The circuit
The 82\times309 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.
| wire | 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 |
|---|---|
| out 0 (127) | 1111·11··11·1·1···11··········11·1·1····1·1···1···1·11··11·11·11···11······1·1··1·1··11·1·····11··1111·····1·111····1·111···1··1····1·111·1·1···1··1·······1111111·1··11·11····11·········1·1·11····1·1·1·111··11··11·11··11·····1·1·····1·1··1111····111111········1·1·1·1····1·111··1··1···1·111··11··11········1·1 |
| out 1 (125) | ·1·1·111111·1·1·1·1··1··1·111·1·····1·1·······1······1·····1····1·······1···1··1111·1·1····1··1···111··111111111·····1·11·1····1··1·11·1··1····1·1·11·1···1·1·1·11·11111·11··1·1·1··1··1111······1·1····1···1······1····1·····1···1·····1111·1·1···1··1·111··111··1·111·1·1·····1·111··1·1···11·1···1··1·11·1··1····1 |
| out 2 (119) | ··11·1··11111···1·1111··1···1··111··11····1··1·1··1·····1···1··11···1···1··11···1111·11·····1·········111·1··1··1·1···111·1·1··1···1···111·········1··11·1·····111···11111···1·111··1····1··111··11···11·11····1····1··11··1··1··11······1111·11····1·······111···1···1·····1·1··1111·1··1··1···111······1··111······ |
| out 3 (119) | ·11··11·111·1···1··1······1····1···1·1··1·1···1·····1··1·1·1··111··11···1·1··1·11··111··1··1111···1··1·11·11··1··1····1····1·1·1···1····1···1·1·····1··1·1·1··11·1·1·111·1···1··1······1····1··1··1·1·1·1··1·1··1··1··111·11··111··1····11··111··1·1111·1··1·11···1·1···1····1···1···1··11··1····1···11···1··11···1·· |
| out 4 (127) | 1··1·1··1111··1···1··1··1·11··1··1········1···1···1··1·11··11··11·······1·111··11·1111·····11··1····1·11·····1·1·11·1··1···1·1·····11·11·11·1·1·1··11··1···111··11···1111·1····1·11·1··11·1···1·······1·1·1·11·1···11··11·····1·111·····11·1111····11··1··1·11········1···1··111··1··1··1···11·11·1·111·111··1····1·1 |
| out 5 (109) | 1··1··1··11·1·····1·····1·11·······1··1········1····1··1·1·1··11···1·········1·1····1·1·1··11··1··1··11·11··111·1···1··11··1···1···1·1·1·······111·11··1·111·1··1··1··11·1·····1····1··11······1···1·····1·1·1··11·1··11··1········1····1····1·1·1·11··11··11·11·····11·1···1··1··11·1·1·1··1·1·1······1111··111··1·· |
| out 6 (111) | 1··1·1···1·1··1···1··1····11··1··1········1···1···1··1·11···11·11·······1·11··111·11·11····11··1····1··11····1·1·11·1··1···1·1·····11·11····1·1·1··11··1·····1··11····1·1·1····1·1·····11·1···1·······1·1·1·11·1····11·11·····1·11······11·11·11···11··1··1··11·······1···1··111··1··1··1···11·11····11·111··1······· |
| out 7 (135) | 1111·11···111·1·1111··········1111·1·1····1··11···1·11··11·11·11···11······1·1··1·1···1·1····11···1111·····1·1·1··1·11111··11··1····1·111·1·1···1··1·······1111111·1···1111··1·11·········1·1111··1···111·111··11··11·11··11·····1·1·····1·1···1·1···11·1111········1·1···1···111111·11··1···1·111··11··11········1·1 |
| out 8 (119) | 1··1··111·11··1·1·1··1····11··1··1········1···1···1··1·11··11··11·······1·111··1····1·······11·1····1··11····1·1·11·1··1···1·1·····11·11·11·1·1·1··11··1···111··1··111·11·11·1·1·1·····11·1···1·······1·1·1·11·1···11··11·····1·111·····1····1······11·1··1··11·······1···1··111··1··1··1···11·11·1·111·111··1····1·1 |
