The circuit
The 98\times359 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.
| wire | 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 |
|---|---|
| out 0 (135) | ··11···1···11·····11··1·····11··111····11····11···1···11·1····1··111·····1··1·······1···11·111·····11·111···1·1··11····1········1·11···1·111·11··111···1·1··1··1··1··1··1···1···11···1···1···11···1···1·1····11·1·11··111···1·1··11·····1···11·1··1·111··1·1··1·····1··11·111···11·111··1·1·11······1·······1·11·1·1··1·1·11·111··11·1··1······1··1···1·1···11··1···1·· |
| out 1 (133) | 1·1·····1··11··1··1·1········11···1···1·1·1··11·1··1··11···1····1111···1·1·111··1····1·1·11·1·····1·1·1111···11··1·1···1·1·1···1··1····1···11·1··1·11·1····1···1·1·1··1·····11··1··1·······1·1·····1··1·11···1·1···11···1··1··11·11···1··1··11···1·1111···11·111······1·11·1···1·1·1111··11·1·1·····1··1··1···1··1······11·1·1·111··1···1···1···1··1····11··1··1······· |
| out 2 (127) | 11····1·1······1·1··1·1·····1111····1··11·11·1········1·1········11······1·····1·1··1···1·1········111··111··11·1··1··11········11·1···11·1··11····11··1·1···11····1111·1····11······1··11·11····1·1·····1··1··11·1111····1·1·1111··········1·1·····11·····1····11··1··1·1······111··111·11···1···1·1·······11·1·11···1···11···11·11··11········1111··1··1·1····1·1·1·· |
| out 3 (133) | 1··········11··1··1·1·········1···1·1·1·1·1··11·1··1··11·1·1····1·11···1·1·111··1······1·11·11····1·1·1·11···11··1·1···1·1·11··1··11···1···11·1··1·11·1········1···1··1·····11··1··1·1····11··········1·11···1·1····1···1·11··11·11···1··1··11·1·1·1·11···11·111······1·11·111·1·1·1·11··11·1·1·····1··1·11···11·1······11·1·1·111······1·······1··1····11··1··11·····1 |
| out 4 (141) | ··11···1··1·········1··1··1·1····11·1·1·1····11·1·11··11·1······1··1······11···11···1·11·111·1·····111···1···11··11···11111·1··1·1·11····111···1·······1·1··111·1·1··11······11·11···1··1·1··11···1··1·········1·11····11·11··1··11···1·11··11·1···1··1·····11··1···111·111·1···111···1··11·11····1·111··11··1·11··1··1·1···1·····11·111··1····1··11·····1·111··1·1···1 |
| out 5 (143) | 11····11····1····1··1·1···1·11111···1··1··11·11·······111·11······1·····11···1·1·1··1···1·1········11111111···1····1··11··1····111·1···1··11·11····11··1····1·1··1·1111·····111······1··11·11····11·····1···1··11111111···1·1··1111·········111·11···1·····1···111··1··1·1······11111111··1···1···1·1·1···1·11·1·1····1·1·11···11·1··1·1····1···1111····11·1····1·1·1·· |
| out 6 (31) | ·······11·················1··1·························1··1································11·········11··················1·1····························1··1····························1········11·············1·1·························1··1·························11·······11·················1··1·························1·1······························11· |
| out 7 (135) | ··11··1·1·111·····11··1···1·1····11·1··11····1········1·1111··1··111·····1··11······1···1···11·····111··1·1·1·1··11····1··1·1··11·1····1·11··11··11····1··1··1·1··1··11·1·······11···1··1····11··1·1·11·1····11·111····11·1·1·1··1··········1·11111·111····1··11····1··1···11···111··1·11·1·11······1·1··11·1·1··1·1··1···11·11···1···1·1······1··11··1·····11··1·1···· |
| out 8 (135) | 1111··1····1·····1111·····1··11111········11··1···1·····111···1····1··1·····1··1·1·······11111·······1···11·1····111··1···1·1···1111····11·1·····11·1····1···111··111··1····111·11······1··1111··1····1·····1111·1·11111·······11·1·····1·····111·1···1·······1·11······11111·····1···111···111···1···1··1··1111··11····1····11·1··1··111······111··1···11·111····1···· |
| out 9 (143) | 1··1··1·1·11···1··1·······1·111·11········1········1·····1·1·····11····1·11·1··1····1·1··1·111····11···11····1····11··111·111··1·11·1··1·11·1·11·1····11·1·1111111·1·1········1··1·1······11··1··1·1·11··1···1···1111·11·······1·········1·····1·1··11·1··111·1·1···11··1·111··11···11···1···11···1·1111·11··11·11·1··1··1·111···11111111·1·1···1·1········1·1·1······1 |
| out 10 (127) | ·11···11·······1·1·11·······1··1···11···1··1············11·1··1··111···1·11······1··1·1··111······11··1·11··11···1·····11··1···11·1·1··1··1·1·11··11··11········11··11······11··1··1·····11·11···11······1··1·11··1··1····1···1·1·············11·11·111···111····1··11··111····11··1·11·11··1·······11·1··1·1·1·11····1··1·11·11·11·······1·1····11·····11··1··1····1·1 |
| out 11 (127) | 1111···11·11·····1111·····1··111·1··1···1·1············11··1··1····1········11·1·1········1·11········11·1··1····111··1···1·1··1111······1·······1111······11·11··111········11·11·······1·1111···11·11·····1111·1·111·1··1···11·············11··11···1·······1111·······1·11······11·1·1···111···1···1··11·111····1·1·······1111···11·11······111·······1·111······1·· |
| out 12 (141) | ·111···11·1······1····1···1···11·11·1·111·11··1·1··1···111·1····1·11·····111····11····111····11······1··1·1······111···1111····11··11··1·1·1·111····1·······11··11111···1·······11······1·1·111···11·1······1···11··11·11·111·111·1···1··1···111·1·1·11····111···1···111····1·····1··1·1····111·····111···1·1··111·1····1·111···1····11···1·1··111····1·····11····1···1 |
| out 13 (143) | ·1·1········1·····1·1·1···1··1·1111·1·1···1···1···11···1111···1·1111······1·11···1·····1·1···1····1·1·1·1·1·1··1·1·1····1·11···111·····11·1··1·1·1··1·1·11·1··1··1·1·1·11···11···1·1·1···1··1·1·········1····1·111·1·1111·11···1··1·····11···1111·11111·····1·11·1····1·1···1··1·1·1·1·11··11·1······111··1·11···11···1···1·11··11·11··1····1···1·1·1·1·11···1·11···1·· |
| out 14 (143) | ·1·1··1···1·1·····1·1·1···1····1·11·1·1···1···1···11··111·1···1·1111······1·11···1····11·1·1·1····1·111·1···1··1·1·1····1·111···11·····11·1··1·1·1··1·1··1····1··1·1·1·11···11···1·1·11·····1·1··1···1··1····1·111···1·11·11···1··1·····11··111·1·11111·····1·11·1···11·1·1·1··1·111·1··1··11·1······111·1··11···11···1···1·11··11·1···1····1···1·1·1·1·11···1·11······ |
| out 15 (125) | ··11··11··················1·11··111·1·1·11···1··1·11··1·········1··1······11···11···1·11·11········11····11··11··11··11·111······1·11·····1····1·······1···1111·1·1··11······11·11···1··11···11··11··············111··111·11··1··1····1·11··1······1··1·····11··1···111·11······11····11·11·11···11··11······1·11·····1·····1·····1·1111··1····1··11·····1·111··1·1·1·· |
| out 16 (133) | ·1·1···1··1····1·1·11·····1····1·11·1·1····1·11·1··1··111·····1·1·1····1·1·1···111·····1·1·1·1····1·1···1···1·1···1··111·1111···11·····1·1·11·····1···1··1··1·1···1·1·1·····1·1··1·1·1······1·1···1··1···1··1·11·1···1·11·11····111··11··1··111···11·1····11·1··11····1·1·1·1··1·1···1··1·1··1···11·1·11·1··11···1·1····11····1··1·1·1·1·······1·1·1····1··1·1·11······ |
| out 17 (143) | 11····11····1····1··1·1·····11111·1·1··1··11·1····1···111111·····111·····1···1·1·1··1···1·1········11111111···1····1··11·······1·1·1···1··1··11·····1··1···11·1····1111·1···111······1··11·11····11·····1···1··11·11111·1·1·1··111······1···111111··111····1···111··1··1·1······11111111··1···1···1·1·····1··1·1·1····1···11····1·1·11·1······1·1111··1·11·1····1·1·1·· |
| out 18 (31) | ······1·1··················1·1·························1·1·································1·1·······1·1···················11····························1·1·····························11······1·1···············1·························1·1··························1·1·····1·1··················1·1·························11·······························1·1 |
| out 19 (133) | ··11··111··1···1·1········1·11··111·1··1··11··1·1·11··1·······1··11····1··11···11···1··111··1······1111·1···1··1···1·11·111·····1·1····1····1··1·······1···11··1···11··1·····11·11···1·1··1··11··111··1··1··1····111··111·1·1··11·1···1·11··1·····1·11····1·11··1···1·111··1····1111·1··1··1··1··11··11·····1·1··1·······1··1·····1·11··1·······11··1····1·111··1·····1 |
| out 20 (141) | 1··1··111·1····1···11·1···1·111··11···11··1···1·1··1···1··1···1·1······1···1····1··11··1111··1····11·1···11·11····11·····1111······1·····11111····111·11·····1···111·1··1···11···111····1··1··1··111·1···1····1111111··11··11··1··1···1··1···1··1·11······1··1······1·1111··1··11·1···1111···11·······11·1·····1···1··1·111···11111···1·····1··11·1···1·11···111··1···· |
| out 21 (125) | 1·1··11·····1····11·1········11·1······11··1····1·1···11·1····1··········1·111··1·····1·11········111··1··1·1··1··1····1·1·1·····1·11···1111··1··1····1·······1·111·11·1····11··1··1·1··1111·1···1······1···11·1···11·1·····1·1·1·····1·1···11·1··1········1·111·····1·11······111··1··11··1·1······1··1·····1·11·11··1·1··1·1···1·····1··1·1··1·11·1···11··1··11·1·1·1 |
| out 22 (133) | ········1··11·····11··1···1·····1·1···111·······1········1····1·1·1······11111·11·····111·1·1········11·111·11·······111111····1·1111···1····111·1111······1·11111······1····11·········111········1··1·1····11·11····1·1··1111·······1········1··11·1·····111111····111·1·1······11·11111·······11·111···1··1111·1·······1111111···1·111·1·1·········1··1·1······1·1·1 |
| out 23 (141) | 111····11··11··1··1·1·····1··11·······1·1·1··11·1··1··11·1·1····1·11···1·1·111··1······1·11·11·1··1·1··111···11··1·1···1·111···11·1····1···11·1··1·11·1········1···1··1·····11··1··1·1····1111····11··1·11···1·1·1·11······1··11·11···1··1··11·1·1·1·11···11·111······1·11·11··1·1··111··11·1·1·····1·11··1·1·1··1······11·1·1·111······1·······1··1····11··1··11·····1 |
