, 159, 161, 163, 168, 169, 170, 171, 172, 176, 179, 181, 183, 186, 188, 189, 190, 192, 193, 195, 203, 204, 206, 207, 209, 215, 216, 217, 218, 219, 222, 224, 227, 229, 231, 233, 234, 239, 240, 241, 242, 245, 246, 253, 255, 258, 260, 265, 269, 271, 272, 274, 277, 278, 281, 282, 283, 285, 287, 290, 294, 295, 296, 297, 303, 307, 308, 310
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/312.70.3.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-312.70.3.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 601 faults of weight 3 are undetectable and damaging, so A_{3}=601. 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 [0,1,63].
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
a paired-column contraction of an existing triorthogonal code, 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): contraction of an existing code
Discovery: AI search
1 recorded source
[
{
"regime": "AI search (gamma frontier): contraction of an existing code",
"file": "gamma_frontier_release/protocols/paired_column_contraction_312_70_3_d96036de1dc4.json",
"label": "paired_column_contraction_312_70_3_d96036de1dc4",
"N": 83,
"d": 3,
"d_is_exact": true,
"origin": "Existing triorthogonal code with physical paired-column contraction",
"provenance": "gamma frontier release record paired_column_contraction_312_70_3_d96036de1dc4 (source catalogue id paired_column_contraction_312_70_3_d96036de1dc4); construction: Existing triorthogonal code with physical paired-column contraction; matrix d96036de1dc4d4cc...; the release states d=3 (exact), gamma=1.3603597567363581 (exact)",
"notes": "matrix gamma_frontier_release/matrices/d96036de1dc4d4cc62dad5d3eaae70da727fdf4f96d50a7e9dd2b770a530d6f3.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/312.70.3.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[968].