| out 9 (111) | ·1·1·1··11·1····1·1··1····1·1····1·1······1··111··1·1··111··1·11···1······11·1·111···11·1··1·········11·1··1·1··1·1··1·1··1111·········1······1····11·1··1····1·11···11·1····111·1·····1·1····11······111111·1·11···1·11··1·····11·1····111···11·1·1·······11·1·····1·1·····1·1·1·1·111·1·······1·····1··11·1·1······ |
| out 10 (141) | 1·1··1111··1·1··1··1·1··1·111··1·1·11·1·1·1·······1·1··1·1·111111··11···1··111·1111·11·····1···1·····1·1111·1·······111···1·1·······111·111·1··111··1·1···11·1·1·1·111··1····1··11··1··111··1·11·1·11·1···11·1··1··111111·11··1··111····1111·11····1···1···1·111··1··1·········111··1·11·····111·11·11·11·1·1··1··1·· |
| out 11 (117) | ·11·····11·1··1·1··1·1··1·1···11·1·1111······1·1··1··1·1····11·1····1······1···1··1········1111·····1·1·11111··1111··11·1··········1·1··1······1·1··1··1·11·1·11·····11·1·1··1··11··1··1··1·1·11·111···1·11·11······11·1···1·····1······1··1·······1111···1·1·11··1·11····11111·11·1···1····1·1··1·····1··1··111····1 |
| out 12 (117) | ·1·1······11····1·1·······111·1·11·1·1·········11·1·1··11··11·11··········1111·1·1··1···1··1··1····1·11·1·11111·1····1·11·1··1·······1·1·1····1··1·11·1··1·1··1·1······11····1·1·······1111··111··1······111·1·1···11·11········1111····1·1··1···1·1··1··1·11·1···1·111·1···1···1·111··11·····1·1·1···1··11·1·1···1·· |
| out 13 (111) | ·11··1··1·1·1······1····1·1···1111·111····1·········1··1·1····1·1··11···1·1·11·11·111···1··11·1···1··1·1··111········11····111·1···1····11····1·····1··1······11·1···1·1·1······1···1··1··1·1111·11···1····1·1··1·····1·1·11··1·1·11····11·111···1·11·1·1··1·1····1·11···1······11···11·11··1····11···1···1··1······· |
| out 14 (127) | 1111··1·1·111·1·1·11·1·······111·1·1·1·······1····1·11··11·11·11···11······1·1····1·1·1·1····111··1·11·······111··1·1111···1···1····1·111·1·1···1··1·······111111··1·1·1111··1·111········1·1·11··1····1··111··11··11·11··11·····1·1·······1·1·1·1···1111·11··········1·1·1···11111··1···1···1·111··11··11········1·1 |
| out 15 (125) | 1·1···1····1·······1····1·1·1··111·11·1······11···1·1··1···11·1·1··11···1··111·1·111·1··1··1·1·1···1·1·111··1·1·····1·1·1·11·······11·1·11·····111··1·1···11·1·1···1····1·······1···1··1·1··1111·1·1···11·11·11····11·1·1·11··1··111····1·111·1··1·1·1·1·1·1·111·····1··1······1·1·111·1····11·1·11····11·1·1··1··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···11········1·1 |
| out 17 (119) | 1··1···11··1··1·1·1··1····1···1··1···1············1··1·11··11··11·······1·111··1··1·1·1····111·1····1···1·1··1·1·1··1··11··111·····11·11·11·1·1·1··11··1···111··1···11··1·1··1·1·1·1···1··1···1···1·······1·11·1···11··11·····1·111·····1··1·1·1···111·1··1···1···1···1···1··1·1··11·11·1···11·11·1·111·111··1····1·1 |
| out 18 (133) | 1··1·1·1··1·1·····1·····1·1········11·1······111····1··1·1·1·111···11·······11·11·11111·1··11··1··1··11·111·111·11··1··11···1··1···1·111··1····111111··1·11··1··11··1··1·1·····1····1··1·······1·1·1···111·1·1··1··1·111··11······11····11·11111·1·11··11··11·11··1··11·1···11·1··11··11·1··1·111···1··1111··111····· |
| out 19 (127) | ·1·1··111··1······1·····111·1·1·11·11·····1··111··1·1··111··1·11···1······11·1·1·111··1·1··1·11····1·11····1111·111··1·1··1111·········1······1····11·1··1····1·1··111··1······1····1·11·11··111·1····111111·1·11···1·11··1·····11·1····1·111··1·1·1·11··1·11···1···111·1···111·1·1·111·1·······1·····1··11·1·1······ |