| out 24 (127) | 1·1···1····11····1·1··1······11·····1·1····1··1··1·1··11···1····111·······1····1·······1··111·····1·111·11·····1··1···1·1··1···11·11···1·11··1·1······1····1···1·11·11·11···1·1·1··1·1··11·1·1···1····1·1···1·1·1··11·····11····1·1······1··11···1·111······1···1·····1··111···1·111·11····1·1····1··1·1··1·1·11·1·1··1···1·1····1··1···1···1··1·11·1·1·1··11··11·1·1·· |
| out 25 (135) | ·11····1···1·······11·······1··1··1·1·111·1··11···11····1·1···1·1········11······1··1··11··11·····11···1··1···11··11···11··1···11111····11····11··1·1·11···11·11·111··11····11··1··1········11····1···1·······11··1··1··1·111·11·11·····11····1·1·11·······11····1··1·11··11···11···1··1··11·11·····11·1··1·1111··11·······11·1·111·11·111··1··11··11···11··1··1······· |
| out 26 (141) | 11·1··1·1··11····111······1·1111··1·1·1···11·11·1··1··1·11····1·11········1111··11··1·11····1···1··11·11····1·1····1····111·····1·1·1·····11···1·11·1··1·1·1···111·1111··············1····111·1··1·1··1·1···111··11111··1·11···1111···1··1··1·11··111·······1111·1··111····1····11·11···1·1···1······11·····1·1·1·····1·1···111·1·111···1·1·1···1111············1·····1 |
| out 27 (149) | 11····1·1·11·····1·1········1·111·1···1···11·1··1·11··1·11·1··1·1·········1111··11··1·11·1·11······11·11··1·111····11···11··1··11·111·····1····1·1111··1·1·1·1·11··1111··············1··11111····1·1·11·····1·1···1·111·1··1···111····1·11··1·11·111········1111·1··111·1·11····11·11··1111···1······1···11·1·111·····1·····11111·111·1·1·1·····1111············1·1·1·1 |
| out 28 (141) | 1·1····11·11···1··1···········1·1···1·1·1·1··1··1·11··1·········1111···1·1·11··11······1··1111····1·1··1111···1··1·1·1·1·1·11···1·11···1····1·1··1··1·1··1·1·1·1·1·1··1······1··1··1·1··1111·1····11·11··1···1······1·1···11··11·1····1·11··1······1111···11·11·1·····1··1111··1·1··1111··1·1·1··1··1··1·1··1·11·1·······1·1·1··11·11·1·1···1···1··1·····11·1··11·1·1·1 |
| out 29 (149) | 11····1·1·111····111······1·11111···1·1···11·11·1··1··1·1··1··1·11········1111··111·1·11···11······11·11··1·1·1····1····111····1··1·1·····11···1·11·1··1·1···1·111·1111··········1···1···1111····1·1·11·1···111··111111···11···1111···1··1··1·1··1111·······1111·1··111···11····11·11··11·1···1······11···1···1·1·····1·1···111·1·11··1·1·1·1···1111·········1··1···1·1 |
| out 30 (127) | 11······1·1·1····1··1·1·····1·111···1··1··11·11·1·1···1·1··1······1······1·····1·1··1···1111·······11···11····1····1··11····1··111·1···1··11·11·1···1··1·1····1··1·1111·1····11······1·····11······1·1··1···1··11·1·111···1·1··1111···1·1···1·1··1···1·····1····11··1··1111·····11···11···1···1···1·1····11·11·1·1····1·1·11····1·11···1····1···1111··1··1·1····1······ |
| out 31 (135) | 1111···11·111····1111·········11·11·····1·11··1···11····11····1··1·1········11·1·1·······11·1·········11·1··11····11··1········1·111·····1·1·····11······1··1111·1111········11·11······1111111···11·11·1·1·1111····11·11·····111·1·····11····11··1·1·1·······1111······11·1·······11·1·11···11···1·······1··111···1····1····11····1·1111···1··111·······1·111····1·1·1 |
| out 32 (143) | ·11···1·1·11·······11·····1·11·1····1··11·1··11···11···11·······11·······11······1··1··111··1·····11·11·······11··11···11·111··1·111·1··11····11··1·1·11·1·1··11··11··11····11··1··1····11··11···1·1·11·······11·111·1····1·1·11·11·····11···11····11······11····1··1·111··1···11·11······11·11·····1111·11··111··11·······11·1·11111··11······11··11···11··1··1··1·1·· |
| out 33 (143) | ·1·1··1···1······11·1·1···1····1·11·1·1·1·1···········1111·1··1·1·11······1·11···1·····1·1·1······1·111·1···11·1·1·1····1·111···11·····1··11·1·1·1·1··1··1·1111····1·1·11···11···1·1·1····1·1·1··1···1······11·111···1·11·11··11············1111·111·11·····1·11·1····1·1·1····1·111·1··11·11·11·····111·1··11···1····1·1·1·11·1·1·11111········1·1·1·1·11···1·11·····1 |
| out 34 (135) | 11········1······1····1·····1·11··1·1··11·11·11····1··1111·······11······1·····1·1··1···1·11·1···1·11··111···11····1·111····1····1·1···11·11·11····1···1···1·11····1111·1····11······1··1·111··1·····1······1···1·1·11··1·1·1·11111······1··1111····11·····1····11··1··1·11·1·1·11··111··11···1··11·1····1···1·1·11···1·1·11···1··1·1·11········1111··1··1·1····1·1···1 |
| out 35 (127) | 11····1·1·······11··1·1·····1111····1··1··11·11·······1·1··1······1······1·····1·1··1···1111·······111··111··11···11··11········11·1···1··11·11····11··1·1····1··1·1111·1····11······1·····11····1·1········1··11·1111····1·1··1111·········1·1··1···1·····1····11··1··1111·····111··111·11··11···1·1·······11·1·1····1·1·11···11·11···1····1···1111··1··1·1····1······ |
| out 36 (151) | ·1·1··111·1·1·····1·1·1···1····1111···1·1·1···1····1··1·11·1··1·1111······1·1····1·····1···1·1····1·11·11···1··1·1·1····1·111··111·1···1··1··1·1·1·11·1····1111··1·111·11····1···1·1·1··1···1·1··111·1··1····1·111···1111··1··11··1······1··1·11·111111·1···1·1··1····1···1·1··1·11·11··1··11·1······111·11·11·1·1····1···1·11·111··1111····1···111·1·1··1···1·11·1···· |
| out 37 (149) | ·1·1···········1·1·11·····1··1·1111·1·1·1··1·1··1·11··1·1·11··1·111····1·1·111·111·····1···1······1·1·1·1·1·1·1···1··111·111···111·····111··1·1···11··1······11··11·1·1····1··1··1·1·1··1·1·1·1··········1··1·11·1·1·1111·11··1·11····1·11··1·1·111111····11·11111····1···1····1·1·1·1·11·1··1···11·1·11··1·11···111·····1·1··11·1····11····1··1·1·1·······1·1·11·1···1 |
| out 38 (149) | ·1·1··11·······1·1·11·····1··1·1111·1·1·1··1·1··1·····1·1·11··1·111····1·1·1···111·····111·1······1·11··1·1·1·1···1··111·111···111·····111··1·1···1·1·1······11··11·1·1·····1·1··1·1·1····1·1·1··11······1··1·11·1·1·1111·11··1·11····1·····1·1·111111····11·1··11····111·1····1·11··1·11·1··1···11·1·11··1·11···111·····1·1··1·11····11····1··1·1·1····1··1·1·111····1 |
| out 39 (125) | ······1·1···1··1·111··1···1··1··········1·11·11·1·11·1·····1·······1···1·11111·11········1···········1·1······11·111·111111·1············11·1111·11····1·····1····1111111····11·········1········1·1····11··111·11·1··········11111···1·11·······1····1···1111111·······1·········1·1·····11111··11·111··1·········1··1··111111···1···1········111111·1··1·1······1···· |
| out 40 (133) | 1111········1····1··1·1···1···1111··1·11···1····1·11····1·······1111·····111····11····1111···········1111····1···111·1·1111········11··111···111···11····1·11···1·111···1·······11·········1111·········1···1··111··1111··111···1·····1·11····1····1111····111···1···1111·········1111···1··111··1··111········111111·····111··11··111····1····111····1·····11········· |
| out 41 (135) | 11····11····1····1··1·1·····1111····1··11·11·1········111·1······11······1···111·1··1···1·1········11111111···1····1··11········11·1···11·1··11····11··1····111····1111·1···1·1······1··11·11····11·····1···1··11·1111····1·1·1111··········111·1···11·····1···111··1··1·1······11111111··1···1···1·1·······11·1·11···1···11···11·1··111········1111··1·1··1····1·1·1·· |
| out 42 (149) | 1111··1···1······1····1···1··111·1··1·111·11··1·1··1····1·11····1111·····111····11··1·111··1·1········111·1······111···1111·1··1···11··1·1·1·111····1····1·1·1··1·111···1·······11··1···1111111··1···1······1···11·111·1··111·111·1···1··1····1·11·1111····111···1··1111··1·1······111·1····111·····111··11····111·1····1·111···1··11·1···1····111····1·····11····1·1·1 |
| out 43 (135) | ··11···1··111·····11··1···1·1····11·1··11····1········11···1··1··111·····1··11······1···1···11·····11·11··1·1·1··11····1··1·1··11·1····1·11··11··11····1·1·111·1··1··11·1·······11···1··1····11···1·111·1····11·111····11·1·1·1··1··········11···11·111····1··11····1··1···11···11·11··11·1·11······1·1··11·1·1··1·1··1···11·11···11111·1······1··11··1·····11··1·1···· |
| out 44 (157) | ·11·····1·1·1·····1·1·1·····11·11·1·1·····1··11·1·11···111·1·11··11········111·111··1·1··111·1····11·1·1111·1111··11·11··1·11·······1··1·1···1···1·1··11·1·····11111··111···1·1·1··1·····1··11·····1·1··1····1·11·11·11·1·1····1·11···1·11···111·11·11·······11111··11··111·1··11·1·11111111·11··11····1·1······11·1······1··1·1·111····1·1·1··11··11·1·1··11··1····1·· |
| out 45 (135) | 1·1···1····11····1·1··1···1···1···1···1····1·1····11··11···1····111·······1····1·······1··111·····1·111·11·····1··1···1·1·111··1··1····1·111·1·1··11··1····1···1·11·11·11···1·1·1··1·1··11·1·1···1····1·1···1·1·11··1···1··1····11······11··11···1·111······1···1·····1··111···1·111·11····1·1····1··111·11···1··1·1··111·1·1·11·1··1···1···1··1·11·1·1·1··11··11·1·1·· |
| out 46 (143) | ·1·1··11··111··1·11·1·1···1····1·1·····1···1·1········1111·····1·1·····1··1·11···1····1·111·1·····1·1·11·11··11···1·····1·111···1·1·1····1··11·1·1·1··1··1·111·1··1·1·1·1···11···1·1·1··1···1·1··11··11·11··11·111···1·1····1···11··········1111····1·····1·1·11·1···1·111·1···1·1·11·11·11··1·······111·1··1·1·1··1·····11·11·1·1·1111·1······1·1·1··1·11···1·11·1···· |
| out 47 (149) | 1111··111·1······1····1···1··111·11···111·11··1·1··1···11··1····1111·····111····11····111··1·1··········1·1······111···1111·1··11···1··1·1·1·111····1······111··1·111···1·······11·1····1111111··111·1······1···11·111·11··11·111·1···1··1···11··1·1111····111···1·1·111··1·1········1·1····111·····111··11·1···11·1····1·111···1···111···1····111····1·····11·1··1·1·1 |
| out 48 (135) | 11····1·1········1····1·····1111····1··11·11·11····1··1·1·1·······1······1·····1·1··1···111········111··111··11····1·111········11·1···11·11·11····1···1·1··111··1·1111·1····11·1····1···1·11····1·1········1···1·1111····1·1·11111······1··1·1·1····1·····1····111·1··111······111··111·11···1··11·1·······11·1·11···1·1·11···1··11·111····1···1111··1··1·11···1···1·· |