| out 20 (119) | 11····1·11····1·1····1··········1··111········11····11···1·1··1·1··1····1···11···1·1·1··1···1·11···11111··111·111·1·11····11·······11·1··11·1···1·····11·1·1111····1·11···1··1···1···········1·1·11·····11·11···1··1··1·1·1···1···11······1·1·1··1··1·11·11111····1111··1·1·1·111···11······11·1··1·11··1···111···1·1 |
| out 21 (125) | 1111····1·1·······11·11········11····11······1·1········1··1·1··1···1···1·1·1······1·1········11···11·1111·1111·11··1111···111······1111111·1·1111·1·····111·1111····1·1·······111··········11····11···1·1·····1···1·1··1··1··1·1·1·········1·1·······11·11·1111····111·1···11·1111··1111····111111·111111····11··1·· |
| out 22 (141) | 1··1·11··11·1·1·1·1··1··1·1·····1··1··1·1·1··111····1··111·1·11····1·········1·11···1·1·11·111·1··11·11·111·11··1···11·1····1··1···11111··1·1··111·11··1·111·1··11·1··11·11··1·1·1··1··1·····1·1···11·1111·1·1·11··1·11···1········1····11···1·1·1·111·111·11·11··1··11·····1··11·1···11·1··11111···11·1111··111··1·· |
| out 23 (125) | ·1·1····1·1·1·1·1·1··1··1·111·1·····1·1·······1······1·11··1···111······1···1··1·1·1111····1··1···111··111111111·····1·11·1····1·····1·1··1·1·11·1·11·1···1·1·1·1····1·1·11··1·1·1··1··1111······1·1····1···11·1···1···11·····1···1·····1·1·1111···1··1·111··111··1·111·1·1·····1·111··1·1····1·1···1111·11·1··1····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 (133) | ··11·1·1111···1·1·11·1······1·111··1··1···1···1·····11········1·1··11·····1··1··11111···1···1······111··111·1111··1···111·1111·····11··11·1··111·1·1··11··1·1··111··1111··1··1·111·······11·11·1···1··1·1··11·········1·1·11····1··1·····11111···1··1····111··11··1··11·1·1···1··11111111···11··11··1·11·1··11·1····1 |
| out 26 (117) | ·····1·11··11·1·1····1···········111··1···1··1·1··1·11···1··11111··1····1·1111··1····11·1····1····1·111111····1·111·····1··111·1·····1···1····11·1·······11·1····1··11··111··1···1············11···1··11·1111···1···11111·1···1·1111·····1····11·1···1··1·111111········1···111····1·11111····1···1···11······11····1 |
| out 27 (125) | ·····1·11··11·1·1····1·····1··1··1·11·1···1··1·1··1·11··1···11··1··1····1·1111··1····11·1····1····1·1111111·1·111·1·····1··111·1····1····1·11·11·1·······11·1····1··11··111··1···1······1·1···11·1·1··11·1111··1····11··1·1···1·1111·····1····11·1···1··1·111111··1··1··1·1·1·1····1·11111···1····1··111······11····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 (125) | 11···1·11·111···1····1·11···1····1··1·1···1·······1········111·1··········11····111111······1·11··1··1···1111·1··11·11··1·11·1·1···1111···1·1·1111····11··11·11··1··11·111···1···1··1····1····1··1·1··1···1········111·1········11·······111111·····1·111··1···1··1·11··1····1111··111·111··1111····11111···11·1··1·· |
| out 30 (111) | ·11··1··1·1·1······1····1·11···11··11·····1·········1··11··1··1·1··11···1·1·11·11·111···1··11·1···1··1·1···1······1··11····111·1···111··1·····11····1··1······11·1···1·1·1······1···1··11···11·1·1····1····1·1·1···1··1·1111··1·1·11····11·111···1·11·1·1··1·1······1·········1·11···11·11··111··1····11··1··1······· |
| out 31 (127) | ·1·1·1··11·1······1·····1·111·1·11·1··1···1··111··1·1··111··1·11···1······11·1·111···11·1··1·11····1·11···11111·1·11·1·1··1111·········1······1····11·1··1····1·11···11·1······1····1··1111··111···1··111111·1·11···1·11··1·····11·1····111···11·1·1·11··1·11·····1·111·1···1·1·1·1·111·1·······1·····1··11·1·1······ |
| out 32 (125) | ·····1···1111·1·1····1·····1··1··1·11·1···1··1·1··1·11··1··1··1·1··1····1·1111··1··11···1····1····1·1111111·1·111·1·····1··111·1····1·····1·1·11·1·······11·1····1····11111··1···1······1·1···11·1·1··11·1111··1···1··1·1·1···1·1111·····1··11···1···1··1·111111··1··1··1·1·1·1····1·11111···1·····11111······11····1 |
| out 33 (127) | 11···11··11·1·1············11·1·1··11···1·1··1·1····11···1·1··1·1··1····1···11··11·111111···1111····1111···1··111···1···1·1·1······11·1··11·1···1·····11·1·1111··1·1··11·11·············111··1·1·1··1·11·1·11···1··1··1·1·1···1···11·····11·1111·1··1111··1111······1···1·1·1··1···11·1·····11·1··1·11··1···111···1·1 |
| out 34 (127) | ·1·1·1·1··11······1·····1·111·1·11·111····1··111··1·1··111··1·11···1······11·1·111·11···1··1·11····1·11···11111··1···1·1··1111·········1······1····11·1··1····1·11··1··11······1····1··1111··111111···111111·1·11···1·11··1·····11·1····111·11···1·1·11··1·11·····1·111·1····1··1·1·111·1·······1·····1··11·1·1······ |
| out 35 (93) | 11·········11···············1···11····1·1·········1······1··1·············111····11··11·····1111··11····11111·····1·1·····11·1·1···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···111···1··1····· |
| out 36 (119) | 1··1····1·11··1·1·1··1··1··1··1··1···1····1··1····1··1·11··11··11·······1·111··1··111······111·1····1··1·····1·1·1··1··1····11·····11·11·11·1·1·1··11··1···111··1····1·11·1··1·1·1··1···1·1···1···1···11··1·11·1···11··11·····1·111·····1··111·····111·1··1··1···1····1···1··1·1··1···1·1···11·11·1·111·111··1····1·1 |
| out 37 (127) | 11···11···1···1······1··1···1···1··11·····1·11·1····11···1·1··1·1··1····1···11··11·11·1·1···1111···111111·111·111···11··1···1······11·1··11·1···1·····11·1·1111··1·1···1··1······1··1····1···1·1·1····11·1·11···1··1··1·1·1···1···11·····11·11·1·1··1111·111111···1·11··1·1·1··11··1··1·····11·1··1·11··1···111···1·1 |
| out 38 (133) | 1··1·11···1·1········1··1·1········11·1······111····1··111·1·11····1·········1·11···111·1··11··11·11·11·111·111·11··1··11···1··1···11111··1·1··111·11··1·111·1··11·1···1·1·······1··1··1·······1·1·1···111·1·1·11··1·11···1········1····11···111·1·11··111·11·11··1··11·1···11·1··11··11·1··11111···11·1111··111··1·· |
| out 39 (119) | 1··1····1·11··1·1·1··1··1·1···1··1··1·········1··11··1·11··11··11·······1·111··1··111······111·1····1··1··1··1·1··1·1··11··1·······11·11·11·1·1·1··11··1···111··1····1·11·1··1·1·1··1··1··1···1··1······1·1·11·1···11··11·····1·111·····1··111·····111·1··1··1····1···1···1···11··11·1······11·11·1·111·111··1····1·1 |
| out 40 (109) | ·1·1·111···1····1··1······1·1·11····11····11······1·1··1·1·1·1··········1··111·······1··1··1···1··1·1·1·1·····1111···1·11··11·······111·1···1·1··1·1·1·1··11··1·11·11···1····1··1······1·11·1····11···1···11·1··1··1·1········1··111··········1··1·1···11·1·1·1·········1·1·11··1·11·111·····111·1···11··1·1·1·1··1·· |
| out 41 (125) | ··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··1·11·····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····11·1··11·1····1 |