| out 49 (143) | ·1·1··111·1·1·····1·1·1···1··1·1111·1·1·1·1·······11··1·1··1··1·1·11······111····1·····1···1·1····1·11·11···1··1·1·1····1·11···111·····1··11·1·1·1··1·1·····111····1·1·11·1··1···1·1·1··1···1·1··111·1··1····1·111·1·1111·11··11········11··1·1··111·11·····111··1····1···1·1··1·11·11··1··11·1······111··1·11···1····1·1·1·11··11···111········1·1·1·1··1···1·11·1···· |
| out 50 (159) | ·1·1···11·111··1·11·1·1···1····1·1··1··1···1·1········1111·············1··1·11···1····1·111111····1·111··11··11···1·····1·111···11111····1··11·1·1·1··1··1·111·1111·1·1·1···11···1·1·1··111·1·1···11·11·11··11·111···1·1·11·1···11··········1111··········1·1·11·1···1·111111··1·111··11·11··1·······111·1··11111··1·····11·11·1·1·1111·1·1·1··1·1·1··1·11···1·11·1·1·1 |
| out 51 (127) | ·11···111··1·······11·····1·1··11·····11··1··1··········1·1·····11·······1···1···1··1··11···11····11·1····1···11··11···11·11·····11······1·1··11··11··11···11·11··11··11·1···1··1··1·····11·11···111··1·······11·11··11····11··1·1············1·1··11······1···1·1··1·11···11··11·1····1··11·11·····1111·····11····1····1··11·11·11·11·11······11··11····1··1··1····1·1 |
| out 52 (111) | 1111······11·····11···········11·1··1·····11···········11··1··1····1········11·1·1········1·11···········1··1····111·11········1111·····11·······1111······11·11··111········11·11·······1·1111······11·····11······11·1··1····11············11··11···1·······1111·······1·11·········1·1···111·111·······1·111···11·········1111···11·11······111·······1·111······1·· |
| out 53 (135) | ·1·1··111·1·······1·1·1······1·1·11·1·1·1·1·······11··1·1··1··1·1·11······1·11···1·····1·1···1····1·11·11···11·1·1······1··1····11·····1··11·1·1·1··1·1·····111····1·1·11···11···1·1·1···1··1·1··111·1·····1·1·11··1·1·11·11··11········11··1·1··111·11·····1·11·1····1·1···1··1·11·11··11·11········1·1····11···1····1·1·1·11··11···111········1·1·1·1·11···1·11···1·· |
| out 54 (141) | 11····111··1·····1111·····1·1111··1·1·1···11·11·1··1··1111····1·1······1··111···11··1·11····1······11··1····111····1·1··111·····1·1·1·····11···1·11·1··1···1···11··1111·····1········1····111····111··1·····1111·11111··1·11···1111···1··1··1111··11······1·111··1··111····1····11··1···111···1··1···11·····1·1·1·····1·1···111·1·1·1···1·1·····1111·1··1·······1·····1 |
| out 55 (141) | 1··1··1···1·1··1···1··1·····1·1··11···111·1···111··1···1······1·11·····1···1····1···1··11111·1····11·111·11·1·····11·1···1·1·······1····111111·1··111·11····11····11·1··1···11···1·1····11·1··1··1···1··11····1·1·1·1··11··11·11··1···1··1···1····111·····1··1······1·11111·1··11·111·111····11··1·····1·······1··11··1·111·1·11111··11········11·1···1·11···1·1··1·1·· |
| out 56 (141) | ·11····11·11·1·1·11·1·1·····11·11·····11···1····1·11···111······1··1···1···111·111··1··11··111····11·········11··1···11··1·11····11·····1·1·11···1·1··11·1····11·1··11··1···1·1·1··1······1·11····11·11··1··11·11·11·11····11···1·····1·11···111···1··1···1··11111··1·11··111··11········11·1····11····1·1···11···1···1··11··1·1·111···11···1····11···1·1··11··1······1 |
| out 57 (133) | 1··1···11·····11···1··1···1·1·1·111···11··1·····1·11·····1·1··1·1······1···1····1···1··11·11······11·····1··11·1··11·1···111···1···1·····11·11····1·1·11·1·11····111·1··1···11···1·1·····111··1···11·····1····1·111·1·111··11··1······1·11·····1·111······1··1······1·11·11····11·····1·11·1·11··1····11··1····1···1··1··11···1·111111······1··11·1···1·11···1·1····1·1 |
| out 58 (133) | ······111···1··1·111··1······1··1·······1·11·11·1·11···1···1·······1···1·11111·11··········1·········111····1·11·111·11111··1··1·········11·1111·11······1···1····1111111····11··········1·······111···111··111·1··1··1·······11111···1·11···1···1····1···1111111·········1·······111···1·11111··11·11···11········1··1··111111····1··1········111111·1··1·1········1·· |
| out 59 (127) | ··11··1·1·111·····11··1·····11···1·····11····1········1···11··1·1·11·····1··11······1···1···11·····111··1·1·1·1··11····1·······1··11···1·11··11··11····1···1·1·1·11··11·1·······11···1··1····11··1·1·11·1····11·1·11···1····1·1··1··········1···1111·11····1··11····1··1···11···111··1·11·1·11······1·····1···11·1·1··1···11·11···1·1·1·1··11··1··11··1·····11··1·1···· |
| out 60 (143) | ·1·1··11··111··1·11·1·1······1·1·11·1··1···1·1········1·111······11····1··1·11···1····1·111·1·····1·1·11·11··11···1·····1··1······111····1··11·1·1·1··1····1·1·11·1·1·1·1···11···1·1·1··1···1·1··11··11·11··11·11··1·1·11·1·1···11··········1·111···11····1·1·11·1···1·111·1···1·1·11·11·11··1·······1·1······111··1·····11·11·1·1··1·1·1·1··1·1·1·1··1·11···1·11·1···· |
| out 61 (135) | ·11·····1·1········11·····1·11·1······111·1··11···11···11··1····1········11······1··1··11··11·····11··1····1··11··11···11·111··1·11·····11····11··1·1·11·1·1·111·111··11····11··1··1········11·····1·1········11·111·1·····11·11·11·····11···11··1·1·······11····1··1·11··11···11··1······11·11·····1111·11··11···11·······11·1·11111·111···1··11··11···11··1··1······· |
| out 62 (135) | 1·1···1····1·····1·11·1···1···1···1···1····1······1···1····1····1·1·······1····1·1·····1·1111·····1·111·11···1·1··1··11·1·111··1··1····1·111·1·1··111·1··1·1···1··1·11·11···1·111··1·1···1·1·1···1····1·····1·1111··1···1··1····1·······1···1····1·1·1······1···11····1·1111···1·111·11··1·1·1···11··111·11···1··1·1··1·1·1·1·1111·11···1······1·11·1·1·1··11··11···1·· |
| out 63 (135) | ··11···1···11·····11··1·····1···111·1··11····1······1·11·1·1··1··111·····1··11······1···11·111·····11·111···1·1··11····1····1···1·1····1·11··11··11··1·1·1··11·1··1··11·1·······11···1···1···11···1···1·1····11·1·1···111·1·1·1··1········1·11·1·11·111····1··11····1··11·111···11·111··1·1·11······1····1··1·1··1·1··1···11·11···11·11·1······1··11··1·····11··1···1·· |
| out 64 (141) | ·1·1···1··1····1·1·11·····1····1·11·1·1·1··1·1··1·····111·11··1·111····1·1·1···111·····1·1·1·1····1·1···1···1·1···1··111·1111···11·····111··1·1···1·1····1···11··11·1·1·····1·1··1·1·1······1·1···1··1···1··1·11·1···1·11·11··1·11····1····1111·111111····11·1··11····1·1·1·1··1·1···1··1·1··1···11·1·11·1··11···111·····1·1··1·1··1··11····1··1·1·1····1··1·1·11······ |
| out 65 (133) | ··········111·····11111···1·····1·····111·······1·11·····1·1··1·111······11111·11·····1111111········11111··11·········1111····111111··11····111·11········1··111·······1····11···········1··········11·1····11111····1····11·1·······1·11·····1·11111·····111111····1111111······11111·11··········111···1·1111111·······11111·····1··11·1···········1··1·1··········1 |
| out 66 (143) | ·1·1··111·1·1·····1·1·1···1·····111·1·1···1···1···11··1·1·····1·1111······1·11···1·····1···1·1····1·11·11···1··1·1·1····1·111·1111·····11·1··1·1·1··1·1·····1·1··1·1·1·11···11···1·1·1··1···1·1··111·1··1····1·111····111·11···1··1·····11··1·1···11111·····1·11·1····1···1·1··1·11·11··1··11·1······111·11·11···11···1···1·11··11···1·1····1···1·1·1·1·11···1·11·1···· |
| out 67 (127) | ··11···1···11·····11··1···1·1····1··1···1····1········11······1···11·····1··11······1···11·111·····11·111···1·1··11····1··1·1··1··1···11·11··11··11····1·1·11··1·11··11·1·······11···1···1···11···1···1·1····11·111····1··1···1··1··········11····1··11····1··11····1··11·111···11·111··1·1·11······1·1··11···1··1·1··1···11·11···1111··1···1··1··11··1·····11··1···1·· |
| out 68 (135) | ··11···1···11·····11··1·····1···111·1··1·····11···1···11······1···11·····1··11······1···11·111·····11·111···1·1··11····1····1···1·1····11111··1··111···1·1·11··1·11··11·1·······11···1···1···11···1···1·1····11·1·1···111·1·1····11·1···1···11····1··11····1··11····1··11·111···11·111··1·1·11······1····1··1·1··111··1·1··1·111··1111··1···1··1··11··1·····11··1···1·· |
| out 69 (141) | ·11···1·1·111··1·11·1·1·····11·1·1····11···1····1······111······1··1···1···111·111··1··11··111····11·11··········1···11··1·11··1·11·····1·1·11···1··1·11·1····11·1··11··1···1·1·1··1······1·11···1·1·11·11··11·11·11·1·1···11···1·····1······111···1··1···1··11111··1·11··111··11·11········1····11····1·111·11···1···1··11··1··1111···11···1····11···1·1··11··1······1 |
| out 70 (135) | ··11····1·1·1··1·111··1···1·1···111···1···11··1···1···1··11·····1···1··1·1··1·······1·11·11··1·····11111·1···1·1···1···1··1·1····1··1·······111··111···1·····11·1···1··11···1···11···1··111··11····1·1··11··111·111···111··1···11·1·····1···1··11··1······11··1·····111·11··1···11111·1··1·1··1·····1·1··1···1··1········111·111··1···11··1······1··1·1·1···11··1·1·1·1 |
| out 71 (135) | 1··1····1·1······11·······1·111··11···111··1·11···1···········1·1··1·····11·11·1····1··11·11·1····11··1··11·1·11·1····111·111······1··········11···11·11·1··11···1··1·11····1·1··1·1·····1·1··1····1·1······11···1111··11··11·1·111····11·········11··1····11·111···1·11·11·1··11··1··111·111·····1·1111·1·····1···········11··11111·11·····1····1·11···1··1·1·1····1·· |
| out 72 (143) | 1··1··1·····1····11·1·····1·1·1··11·1·111··1·1····1····1·1····1·1··1·····11·11·1····1··11·1·······111111·1··1111·1···1111·11···············1··11·1·11·11···111···1··1·11····1·1··1·1······11··1·11······1···11·1·11·1··11·111·1·11······1····1·1··11··1····11·111···1·11·1·····111111·1·11111····11·1111················1··111·1111·111·····1····1·11···1··1·1·1······1 |
| out 73 (125) | ··11··11··················1·11··111·1·1······1··1·····1··1111···1··1······11···11···1·11·11········11····11··11··11··11·111······1·11···111····1···11··1········1·1··11······11·11···1··11···11··11··············111··111·11·····1····1·····1··111·1··1·····11··1···111·11······11····11·11·11···11··11······1·11·11··1·····1··11·1·······1····1··11·····1·111··1·1·1·· |