| out 42 (127) | ···1····1111··1···1·····1·11··1·11··1···1·····1···1··1·11··11··11·······1·111··1··1111·····11··1···11··1·····111··1·11·11··1·1·····11·11·11·1·1·1··11··1···11···1····1111·1····1····1··11·1··11··1··1···1·1·11·1···11··11·····1·111·1···1··1111····11··1·11··1········1·1·1···111·11·1··1···11·11·1·111·111··1····1·1 |
| out 43 (125) | 1111··1111······1·11····1·····11····1·1·1····1·1·····1··1··1·1··1···1···1·1·1·····1···1······111······11·1·1·1··1·1·1·11···111··1···1111111·1·1111·1·····111·1111··1111······1·11···1·····1·1····1·11··1·1··1··1···1·1··1··1··1·1·1········1···1·····111····11·1····1·1·····1·11·11··1111····111111·111111····11··1·· |
| out 44 (133) | 1·1··1·1·1·1·······1····1·111··1·1·1·11·1····1····1·1··111·11·111··11·1·1··1·1·111······1··1·1·1···1·1·1111·1····11·111·1·111········11·11··1··111····1···1··1·1·1··1·1·1·······1···1··111··1·11··111··1··11·1·11··11·111·11··1··1·1····111······1·1·1·1·1·1·111··1··1·······11111·11111······11·11··1·11···1··1····· |
| out 45 (109) | ·11·····11·1··1·1··1·1··1·1···1111····1·111····1··1··1·1····11·1····1······1···1··1········1111·····1·1·11111·111··········1·······1·1··1······1·1··1··1·11·1·11·····11·1·1··1··11··1··1··1·111····11·1··11·11······11·1···1·····1······1··1·······1111···1·1·11··1·11··1·1·1········1·1····1·1··1·····1··1··111····1 |
| out 46 (117) | 111··1111·111···1····1······1···11····1·1·········1········111·1··········11····11·111······1·11··1·····11111·····1·1·····11·1·1···1111···1·1·1111····11··11·111·1·111·111···1···1·······1···11····11·····1········111·1········11····1··11·111·····1·111·····11··1·11········11····11·111··1111····11111···11·1··1·· |
| out 47 (109) | ········1··11·1······1··1·····1··1·1111······111··1·11··1···1·1·1··1····1·1··1·····1·11·1·········1·1111·1··1·111··········1·1·1····1····11·1·11·1·······1111········1··111······1··1·····1···11·111···111111··1····1·1·1·1···1·1··1········1·11·1······1·1111·1·····1··1·1·1········1·111···1····1·1111······11·11·1 |
| out 48 (119) | ·111·11·11111···1·11·1······1··1·1··1···1·1····1··1·····1···1··11···1···1··11···11·1·11·····1·····1···11··1··11·1····1111·111··1···1···111·········1··11·1····1111·1·11111···1·111·······1··1·1··1··1·1··11····1····1··11··1··1··11··1···11·1·11····1···1···11····1···1·1···1···1111111··1··1···111······1··111······ |
| out 49 (127) | 1··1·1···111··1·1·1··1··1·1···1··1··1·····1··1····1··1·11··11··11·······1·111··11111·1·····111·1····1··1··1··1·1··1·1··1····11·····11·11·11·1·1·1··11··1···111··111···111·1··1·1·1··1··1··1···1··1····11··1·11·1···11··11·····1·111·····11111·1····111·1··1··1····1···1···1···11··1···1·1···11·11·1·111·111··1····1·1 |
| out 50 (117) | 1111···11·········11··········111····11···1····1········1··1·1··1···1···1·1·1········11·······11······1111·1··1·11··11111···11······1111111·1·1111·1·····111·1111···11·········11·········1111····11··1··1·····1···1·1··1··1··1·1·1···········11······11····1111····1···1···11·11111··111····111111·111111····11··1·· |
| out 51 (119) | ·11··11·111·1···1··1······11···1···111··1·1··1······1··111·1··1·1··11···1·1··1·11··111··1··1111···1··1·11··1··1·······1·····11·1···11···1·····1·····1·11···1··11·1·1·111·1···1··1······11···1··1·11·1·11···1·1·11··1··1·1·111·1·1··1····11··111··1·1111·1··1·11·····1···1········1····1·11··11···1····1···1·11····1·· |
| out 52 (135) | 1111·11··1·11·1···11·1··1··1···1·1·1···11·1··11···1·11··11·11·11···11······1·1··1·1··1··1·····11··1·11··1·111111······111··11··1····1·111·1·1···1··1·······1111111·1··1·111····111··1···1···1·11····1·111·111··11··11·11··11·····1·1·····1·1··1··1····111·11··1···1·111·1·1······111·11··1···1·111··11··11········1·1 |
| out 53 (125) | 1··1·1·1··1·1·····1·····1·11·······1··1········1····1··1·1···111···1·········1·11·11111·1··11··1··1··11·11··111·1···1··11··1···1···1·111111····111·11··1·111·1··11··1··1·1·····1····1··11······1···1·····1·1·1··1·1··111··1········1····11·11111·1·11··11··11·11·····11·1···1··1··11·1·1·1··1·11111·1··1111··111··1·· |
| out 54 (109) | ·111·····1·1··1····1····1·11··11·1····1·1·1···11··1··1·1····11·1····1······1···1··1·1······11·1····11·1·11·11··11·····1····11······1·1··1······1·1··1··1·11·1·111·····1·1·1·····1···1··11·1·1·1····11·1·111·11······11·1···1·····1·····11··1·1·····11·1··11·1·11····11····1·1····1···111····1·1··1·····1··1··111····1 |
| out 55 (125) | ·1·1·111111·1·1·1·1··1··1·111·1·1·····1·1·1···1······1·1·1·1····1··············1111·1·1····1··1···111··1111111·1·1·····1··1····1····1··1··1····1·1·11·1·1·111·1·11·11111·11··1·1·1··1··1111··1·····11·1·1···11··1··1····1···············1111·1·1···1··1·111··111··1·111···1··1····1·1··1·1···1··1···1··1·11·1··1··1·1 |
| out 56 (133) | ·····11···111·1······1··1··1··1··1·11·1···1··1·1··1·11··11·11·1·1·11····1·11·1··1·1111··1·········1·1111·11·1·111·1·····1··111·1····11····1·1·1111·······1111····1·1···1111······1··1···1·1···11·1·1··11·1111··11··11·1·1·1···1·11·1·····1·1111··1······1·1111·1··1··1··1·1·1·1····1·11111···11·····11111·····11··1·1 |
| out 57 (127) | 1··1··1·1111··1···1··1····11··1·11··1···1·····1···1··1·1·1·11··11·······1111···1···111·····11··1····1··11····111··1·11·11··1·1·····1·111·11·1·1·1··11··1··1·11··1··1·1111·1····1·1·····11·1··11··1··1···1·1·11··1··11··11·····1·11······1···111····11··1··1··11·······1·1·1···111·11·1··1···1·111·1·111·111··1·1····1 |
| out 58 (125) | 1·1···1····1·······1····1·1·1··1·1·1111·1·····1···1·1··1·1·11·1·1··11···1·11·1·1·111·1··1··1·1·1···1·1·111··1·····1·111·1·1·········111·11·····111··1·1···1··1·1···1····1·······1···1··1·1··1·11·1111···1·11·1··1··11·1·1·11··1·11·1····1·111·1··1·1·1·1·1·1·111·····1········1111·11··1·····111·11····11·1·1··11···· |
| out 59 (123) | 11·····1······1···11·1··1···1··1·1···1····1··111····11··11··11·11·········1··1·11··1·11·1···11····1···111·1··11·111·11···1·111·····1·1·1111·····11··11····1·111·····1·····1····111··1····1··1·1···1···1111·11··11···11·11·······1··1····11··1·11·1··11··1···111···1···1·1···11111····1111···1·1·111·1···1·11···1····1 |
| out 60 (95) | ·11···1·····1······1····1·11···11··11···1·····1····11··1·1····1·1··11···1·1·11·1···1··1·1··11·1···1··1·1···1······1···1·1··1·1·····1····11····1·····1··1······11···1·····1······1···1··11···11·1·1··1···1··1·1··1·····1·1·11··1·1·11····1···1··1·1·11·1·1··1·1······1·········1··1·1·1··1···1····11···1···1··1······· |
| out 61 (119) | 1··1··1·1··1··1·1·1··1····11··1··1··11·······11···1··1·11··11··11·······1·111··1···11·1····1·1·1····1··11····1·1····1··11····1·····11·11·11·1·1·1··11··1···111··1··1·1··1·1·11·1·1·····11·1···1··11····11·1·11·1···11··11·····1·111·····1···11·1···1·1·1··1··11·······1···1····1··11····1···11·11·1·111·111··1····1·1 |