| out 74 (135) | 11·····11···1····1··1·1·····1·111···1··1··11·11···11··1·1··1······1··········1·1·1··1···1·11·1·····11·1·111···1····1··11····1··111·1···1··11·11········1·1····1··1·1111·1···111······1··1·111·····11····1···1··11·1·111···1·1··1111·····11··1·1··1···1·········111··1··1·11·1···11·1·111··1···1···1·1····11·11·1·1····1·1·11······11···1····1···1111··1111·1····1·1···1 |
| out 75 (125) | 1·1··············11·1···1····11···1····1···1····1·····11·1····1··········1·111··1·····1·11········1·11·1··1·11·1··1····111·1···111·11····111··1··1·1··1·······1·111·11·1····11··1··1·1··1111·1··············11·1···11···1···1···1·····1·····11·1··1········1·111·····1·11······1·11·1··111·1·1······11·1··1·11·11··1··1·1··1·1·1·1·····1··1·1··1·11·1···11··1··11·1·1·1 |
| out 76 (141) | ·1·1···1··1····1·1·1··1···1····1·11·1·1····1·11·1·····111··1··1·111····1·1·1···111·····1·····1····1·1···1···1·1···1···11·1111···11·····1·1·11·1···1·1·1··1··111··11·1·1·····1·1··1·1·1··11··1·1···1··1···1··1·1·11···1·11·11····111···1·····111··11111····11·1··11····1·····1··1·1···1··1·1··1····111·11·1··11···1·1····11·1··1·11·1·111····1··1·1·1····1··1·1·11·1·1·· |
| out 77 (133) | ······111·1·1··1·111··1······11·········1·11·11·1·11·····1·1·······1···1·11111·11············1·······111··1···11·111·11111··11···········11·1111·11········1·1····1111111····11···········1······111·1··11··111·1··11·········11111···1·11·····1·1····1···1111111···········1·····111··1··11111··11·11···1·········1··1··111111·····1·1········111111·1··1·1··········1 |
| out 78 (127) | ··11······111·····11··1··········11·1··11····1········1··1·1··1··111·····1··11······1···1··11······11··11·1·1·1··11····1····1··11·1····1·11··11··11····1····11·1··1··11·1·······11···1··111··11······11·1····11·1······11·1·1·1··1··········1··1·11·111····1··11····1··1··11····11··11·11·1·11······1···111·1·1··1·1··1···11·11···1··11·1······1··11··1·····11··1·1·1·1 |
| out 79 (135) | 11····111··11··1····1·1·····1111··1···1·1···1·········1·1·····1·1··1···1·1·····1·1··1·11·1·111·····11··1····11·1·11···11········1·111····111111····11··1·1·····11·1····11····11······1··11·11····111··1·11·····11·1111··1··1··1·············1·1···11··1···11····11··111·1·111···11··1···11·111····1·1·······1·111··1··1·1111···11·11····1·1····1····1·1··1·1····1·1·1·· |
| out 80 (133) | ··11··1···1···············1·11···11···1······11·1··1··11·111····1··1·1····11·1·11···1·11··1··1·····11·1··1···11··11··11·111····1·1··1···1111···1···1···1·1····1·1·1···1·····111·11···1···11··11··1···1···········111···11··1·····11···1··1··11·111·1··1·····11·11···111··1··1···11·1··1··11·11···11··11···1··1··1·11··1·1···1··1··11···1··1····1···1····11·111··1···1·1 |
| out 81 (135) | ··11··11··111·····11··1·····11···11·1··11····1········1···11··1··111·····1··11······1···1·1·1······111111·1·1·1··11····1·······11·1····1·11··11··11····1···1·1·1··1··11·1·······11···1··1·1··11··11··11·1····11·1·11···11·1·1·1··1··········1···111·111····1··11····1··1·1·1····111111·11·1·11······1·····1·1·1··1·1··1···11·11···1·1·1·1······1··11··1·····11··1·11··1 |
| out 82 (149) | 11··1·1·1··11····111········11111·1·1·1···11·11·1··1··1·11·1··1·1·········1111··11··1·11·1·11·····111·11····1·1····1····11·····11·1·1·····11···1·11·1··1·1·1·1·11··1111··············1··11111····1·1··1·1···111···11111·1·11···1111···1··1··1·11·111········1111·1··111·1·11···111·11···1·1···1······1····1·1·1·1·····1·1···111·1·111·1·1·1·····1111············1·1·1·1 |
| out 83 (149) | ·11····11···1·····1·1·1·····11·11···11····1··11·1·11···111·1··1···1········111·111··1·1···11······11·11111··1111··11·11··1·11···1······1·1···1···1·1··11·1······1·11··111···1·1·1··1····111·11····11····1····1·11·11·11···1····1·11···1·11···111·11··1·······11111··11···11····11·11111·1111·11··11····1·1··1····1·1······1··1·1·111······1····11··11·1·1··11··1··1·1·1 |
| out 84 (141) | ·11···1···1·1··1·1·11····1··11·11··········1·······1···11·11··1···11···1·11·····11··1·1···11······11····111·1····1·····111·11···1··11··11·1·1·11··111·11·1·11···1···11······111·1··1····111·11···1···1··11··1·11··11·11·········1········1···11·111··11···111····1··11···11····11····1111···1·······11·1·1··1··1111···1··1·11·11111111····1······11·····11·11··1··1·1·1 |
| out 85 (149) | ·1·1···1111····1·1·11··········1111·1·1·1··1·1··1·····111··1··1·111····1·1·1···111·····1·····1····1·1··111··1·1···1··111·1·11··111·····111··1·1···1·1·1··1··111··11·1·1·····1·1··1·1·1··11··1·1···11·1···1··1·11·····1111·11··1·11····1·····111··11111····11·1··11····1·····1··1·1··111·1·1··1···11·1··1·11·11···111·····1·1··1·11·1·111····1··1·1·1····1··1·1·11·1·1·· |
| out 86 (143) | ·1·1··11··111··1·11·1·1······1·1·11·1··1···1·11···11··1·1··············1··1·11···1····1·111·1·····1·1·11·11··11···1·····1··1······111····1·1·1·1·1··1·1·····11·1111·1·1·1···11···1·1·1··1···1·1··11··11·11··11·11··1·1·11·1·1···1111····11··1·1···········1·1·11·1···1·111·1···1·1·11·11·11··1·······1·1······111··1····1·1·11··11···11·1·1·1··1·1·1··1·11···1·11·1···· |
| check 87 (134) | 1··1···11·111·····1·1·1···1·11·1··1·1···1··1··1····1····1··1··1···11···1·11·····1······11···1····1··1········111··11·11··1111··1····1··1··111·11··111·11···1····1···11······11···11··1···1·1··1···11·11·1····1·11111·1··1·1···1·1·1······1····1··11··11···111·········11···1··1··1·······111·11··11···11·11·····11····1·11·11·11111·1·····1······11·····11···11·1···1·· |
| check 88 (144) | ·11···1····1·······11········11·11·········1··1·1·1····11111····1········11···········1···11·1····11·111··1···11··11···11·1····11··11··11·1111···1·11·11·1··1111·111··11····111··11··1··11··11···1····1·······11···11·11········1·1···1·1····11111·1·······11········1···11·1··11·111··1··11·11·····111···1·1··1111···1·111··1·11111·1111···1··11··11···11·1·11·1·1·1·· |
| check 89 (128) | ······111··1···1·1····················11··11·11·····1·1·1·11·····1·······11111·1·1··1····1·1············111·1111·111············11111··1111·1·········11·1·1·1···1······1····11·1111·1··11·······111··1··1··1··············11··1111·······1·1·1·11··1······1111111··1···1·1··········1111111111·············11111111··1··1·······1111·1·····1·········1··1·111111·1·1·· |
| check 90 (174) | 1·1·11·1111·111···1·11·11·111·1·111····1·····1·11·1··111·11·····1··1··1····111·1··1···1···11··1·1·1·11·1·······1·11·1··1·11111···1··111·111·········1····1···11·1·1··111·1·111··1···11·1·····11······1·11·1·1··1·1····1···11··1·1·1··11111·11··1·11·1···11·111·1···11111··1·1···1111··1·1·1··1·1··1··11·11·111·11··1·1111··111···11··1·1·1111·11·11····1111111·111·1··1 |
| check 91 (192) | 11··1······111··1·1·11·1·111111111··1·1·111···1·11····1·1·1·1····11····1·1111··1·11·1111·1·111·11··1·1··1·1···1·1··1·1··111·1·11·11111·11·111·11111·1·11111····11111·1····1···11···1·1·1··11··1·1·1·111111··1111·11·1·1··1···1111111·1···1·1······111··111··1·11···111·····1···11111····1····111111·1111··11··1·1·11·1111···11····11·1·1111111··1111·1·11·11·1····1·1·· |
| check 92 (176) | 1····11·1···1·1···1··1··11··111·1111···1··1····11··1·111···1·1····1·1·11·1·11·11··1··11··1·11···1·1····11·11···11·11···1·1·11··111··1·11·11·1·1·11····1·1···111·1·1··1·1·11··11····111·····1·11·11··1·1111·111·1····1···1·1··1··1·11····1····1·1111·1···1··11·1···1·11·1··1·11·111·····11····1·1·11·11·11··111111··1111·1··111·1111·1·11111·11·1111··1····1111·1·11··11 |
| check 93 (182) | ····11··11··1···1·11··11111···111·1··1··1···1···11······1·1···111·1··11··111·1111··111111·111·····11·11·1·1111····1··11···1··111·111·1111·1··111·1·11·····1·1111·1···1·11··1··1···1·11··1·1····11··1·1111·11111··1·····11··1111··111··1111···1·1··1·1····111111····1·111····1·1··111·11··1··1·11·111111····1·1111·1····111111·1····11·111·11·1·····1·11·1111···1··1111· |
| check 94 (176) | ··11····11111··1·1·1111111··11···11111·11·11··11111···1··1·111·111·····11111··1·····1·····11·1·····11111···1·1·1···1111·11·····1·111·11·1···111111·1···1····1··1·1·11··1·11111··11···111··1··11··11·1··111··11····11···1·1·1·1111·1·11·1·1··1··1··1··1····1···111···11111··1····11···11111·1··1·1··11·····1·1···111······1····1·1·1··111·111·1··11··1·11··1·11··111111· |
| check 95 (174) | 11·····11····11·1··1·1·111··1·11··1·1··111··1·11·1····1·111······11111111····11·11··1···111········11·1·111···1·11··1·11····1····1·1···1··1·1···11·····1·1·1111···11·1··1111·1·······1···1·11·····11····111111·11·1·11··1·1·1··111·1111111··1·111···11·111·1111·11··1··111······11·1·111·1·1·11111·1·1···1···1·1·11111·11·111·111·111111······1··1·111·11·1·····1···1·· |
| check 96 (176) | ·1·1··11··111··1·11·1·1···11··1·1111111·11·1111111·1··1·1··············1··1·11··1·1111·11·111·····1·1·11·11··11···1·····1·1·1111···1·11·1·1111··11111·1·····11·1111·1·1·1···1111··111·11·1··1·1··11··11·11··11·11·11·1···1··11·1···111·11···1·1···········1·1·11·111·1··1···1··1·1·11·11·11··1·······1·11··1111·11·111·1···11····1···11·1·1·1··1·1·1··1·11··11··1111·11 |
| check 97 (174) | 1··1···11···1··1···1··1···1·111·11····11··1···1·1·1·111111··111111··11111·1·1·1··111·11·1111·1····11·····1··1·····11·1···1111··11··1·····11111····1··11·1·1111111·1····1·1111·11··11111111·1··1···11····11····1·11111·11···11··1··1···1·1··1····11···11111·1·1·11·111·1····1···11·····1·1····11··1····11·11·1··1···1··1·111···1···11·····1·1111·1111·111·11·11···1·1·11 |
The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.
Figures of merit
inputs n359Noisy T states per run.
outputs k87
distance d3Exact, proved and witnessed here.
error coefficient A_{3}3,365Faults 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 N98
checks r11
V_{\mathrm{ex}}87T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.2902Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.2902Overhead 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 width87Rank of the output rows modulo the check rows.
Output gate
87 T0 CS0 CCZon 87 output wires
As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}\cdot \mathrm{T}_{77}\cdot \mathrm{T}_{78}\cdot \mathrm{T}_{79}\cdot \mathrm{T}_{80}\cdot \mathrm{T}_{81}\cdot \mathrm{T}_{82}\cdot \mathrm{T}_{83}\cdot \mathrm{T}_{84}\cdot \mathrm{T}_{85}\cdot \mathrm{T}_{86}
As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86 (output wires per term, separated by +)
This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.
Clifford correction
With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 92 single-wire gates and 946 \mathrm{CZ} gates: \mathrm{S} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{Z} on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{Z} on output 16, \mathrm{S} on output 17, \mathrm{S} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23 and 1014 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 1038 correction gates
\mathrm{S} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{Z} on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{Z} on output 16, \mathrm{S} on output 17, \mathrm{S} on output 18, \mathrm{Z} on output 19, \mathrm{Z} 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{Z} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{S} on output 32, \mathrm{S} on output 33, \mathrm{S} on output 34, \mathrm{S} on output 35, \mathrm{S} on output 36, \mathrm{Z} on output 37, \mathrm{Z} on output 38, \mathrm{Z} on output 39, \mathrm{Z} on output 40, \mathrm{S} on output 41, \mathrm{Z} on output 42, \mathrm{S} on output 43, \mathrm{Z} on output 44, \mathrm{S} on output 45, \mathrm{S} on output 46, \mathrm{Z} on output 47, \mathrm{S} on output 48, \mathrm{S} on output 49, \mathrm{S} on output 50, \mathrm{S} on output 51, \mathrm{S} on output 52, \mathrm{S} on output 53, \mathrm{Z} on output 54, \mathrm{Z} on output 55, \mathrm{Z} on output 56, \mathrm{Z} on output 57, \mathrm{Z} on output 58, \mathrm{S} on output 59, \mathrm{S} on output 60, \mathrm{S} on output 61, \mathrm{S} on output 62, \mathrm{S} on output 63, \mathrm{Z} on output 64, \mathrm{Z} 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{S} on output 71, \mathrm{S} on output 72, \mathrm{Z} on output 73, \mathrm{S} on output 74, \mathrm{Z} on output 75, \mathrm{Z} on output 76, \mathrm{Z} on output 77, \mathrm{S} on output 78, \mathrm{S} on output 79, \mathrm{Z} on output 80, \mathrm{S} on output 81, \mathrm{Z} on output 82, \mathrm{Z} on output 83, \mathrm{Z} on output 84, \mathrm{Z} on output 85, \mathrm{S} on output 86, \mathrm{S} on check 87, \mathrm{S} on check 90, \mathrm{S} on check 93, \mathrm{S} on check 95, \mathrm{S} on check 97, \mathrm{CZ} on output 1, output 3, \mathrm{CZ} on output 1, output 4, \mathrm{CZ} on output 1, output 12, \mathrm{CZ} on output 1, output 15, \mathrm{CZ} on output 1, output 16, \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 22, \mathrm{CZ} on output 1, output 23, \mathrm{CZ} on output 1, output 26, \mathrm{CZ} on output 1, output 27, \mathrm{CZ} on output 1, output 28, \mathrm{CZ} on output 1, output 29, \mathrm{CZ} on output 1, output 37, \mathrm{CZ} on output 1, output 38, \mathrm{CZ} on output 1, output 39, \mathrm{CZ} on output 1, output 40, \mathrm{CZ} on output 1, output 42, \mathrm{CZ} on output 1, output 44, \mathrm{CZ} on output 1, output 47, \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 57, \mathrm{CZ} on output 1, output 58, \mathrm{CZ} on output 1, output 64, \mathrm{CZ} on output 1, output 65, \mathrm{CZ} on output 1, output 69, \mathrm{CZ} on output 1, output 73, \mathrm{CZ} on output 1, output 75, \mathrm{CZ} on output 1, output 76, \mathrm{CZ} on output 1, output 77, \mathrm{CZ} on output 1, output 80, \mathrm{CZ} on output 1, output 82, \mathrm{CZ} on output 1, output 83, \mathrm{CZ} on output 1, output 84, \mathrm{CZ} on output 1, output 85, \mathrm{CZ} on output 1, check 87, \mathrm{CZ} on output 1, check 90, \mathrm{CZ} on output 1, check 93, \mathrm{CZ} on output 1, check 95, \mathrm{CZ} on output 1, check 97, \mathrm{CZ} on output 3, output 4, \mathrm{CZ} on output 3, output 12, \mathrm{CZ} on output 3, output 15, \mathrm{CZ} on output 3, output 16, \mathrm{CZ} on output 3, output 19, \mathrm{CZ} on output 3, output 20, \mathrm{CZ} on output 3, output 21, \mathrm{CZ} on output 3, output 22, \mathrm{CZ} on output 3, output 23, \mathrm{CZ} on output 3, output 26, \mathrm{CZ} on output 3, output 27, \mathrm{CZ} on output 3, output 28, \mathrm{CZ} on output 3, output 29, \mathrm{CZ} on output 3, output 37, \mathrm{CZ} on output 3, output 38, \mathrm{CZ} on output 3, output 39, \mathrm{CZ} on output 3, output 40, \mathrm{CZ} on output 3, output 42, \mathrm{CZ} on output 3, output 44, \mathrm{CZ} on output 3, output 47, \mathrm{CZ} on output 3, output 54, \mathrm{CZ} on output 3, output 55, \mathrm{CZ} on output 3, output 56, \mathrm{CZ} on output 3, output 57, \mathrm{CZ} on output 3, output 58, \mathrm{CZ} on output 3, output 64, \mathrm{CZ} on output 3, output 65, \mathrm{CZ} on output 3, output 69, \mathrm{CZ} on output 3, output 73, \mathrm{CZ} on output 3, output 75, \mathrm{CZ} on output 3, output 76, \mathrm{CZ} on output 3, output 77, \mathrm{CZ} on output 3, output 80, \mathrm{CZ} on output 3, output 82, \mathrm{CZ} on output 3, output 83, \mathrm{CZ} on output 3, output 84, \mathrm{CZ} on output 3, output 85, \mathrm{CZ} on output 3, check 87, \mathrm{CZ} on output 3, check 90, \mathrm{CZ} on output 3, check 93, \mathrm{CZ} on output 3, check 95, \mathrm{CZ} on output 3, check 97, \mathrm{CZ} on output 4, output 12, \mathrm{CZ} on output 4, output 15, \mathrm{CZ} on output 4, output 16, \mathrm{CZ} on output 4, output 19, \mathrm{CZ} on output 4, output 20, \mathrm{CZ} on output 4, output 21, \mathrm{CZ} on output 4, output 22, \mathrm{CZ} on output 4, output 23, \mathrm{CZ} on output 4, output 26, \mathrm{CZ} on output 4, output 27, \mathrm{CZ} on output 4, output 28, \mathrm{CZ} on output 4, output 29, \mathrm{CZ} on output 4, output 37, \mathrm{CZ} on output 4, output 38, \mathrm{CZ} on output 4, output 39, \mathrm{CZ} on output 4, output 40, \mathrm{CZ} on output 4, output 42, \mathrm{CZ} on output 4, output 44, \mathrm{CZ} on output 4, output 47, \mathrm{CZ} on output 4, output 54, \mathrm{CZ} on output 4, output 55, \mathrm{CZ} on output 4, output 56, \mathrm{CZ} on output 4, output 57, \mathrm{CZ} on output 4, output 58, \mathrm{CZ} on output 4, output 64, \mathrm{CZ} on output 4, output 65, \mathrm{CZ} on output 4, output 69, \mathrm{CZ} on output 4, output 73, \mathrm{CZ} on output 4, output 75, \mathrm{CZ} on output 4, output 76, \mathrm{CZ} on output 4, output 77, \mathrm{CZ} on output 4, output 80, \mathrm{CZ} on output 4, output 82, \mathrm{CZ} on output 4, output 83, \mathrm{CZ} on output 4, output 84, \mathrm{CZ} on output 4, output 85, \mathrm{CZ} on output 4, check 87, \mathrm{CZ} on output 4, check 90, \mathrm{CZ} on output 4, check 93, \mathrm{CZ} on output 4, check 95, \mathrm{CZ} on output 4, check 97, \mathrm{CZ} on output 12, output 15, \mathrm{CZ} on output 12, output 16, \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 22, \mathrm{CZ} on output 12, output 23, \mathrm{CZ} on output 12, output 26, \mathrm{CZ} on output 12, output 27, \mathrm{CZ} on output 12, output 28, \mathrm{CZ} on output 12, output 29, \mathrm{CZ} on output 12, output 37, \mathrm{CZ} on output 12, output 38, \mathrm{CZ} on output 12, output 39, \mathrm{CZ} on output 12, output 40, \mathrm{CZ} on output 12, output 42, \mathrm{CZ} on output 12, output 44, \mathrm{CZ} on output 12, output 47, \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 57, \mathrm{CZ} on output 12, output 58, \mathrm{CZ} on output 12, output 64, \mathrm{CZ} on output 12, output 65, \mathrm{CZ} on output 12, output 69, \mathrm{CZ} on output 12, output 73, \mathrm{CZ} on output 12, output 75, \mathrm{CZ} on output 12, output 76, \mathrm{CZ} on output 12, output 77, \mathrm{CZ} on output 12, output 80, \mathrm{CZ} on output 12, output 82, \mathrm{CZ} on output 12, output 83, \mathrm{CZ} on output 12, output 84, \mathrm{CZ} on output 12, output 85, \mathrm{CZ} on output 12, check 87, \mathrm{CZ} on output 12, check 90, \mathrm{CZ} on output 12, check 93, \mathrm{CZ} on output 12, check 95, \mathrm{CZ} on output 12, check 97, \mathrm{CZ} on output 15, output 16, \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 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 29, \mathrm{CZ} on output 15, output 37, \mathrm{CZ} on output 15, output 38, \mathrm{CZ} on output 15, output 39, \mathrm{CZ} on output 15, output 40, \mathrm{CZ} on output 15, output 42, \mathrm{CZ} on output 15, output 44, \mathrm{CZ} on output 15, output 47, \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 57, \mathrm{CZ} on output 15, output 58, \mathrm{CZ} on output 15, output 64, \mathrm{CZ} on output 15, output 65, \mathrm{CZ} on output 15, output 69, \mathrm{CZ} on output 15, output 73, \mathrm{CZ} on output 15, output 75, \mathrm{CZ} on output 15, output 76, \mathrm{CZ} on output 15, output 77, \mathrm{CZ} on output 15, output 80, \mathrm{CZ} on output 15, output 82, \mathrm{CZ} on output 15, output 83, \mathrm{CZ} on output 15, output 84, \mathrm{CZ} on output 15, output 85, \mathrm{CZ} on output 15, check 87, \mathrm{CZ} on output 15, check 90, \mathrm{CZ} on output 15, check 93, \mathrm{CZ} on output 15, check 95, \mathrm{CZ} on output 15, check 97, \mathrm{CZ} on output 16, output 19, \mathrm{CZ} on output 16, output 20, \mathrm{CZ} on output 16, output 21, \mathrm{CZ} on output 16, output 22, \mathrm{CZ} on output 16, output 23, \mathrm{CZ} on output 16, output 26, \mathrm{CZ} on output 16, output 27, \mathrm{CZ} on output 16, output 28, \mathrm{CZ} on output 16, output 29, \mathrm{CZ} on output 16, output 37, \mathrm{CZ} on output 16, output 38, \mathrm{CZ} on output 16, output 39, \mathrm{CZ} on output 16, output 40, \mathrm{CZ} on output 16, output 42, \mathrm{CZ} on output 16, output 44, \mathrm{CZ} on output 16, output 47, \mathrm{CZ} on output 16, output 54, \mathrm{CZ} on output 16, output 55, \mathrm{CZ} on output 16, output 56, \mathrm{CZ} on output 16, output 57, \mathrm{CZ} on output 16, output 58, \mathrm{CZ} on output 16, output 64, \mathrm{CZ} on output 16, output 65, \mathrm{CZ} on output 16, output 69, \mathrm{CZ} on output 16, output 73, \mathrm{CZ} on output 16, output 75, \mathrm{CZ} on output 16, output 76, \mathrm{CZ} on output 16, output 77, \mathrm{CZ} on output 16, output 80, \mathrm{CZ} on output 16, output 82, \mathrm{CZ} on output 16, output 83, \mathrm{CZ} on output 16, output 84, \mathrm{CZ} on output 16, output 85, \mathrm{CZ} on output 16, check 87, \mathrm{CZ} on output 16, check 90, \mathrm{CZ} on output 16, check 93, \mathrm{CZ} on output 16, check 95, \mathrm{CZ} on output 16, check 97, \mathrm{CZ} on output 19, output 20, \mathrm{CZ} on output 19, output 21, \mathrm{CZ} on output 19, output 22, \mathrm{CZ} on output 19, output 23, \mathrm{CZ} on output 19, output 26, \mathrm{CZ} on output 19, output 27, \mathrm{CZ} on output 19, output 28, \mathrm{CZ} on output 19, output 29, \mathrm{CZ} on output 19, output 37, \mathrm{CZ} on output 19, output 38, \mathrm{CZ} on output 19, output 39, \mathrm{CZ} on output 19, output 40, \mathrm{CZ} on output 19, output 42, \mathrm{CZ} on output 19, output 44, \mathrm{CZ} on output 19, output 47, \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 57, \mathrm{CZ} on output 19, output 58, \mathrm{CZ} on output 19, output 64, \mathrm{CZ} on output 19, output 65, \mathrm{CZ} on output 19, output 69, \mathrm{CZ} on output 19, output 73, \mathrm{CZ} on output 19, output 75, \mathrm{CZ} on output 19, output 76, \mathrm{CZ} on output 19, output 77, \mathrm{CZ} on output 19, output 80, \mathrm{CZ} on output 19, output 82, \mathrm{CZ} on output 19, output 83, \mathrm{CZ} on output 19, output 84, \mathrm{CZ} on output 19, output 85, \mathrm{CZ} on output 19, check 87, \mathrm{CZ} on output 19, check 90, \mathrm{CZ} on output 19, check 93, \mathrm{CZ} on output 19, check 95, \mathrm{CZ} on output 19, check 97, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 22, \mathrm{CZ} on output 20, output 23, \mathrm{CZ} on output 20, output 26, \mathrm{CZ} on output 20, output 27, \mathrm{CZ} on output 20, output 28, \mathrm{CZ} on output 20, output 29, \mathrm{CZ} on output 20, output 37, \mathrm{CZ} on output 20, output 38, \mathrm{CZ} on output 20, output 39, \mathrm{CZ} on output 20, output 40, \mathrm{CZ} on output 20, output 42, \mathrm{CZ} on output 20, output 44, \mathrm{CZ} on output 20, output 47, \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 57, \mathrm{CZ} on output 20, output 58, \mathrm{CZ} on output 20, output 64, \mathrm{CZ} on output 20, output 65, \mathrm{CZ} on output 20, output 69, \mathrm{CZ} on output 20, output 73, \mathrm{CZ} on output 20, output 75, \mathrm{CZ} on output 20, output 76, \mathrm{CZ} on output 20, output 77, \mathrm{CZ} on output 20, output 80, \mathrm{CZ} on output 20, output 82, \mathrm{CZ} on output 20, output 83, \mathrm{CZ} on output 20, output 84, \mathrm{CZ} on output 20, output 85, \mathrm{CZ} on output 20, check 87, \mathrm{CZ} on output 20, check 90, \mathrm{CZ} on output 20, check 93, \mathrm{CZ} on output 20, check 95, \mathrm{CZ} on output 20, check 97, \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 29, \mathrm{CZ} on output 21, output 37, \mathrm{CZ} on output 21, output 38, \mathrm{CZ} on output 21, output 39, \mathrm{CZ} on output 21, output 40, \mathrm{CZ} on output 21, output 42, \mathrm{CZ} on output 21, output 44, \mathrm{CZ} on output 21, output 47, \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 57, \mathrm{CZ} on output 21, output 58, \mathrm{CZ} on output 21, output 64, \mathrm{CZ} on output 21, output 65, \mathrm{CZ} on output 21, output 69, \mathrm{CZ} on output 21, output 73, \mathrm{CZ} on output 21, output 75, \mathrm{CZ} on output 21, output 76, \mathrm{CZ} on output 21, output 77, \mathrm{CZ} on output 21, output 80, \mathrm{CZ} on output 21, output 82, \mathrm{CZ} on output 21, output 83, \mathrm{CZ} on output 21, output 84, \mathrm{CZ} on output 21, output 85, \mathrm{CZ} on output 21, check 87, \mathrm{CZ} on output 21, check 90, \mathrm{CZ} on output 21, check 93, \mathrm{CZ} on output 21, check 95, \mathrm{CZ} on output 21, check 97, \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 29, \mathrm{CZ} on output 22, output 37, \mathrm{CZ} on output 22, output 38, \mathrm{CZ} on output 22, output 39, \mathrm{CZ} on output 22, output 40, \mathrm{CZ} on output 22, output 42, \mathrm{CZ} on output 22, output 44, \mathrm{CZ} on output 22, output 47, \mathrm{CZ} on output 22, output 54, \mathrm{CZ} on output 22, output 55, \mathrm{CZ} on output 22, output 56, \mathrm{CZ} on output 22, output 57, \mathrm{CZ} on output 22, output 58, \mathrm{CZ} on output 22, output 64, \mathrm{CZ} on output 22, output 65, \mathrm{CZ} on output 22, output 69, \mathrm{CZ} on output 22, output 73, \mathrm{CZ} on output 22, output 75, \mathrm{CZ} on output 22, output 76, \mathrm{CZ} on output 22, output 77, \mathrm{CZ} on output 22, output 80, \mathrm{CZ} on output 22, output 82, \mathrm{CZ} on output 22, output 83, \mathrm{CZ} on output 22, output 84, \mathrm{CZ} on output 22, output 85, \mathrm{CZ} on output 22, check 87, \mathrm{CZ} on output 22, check 90, \mathrm{CZ} on output 22, check 93, \mathrm{CZ} on output 22, check 95, \mathrm{CZ} on output 22, check 97, \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 29, \mathrm{CZ} on output 23, output 37, \mathrm{CZ} on output 23, output 38, \mathrm{CZ} on output 23, output 39, \mathrm{CZ} on output 23, output 40, \mathrm{CZ} on output 23, output 42, \mathrm{CZ} on output 23, output 44, \mathrm{CZ} on output 23, output 47, \mathrm{CZ} on output 23, output 54, \mathrm{CZ} on output 23, output 55, \mathrm{CZ} on output 23, output 56, \mathrm{CZ} on output 23, output 57, \mathrm{CZ} on output 23, output 58, \mathrm{CZ} on output 23, output 64, \mathrm{CZ} on output 23, output 65, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, output 73, \mathrm{CZ} on output 23, output 75, \mathrm{CZ} on output 23, output 76, \mathrm{CZ} on output 23, output 77, \mathrm{CZ} on output 23, output 80, \mathrm{CZ} on output 23, output 82, \mathrm{CZ} on output 23, output 83, \mathrm{CZ} on output 23, output 84, \mathrm{CZ} on output 23, output 85, \mathrm{CZ} on output 23, check 87, \mathrm{CZ} on output 23, check 90, \mathrm{CZ} on output 23, check 93, \mathrm{CZ} on output 23, check 95, \mathrm{CZ} on output 23, check 97, \mathrm{CZ} on output 26, output 27, \mathrm{CZ} on output 26, output 28, \mathrm{CZ} on output 26, output 29, \mathrm{CZ} on output 26, output 37, \mathrm{CZ} on output 26, output 38, \mathrm{CZ} on output 26, output 39, \mathrm{CZ} on output 26, output 40, \mathrm{CZ} on output 26, output 42, \mathrm{CZ} on output 26, output 44, \mathrm{CZ} on output 26, output 47, \mathrm{CZ} on output 26, output 54, \mathrm{CZ} on output 26, output 55, \mathrm{CZ} on output 26, output 56, \mathrm{CZ} on output 26, output 57, \mathrm{CZ} on output 26, output 58, \mathrm{CZ} on output 26, output 64, \mathrm{CZ} on output 26, output 65, \mathrm{CZ} on output 26, output 69, \mathrm{CZ} on output 26, output 73, \mathrm{CZ} on output 26, output 75, \mathrm{CZ} on output 26, output 76, \mathrm{CZ} on output 26, output 77, \mathrm{CZ} on output 26, output 80, \mathrm{CZ} on output 26, output 82, \mathrm{CZ} on output 26, output 83, \mathrm{CZ} on output 26, output 84, \mathrm{CZ} on output 26, output 85, \mathrm{CZ} on output 26, check 87, \mathrm{CZ} on output 26, check 90, \mathrm{CZ} on output 26, check 93, \mathrm{CZ} on output 26, check 95, \mathrm{CZ} on output 26, check 97, \mathrm{CZ} on output 27, output 28, \mathrm{CZ} on output 27, output 29, \mathrm{CZ} on output 27, output 37, \mathrm{CZ} on output 27, output 38, \mathrm{CZ} on output 27, output 39, \mathrm{CZ} on output 27, output 40, \mathrm{CZ} on output 27, output 42, \mathrm{CZ} on output 27, output 44, \mathrm{CZ} on output 27, output 47, \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 57, \mathrm{CZ} on output 27, output 58, \mathrm{CZ} on output 27, output 64, \mathrm{CZ} on output 27, output 65, \mathrm{CZ} on output 27, output 69, \mathrm{CZ} on output 27, output 73, \mathrm{CZ} on output 27, output 75, \mathrm{CZ} on output 27, output 76, \mathrm{CZ} on output 27, output 77, \mathrm{CZ} on output 27, output 80, \mathrm{CZ} on output 27, output 82, \mathrm{CZ} on output 27, output 83, \mathrm{CZ} on output 27, output 84, \mathrm{CZ} on output 27, output 85, \mathrm{CZ} on output 27, check 87, \mathrm{CZ} on output 27, check 90, \mathrm{CZ} on output 27, check 93, \mathrm{CZ} on output 27, check 95, \mathrm{CZ} on output 27, check 97, \mathrm{CZ} on output 28, output 29, \mathrm{CZ} on output 28, output 37, \mathrm{CZ} on output 28, output 38, \mathrm{CZ} on output 28, output 39, \mathrm{CZ} on output 28, output 40, \mathrm{CZ} on output 28, output 42, \mathrm{CZ} on output 28, output 44, \mathrm{CZ} on output 28, output 47, \mathrm{CZ} on output 28, output 54, \mathrm{CZ} on output 28, output 55, \mathrm{CZ} on output 28, output 56, \mathrm{CZ} on output 28, output 57, \mathrm{CZ} on output 28, output 58, \mathrm{CZ} on output 28, output 64, \mathrm{CZ} on output 28, output 65, \mathrm{CZ} on output 28, output 69, \mathrm{CZ} on output 28, output 73, \mathrm{CZ} on output 28, output 75, \mathrm{CZ} on output 28, output 76, \mathrm{CZ} on output 28, output 77, \mathrm{CZ} on output 28, output 80, \mathrm{CZ} on output 28, output 82, \mathrm{CZ} on output 28, output 83, \mathrm{CZ} on output 28, output 84, \mathrm{CZ} on output 28, output 85, \mathrm{CZ} on output 28, check 87, \mathrm{CZ} on output 28, check 90, \mathrm{CZ} on output 28, check 93, \mathrm{CZ} on output 28, check 95, \mathrm{CZ} on output 28, check 97, \mathrm{CZ} on output 29, output 37, \mathrm{CZ} on output 29, output 38, \mathrm{CZ} on output 29, output 39, \mathrm{CZ} on output 29, output 40, \mathrm{CZ} on output 29, output 42, \mathrm{CZ} on output 29, output 44, \mathrm{CZ} on output 29, output 47, \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 57, \mathrm{CZ} on output 29, output 58, \mathrm{CZ} on output 29, output 64, \mathrm{CZ} on output 29, output 65, \mathrm{CZ} on output 29, output 69, \mathrm{CZ} on output 29, output 73, \mathrm{CZ} on output 29, output 75, \mathrm{CZ} on output 29, output 76, \mathrm{CZ} on output 29, output 77, \mathrm{CZ} on output 29, output 80, \mathrm{CZ} on output 29, output 82, \mathrm{CZ} on output 29, output 83, \mathrm{CZ} on output 29, output 84, \mathrm{CZ} on output 29, output 85, \mathrm{CZ} on output 29, check 87, \mathrm{CZ} on output 29, check 90, \mathrm{CZ} on output 29, check 93, \mathrm{CZ} on output 29, check 95, \mathrm{CZ} on output 29, check 97, \mathrm{CZ} on output 37, output 38, \mathrm{CZ} on output 37, output 39, \mathrm{CZ} on output 37, output 40, \mathrm{CZ} on output 37, output 42, \mathrm{CZ} on output 37, output 44, \mathrm{CZ} on output 37, output 47, \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 57, \mathrm{CZ} on output 37, output 58, \mathrm{CZ} on output 37, output 64, \mathrm{CZ} on output 37, output 65, \mathrm{CZ} on output 37, output 69, \mathrm{CZ} on output 37, output 73, \mathrm{CZ} on output 37, output 75, \mathrm{CZ} on output 37, output 76, \mathrm{CZ} on output 37, output 77, \mathrm{CZ} on output 37, output 80, \mathrm{CZ} on output 37, output 82, \mathrm{CZ} on output 37, output 83, \mathrm{CZ} on output 37, output 84, \mathrm{CZ} on output 37, output 85, \mathrm{CZ} on output 37, check 87, \mathrm{CZ} on output 37, check 90, \mathrm{CZ} on output 37, check 93, \mathrm{CZ} on output 37, check 95, \mathrm{CZ} on output 37, check 97, \mathrm{CZ} on output 38, output 39, \mathrm{CZ} on output 38, output 40, \mathrm{CZ} on output 38, output 42, \mathrm{CZ} on output 38, output 44, \mathrm{CZ} on output 38, output 47, \mathrm{CZ} on output 38, output 54, \mathrm{CZ} on output 38, output 55, \mathrm{CZ} on output 38, output 56, \mathrm{CZ} on output 38, output 57, \mathrm{CZ} on output 38, output 58, \mathrm{CZ} on output 38, output 64, \mathrm{CZ} on output 38, output 65, \mathrm{CZ} on output 38, output 69, \mathrm{CZ} on output 38, output 73, \mathrm{CZ} on output 38, output 75, \mathrm{CZ} on output 38, output 76, \mathrm{CZ} on output 38, output 77, \mathrm{CZ} on output 38, output 80, \mathrm{CZ} on output 38, output 82, \mathrm{CZ} on output 38, output 83, \mathrm{CZ} on output 38, output 84, \mathrm{CZ} on output 38, output 85, \mathrm{CZ} on output 38, check 87, \mathrm{CZ} on output 38, check 90, \mathrm{CZ} on output 38, check 93, \mathrm{CZ} on output 38, check 95, \mathrm{CZ} on output 38, check 97, \mathrm{CZ} on output 39, output 40, \mathrm{CZ} on output 39, output 42, \mathrm{CZ} on output 39, output 44, \mathrm{CZ} on output 39, output 47, \mathrm{CZ} on output 39, output 54, \mathrm{CZ} on output 39, output 55, \mathrm{CZ} on output 39, output 56, \mathrm{CZ} on output 39, output 57, \mathrm{CZ} on output 39, output 58, \mathrm{CZ} on output 39, output 64, \mathrm{CZ} on output 39, output 65, \mathrm{CZ} on output 39, output 69, \mathrm{CZ} on output 39, output 73, \mathrm{CZ} on output 39, output 75, \mathrm{CZ} on output 39, output 76, \mathrm{CZ} on output 39, output 77, \mathrm{CZ} on output 39, output 80, \mathrm{CZ} on output 39, output 82, \mathrm{CZ} on output 39, output 83, \mathrm{CZ} on output 39, output 84, \mathrm{CZ} on output 39, output 85, \mathrm{CZ} on output 39, check 87, \mathrm{CZ} on output 39, check 90, \mathrm{CZ} on output 39, check 93, \mathrm{CZ} on output 39, check 95, \mathrm{CZ} on output 39, check 97, \mathrm{CZ} on output 40, output 42, \mathrm{CZ} on output 40, output 44, \mathrm{CZ} on output 40, output 47, \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 57, \mathrm{CZ} on output 40, output 58, \mathrm{CZ} on output 40, output 64, \mathrm{CZ} on output 40, output 65, \mathrm{CZ} on output 40, output 69, \mathrm{CZ} on output 40, output 73, \mathrm{CZ} on output 40, output 75, \mathrm{CZ} on output 40, output 76, \mathrm{CZ} on output 40, output 77, \mathrm{CZ} on output 40, output 80, \mathrm{CZ} on output 40, output 82, \mathrm{CZ} on output 40, output 83, \mathrm{CZ} on output 40, output 84, \mathrm{CZ} on output 40, output 85, \mathrm{CZ} on output 40, check 87, \mathrm{CZ} on output 40, check 90, \mathrm{CZ} on output 40, check 93, \mathrm{CZ} on output 40, check 95, \mathrm{CZ} on output 40, check 97, \mathrm{CZ} on output 42, output 44, \mathrm{CZ} on output 42, output 47, \mathrm{CZ} on output 42, output 54, \mathrm{CZ} on output 42, output 55, \mathrm{CZ} on output 42, output 56, \mathrm{CZ} on output 42, output 57, \mathrm{CZ} on output 42, output 58, \mathrm{CZ} on output 42, output 64, \mathrm{CZ} on output 42, output 65, \mathrm{CZ} on output 42, output 69, \mathrm{CZ} on output 42, output 73, \mathrm{CZ} on output 42, output 75, \mathrm{CZ} on output 42, output 76, \mathrm{CZ} on output 42, output 77, \mathrm{CZ} on output 42, output 80, \mathrm{CZ} on output 42, output 82, \mathrm{CZ} on output 42, output 83, \mathrm{CZ} on output 42, output 84, \mathrm{CZ} on output 42, output 85, \mathrm{CZ} on output 42, check 87, \mathrm{CZ} on output 42, check 90, \mathrm{CZ} on output 42, check 93, \mathrm{CZ} on output 42, check 95, \mathrm{CZ} on output 42, check 97, \mathrm{CZ} on output 44, output 47, \mathrm{CZ} on output 44, output 54, \mathrm{CZ} on output 44, output 55, \mathrm{CZ} on output 44, output 56, \mathrm{CZ} on output 44, output 57, \mathrm{CZ} on output 44, output 58, \mathrm{CZ} on output 44, output 64, \mathrm{CZ} on output 44, output 65, \mathrm{CZ} on output 44, output 69, \mathrm{CZ} on output 44, output 73, \mathrm{CZ} on output 44, output 75, \mathrm{CZ} on output 44, output 76, \mathrm{CZ} on output 44, output 77, \mathrm{CZ} on output 44, output 80, \mathrm{CZ} on output 44, output 82, \mathrm{CZ} on output 44, output 83, \mathrm{CZ} on output 44, output 84, \mathrm{CZ} on output 44, output 85, \mathrm{CZ} on output 44, check 87, \mathrm{CZ} on output 44, check 90, \mathrm{CZ} on output 44, check 93, \mathrm{CZ} on output 44, check 95, \mathrm{CZ} on output 44, check 97, \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 57, \mathrm{CZ} on output 47, output 58, \mathrm{CZ} on output 47, output 64, \mathrm{CZ} on output 47, output 65, \mathrm{CZ} on output 47, output 69, \mathrm{CZ} on output 47, output 73, \mathrm{CZ} on output 47, output 75, \mathrm{CZ} on output 47, output 76, \mathrm{CZ} on output 47, output 77, \mathrm{CZ} on output 47, output 80, \mathrm{CZ} on output 47, output 82, \mathrm{CZ} on output 47, output 83, \mathrm{CZ} on output 47, output 84, \mathrm{CZ} on output 47, output 85, \mathrm{CZ} on output 47, check 87, \mathrm{CZ} on output 47, check 90, \mathrm{CZ} on output 47, check 93, \mathrm{CZ} on output 47, check 95, \mathrm{CZ} on output 47, check 97, \mathrm{CZ} on output 54, output 55, \mathrm{CZ} on output 54, output 56, \mathrm{CZ} on output 54, output 57, \mathrm{CZ} on output 54, output 58, \mathrm{CZ} on output 54, output 64, \mathrm{CZ} on output 54, output 65, \mathrm{CZ} on output 54, output 69, \mathrm{CZ} on output 54, output 73, \mathrm{CZ} on output 54, output 75, \mathrm{CZ} on output 54, output 76, \mathrm{CZ} on output 54, output 77, \mathrm{CZ} on output 54, output 80, \mathrm{CZ} on output 54, output 82, \mathrm{CZ} on output 54, output 83, \mathrm{CZ} on output 54, output 84, \mathrm{CZ} on output 54, output 85, \mathrm{CZ} on output 54, check 87, \mathrm{CZ} on output 54, check 90, \mathrm{CZ} on output 54, check 93, \mathrm{CZ} on output 54, check 95, \mathrm{CZ} on output 54, check 97, \mathrm{CZ} on output 55, output 56, \mathrm{CZ} on output 55, output 57, \mathrm{CZ} on output 55, output 58, \mathrm{CZ} on output 55, output 64, \mathrm{CZ} on output 55, output 65, \mathrm{CZ} on output 55, output 69, \mathrm{CZ} on output 55, output 73, \mathrm{CZ} on output 55, output 75, \mathrm{CZ} on output 55, output 76, \mathrm{CZ} on output 55, output 77, \mathrm{CZ} on output 55, output 80, \mathrm{CZ} on output 55, output 82, \mathrm{CZ} on output 55, output 83, \mathrm{CZ} on output 55, output 84, \mathrm{CZ} on output 55, output 85, \mathrm{CZ} on output 55, check 87, \mathrm{CZ} on output 55, check 90, \mathrm{CZ} on output 55, check 93, \mathrm{CZ} on output 55, check 95, \mathrm{CZ} on output 55, check 97, \mathrm{CZ} on output 56, output 57, \mathrm{CZ} on output 56, output 58, \mathrm{CZ} on output 56, output 64, \mathrm{CZ} on output 56, output 65, \mathrm{CZ} on output 56, output 69, \mathrm{CZ} on output 56, output 73, \mathrm{CZ} on output 56, output 75, \mathrm{CZ} on output 56, output 76, \mathrm{CZ} on output 56, output 77, \mathrm{CZ} on output 56, output 80, \mathrm{CZ} on output 56, output 82, \mathrm{CZ} on output 56, output 83, \mathrm{CZ} on output 56, output 84, \mathrm{CZ} on output 56, output 85, \mathrm{CZ} on output 56, check 87, \mathrm{CZ} on output 56, check 90, \mathrm{CZ} on output 56, check 93, \mathrm{CZ} on output 56, check 95, \mathrm{CZ} on output 56, check 97, \mathrm{CZ} on output 57, output 58, \mathrm{CZ} on output 57, output 64, \mathrm{CZ} on output 57, output 65, \mathrm{CZ} on output 57, output 69, \mathrm{CZ} on output 57, output 73, \mathrm{CZ} on output 57, output 75, \mathrm{CZ} on output 57, output 76, \mathrm{CZ} on output 57, output 77, \mathrm{CZ} on output 57, output 80, \mathrm{CZ} on output 57, output 82, \mathrm{CZ} on output 57, output 83, \mathrm{CZ} on output 57, output 84, \mathrm{CZ} on output 57, output 85, \mathrm{CZ} on output 57, check 87, \mathrm{CZ} on output 57, check 90, \mathrm{CZ} on output 57, check 93, \mathrm{CZ} on output 57, check 95, \mathrm{CZ} on output 57, check 97, \mathrm{CZ} on output 58, output 64, \mathrm{CZ} on output 58, output 65, \mathrm{CZ} on output 58, output 69, \mathrm{CZ} on output 58, output 73, \mathrm{CZ} on output 58, output 75, \mathrm{CZ} on output 58, output 76, \mathrm{CZ} on output 58, output 77, \mathrm{CZ} on output 58, output 80, \mathrm{CZ} on output 58, output 82, \mathrm{CZ} on output 58, output 83, \mathrm{CZ} on output 58, output 84, \mathrm{CZ} on output 58, output 85, \mathrm{CZ} on output 58, check 87, \mathrm{CZ} on output 58, check 90, \mathrm{CZ} on output 58, check 93, \mathrm{CZ} on output 58, check 95, \mathrm{CZ} on output 58, check 97, \mathrm{CZ} on output 64, output 65, \mathrm{CZ} on output 64, output 69, \mathrm{CZ} on output 64, output 73, \mathrm{CZ} on output 64, output 75, \mathrm{CZ} on output 64, output 76, \mathrm{CZ} on output 64, output 77, \mathrm{CZ} on output 64, output 80, \mathrm{CZ} on output 64, output 82, \mathrm{CZ} on output 64, output 83, \mathrm{CZ} on output 64, output 84, \mathrm{CZ} on output 64, output 85, \mathrm{CZ} on output 64, check 87, \mathrm{CZ} on output 64, check 90, \mathrm{CZ} on output 64, check 93, \mathrm{CZ} on output 64, check 95, \mathrm{CZ} on output 64, check 97, \mathrm{CZ} on output 65, output 69, \mathrm{CZ} on output 65, output 73, \mathrm{CZ} on output 65, output 75, \mathrm{CZ} on output 65, output 76, \mathrm{CZ} on output 65, output 77, \mathrm{CZ} on output 65, output 80, \mathrm{CZ} on output 65, output 82, \mathrm{CZ} on output 65, output 83, \mathrm{CZ} on output 65, output 84, \mathrm{CZ} on output 65, output 85, \mathrm{CZ} on output 65, check 87, \mathrm{CZ} on output 65, check 90, \mathrm{CZ} on output 65, check 93, \mathrm{CZ} on output 65, check 95, \mathrm{CZ} on output 65, check 97, \mathrm{CZ} on output 69, output 73, \mathrm{CZ} on output 69, output 75, \mathrm{CZ} on output 69, output 76, \mathrm{CZ} on output 69, output 77, \mathrm{CZ} on output 69, output 80, \mathrm{CZ} on output 69, output 82, \mathrm{CZ} on output 69, output 83, \mathrm{CZ} on output 69, output 84, \mathrm{CZ} on output 69, output 85, \mathrm{CZ} on output 69, check 87, \mathrm{CZ} on output 69, check 90, \mathrm{CZ} on output 69, check 93, \mathrm{CZ} on output 69, check 95, \mathrm{CZ} on output 69, check 97, \mathrm{CZ} on output 73, output 75, \mathrm{CZ} on output 73, output 76, \mathrm{CZ} on output 73, output 77, \mathrm{CZ} on output 73, output 80, \mathrm{CZ} on output 73, output 82, \mathrm{CZ} on output 73, output 83, \mathrm{CZ} on output 73, output 84, \mathrm{CZ} on output 73, output 85, \mathrm{CZ} on output 73, check 87, \mathrm{CZ} on output 73, check 90, \mathrm{CZ} on output 73, check 93, \mathrm{CZ} on output 73, check 95, \mathrm{CZ} on output 73, check 97, \mathrm{CZ} on output 75, output 76, \mathrm{CZ} on output 75, output 77, \mathrm{CZ} on output 75, output 80, \mathrm{CZ} on output 75, output 82, \mathrm{CZ} on output 75, output 83, \mathrm{CZ} on output 75, output 84, \mathrm{CZ} on output 75, output 85, \mathrm{CZ} on output 75, check 87, \mathrm{CZ} on output 75, check 90, \mathrm{CZ} on output 75, check 93, \mathrm{CZ} on output 75, check 95, \mathrm{CZ} on output 75, check 97, \mathrm{CZ} on output 76, output 77, \mathrm{CZ} on output 76, output 80, \mathrm{CZ} on output 76, output 82, \mathrm{CZ} on output 76, output 83, \mathrm{CZ} on output 76, output 84, \mathrm{CZ} on output 76, output 85, \mathrm{CZ} on output 76, check 87, \mathrm{CZ} on output 76, check 90, \mathrm{CZ} on output 76, check 93, \mathrm{CZ} on output 76, check 95, \mathrm{CZ} on output 76, check 97, \mathrm{CZ} on output 77, output 80, \mathrm{CZ} on output 77, output 82, \mathrm{CZ} on output 77, output 83, \mathrm{CZ} on output 77, output 84, \mathrm{CZ} on output 77, output 85, \mathrm{CZ} on output 77, check 87, \mathrm{CZ} on output 77, check 90, \mathrm{CZ} on output 77, check 93, \mathrm{CZ} on output 77, check 95, \mathrm{CZ} on output 77, check 97, \mathrm{CZ} on output 80, output 82, \mathrm{CZ} on output 80, output 83, \mathrm{CZ} on output 80, output 84, \mathrm{CZ} on output 80, output 85, \mathrm{CZ} on output 80, check 87, \mathrm{CZ} on output 80, check 90, \mathrm{CZ} on output 80, check 93, \mathrm{CZ} on output 80, check 95, \mathrm{CZ} on output 80, check 97, \mathrm{CZ} on output 82, output 83, \mathrm{CZ} on output 82, output 84, \mathrm{CZ} on output 82, output 85, \mathrm{CZ} on output 82, check 87, \mathrm{CZ} on output 82, check 90, \mathrm{CZ} on output 82, check 93, \mathrm{CZ} on output 82, check 95, \mathrm{CZ} on output 82, check 97, \mathrm{CZ} on output 83, output 84, \mathrm{CZ} on output 83, output 85, \mathrm{CZ} on output 83, check 87, \mathrm{CZ} on output 83, check 90, \mathrm{CZ} on output 83, check 93, \mathrm{CZ} on output 83, check 95, \mathrm{CZ} on output 83, check 97, \mathrm{CZ} on output 84, output 85, \mathrm{CZ} on output 84, check 87, \mathrm{CZ} on output 84, check 90, \mathrm{CZ} on output 84, check 93, \mathrm{CZ} on output 84, check 95, \mathrm{CZ} on output 84, check 97, \mathrm{CZ} on output 85, check 87, \mathrm{CZ} on output 85, check 90, \mathrm{CZ} on output 85, check 93, \mathrm{CZ} on output 85, check 95, \mathrm{CZ} on output 85, check 97, \mathrm{CZ} on check 87, check 90, \mathrm{CZ} on check 87, check 93, \mathrm{CZ} on check 87, check 95, \mathrm{CZ} on check 87, check 97, \mathrm{CZ} on check 90, check 93, \mathrm{CZ} on check 90, check 95, \mathrm{CZ} on check 90, check 97, \mathrm{CZ} on check 93, check 95, \mathrm{CZ} on check 93, check 97, \mathrm{CZ} on check 95, check 97
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 0, 3, 10, 11, 30, 33, 39, 41, 45, 55, 57, 67, 69, 74, 77, 80, 83, 84, 93, 94, 102, 107, 110, 111 and 125 more (listed below); \mathrm{T}^5 on rotations 1, 5, 6, 7, 8, 9, 13, 16, 17, 19, 24, 28, 31, 54, 61, 70, 71, 73, 75, 101, 200; \mathrm{T}^\dagger on rotations 2, 4, 12, 14, 18, 20, 22, 23, 29, 34, 36, 37, 38, 43, 44, 47, 48, 50, 51, 53, 56, 59, 60, 63 and 11 more (listed below), and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.
All 149 rotations at T³
0, 3, 10, 11, 30, 33, 39, 41, 45, 55, 57, 67, 69, 74, 77, 80, 83, 84, 93, 94, 102, 107, 110, 111, 112, 113, 114, 115, 116, 117, 118, 121, 124, 127, 129, 130, 131, 133, 135, 136, 137, 139, 140, 142, 144, 148, 151, 152, 153, 155, 156, 157, 160, 165, 169, 170, 173, 175, 179, 186, 194, 196, 198, 199, 203, 205, 208, 211, 213, 215, 216, 217, 219, 223, 225, 226, 230, 232, 233, 234, 239, 241, 242, 244, 245, 246, 247, 249, 250, 251, 252, 254, 257, 259, 262, 265, 266, 268, 270, 272, 273, 274, 278, 279, 283, 286, 287, 288, 291, 293, 295, 296, 297, 298, 299, 301, 306, 307, 311, 314, 317, 318, 320, 321, 322, 324, 325, 326, 328, 330, 331, 332, 334, 336, 337, 338, 340, 342, 344, 345, 346, 348, 349, 351, 352, 353, 356, 357, 358
All 35 rotations at T†
2, 4, 12, 14, 18, 20, 22, 23, 29, 34, 36, 37, 38, 43, 44, 47, 48, 50, 51, 53, 56, 59, 60, 63, 78, 81, 86, 95, 97, 109, 122, 187, 191, 193, 209
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/359.87.3.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-359.87.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 3,365 faults of weight 3 are undetectable and damaging, so A_{3}=3{,}365. 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 [0,8,130].
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_359_87_3_b8ef19793a88.json",
"label": "paired_column_contraction_359_87_3_b8ef19793a88",
"N": 98,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=112), with searched graph punctures; 1 paired-column contraction",
"provenance": "gamma frontier release record paired_column_contraction_359_87_3_b8ef19793a88 (source catalogue id paired_column_contraction_359_87_3_b8ef19793a88); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=112), with searched graph punctures; 1 paired-column contraction; matrix b8ef19793a88ca32...; the release states d=3 (exact), gamma=1.290186068783266 (exact)",
"notes": "matrix gamma_frontier_release/matrices/b8ef19793a88ca322c4e8c6388c9ded9c5ed92442e6d769410a93d3c73abbff6.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/359.87.3.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[997].