| out 62 (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 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 (119) | 1··11·111··1··1·1·1··1··1·1···1··1··1·····1··1····1··1·11··11··11·······1·111·······1·1····111·1····1··1··1··1·1··1·1··1····11·····11·11·11·1·1·1··11··1···111··1··111··1·1··1·1·1··1··1··1···1··1····11··1·11·1···11··11·····1·111··········1·1···111·1··1··1····1···1···1···11··1···1·1···11·11·1·111·111··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 (133) | 1··1·111·11·1···1·1·······11··1·1··1··1·1····111····1··111·1·11····1·········1·11··11·1·1··111·1··1··11··1···1··1···11··1···1··1···11111··1·1··111·11··1·111·1··11·11·11·1···1·1·······11·1··1·1···111·111·1·1·11··1·11···1········1····11··11·1·1·111·11··11··1······1·····1··11··1··11·1··11111···11·1111··111··1·· |
| out 67 (125) | 1··1·1·1··1·1·····1·····1·11·······1111···1··1·1····1··1·····111···1········1··11·11111·1··11··1··1··11·11··111·111·1··1·······1···1··11·11····111·11··1·11··1··11··1··1·1·····1····1··11······1·111··11·1·1·1·······111··1·······1·····11·11111·1·11··11··11·11·····11·1···1111··1····1·1··1··11·1·1··1111··111···1· |
| 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 (125) | ······1·11·11·1·1····1········1111·1··1···1··1·1··1·11···1··11111··1····1·1111····11··1·1····1····1·111111··1··1111·····1··111·1·····1···1····11·1·······11·1······1·11·111··1···1········1·1111···1··11·1111···1···11111·1···1·1111·······11··1·1···1··1·111111·····1·1··1·111····1·11111····1···1···11······11····1 |
| out 70 (125) | 1··1··1··11·1·····1·····1·11·······1··1·1····111·······111·1·11····1·········1·1····1·1·1··11··1··1··11·11··111·1···11·11···1··1···11111··1·1··111·11··1·111·1··1··1··11·1·····1····1··11······1···11··111···1·11··1·11···1········1····1····1·1·1·11··11··11·11·····11·1···1··11·11··11·11·11111···11·1111··111··1·· |
| check 71 (126) | 1111·1··1·······1·11····1··1··1·11·1111·1·1····1··1·11···1··11111··1····1·1111·1·11·1·····111·11········1·1·1··11····1··1···11·1·····1···1····11·1·······11·111111···1·······1·11···1···1·1··111·1111·1··1111···1···11111·1···1·1111····1·11·1····111·11······1···1··1····1·1···1··1··1111····1···1···11······11····1 |
| check 72 (120) | ·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···11·····11·11····1·1······11··11···11····111··1···1·1······1··11·1··1···11··1··1·11·1····11·11·11······11·····11·1····1·111·1·11··11·····11··1···1··11·11··1·1···11·11····11····11·11····· |
| check 73 (126) | ·····11···111·1······1··1·····1··1·1··1···1···11··1·11·1···1·1·1····1·······1···1·1111··1·········1·1111·1··1·11111·····1····1·1·1·11111111·1···11·11111···1·····1·1···1111······1··1·····1···11···1··1·111111·····1·1·1···1······1······1·1111··1······1·1111·1·····1··1·1·111····1···111·11111111·11··111111····1·· |
| check 74 (156) | ···········11···1·1·11·11····1·1····1·11···111111···1··1·1····1··111·1·1·1·1·111111·····11···111·111·111·1··11··1·1·1···1···1·111·1···111··111·111·11·11··11·1··111··11··111111111·1···11····1·1··11·1·11·111·1···11····1·1·1··1···11··11··1·11·11·111·1·1··1·11·11·11111··111····111·1··1··1·111·1··111··11·11··11·1 |
| check 75 (158) | ·11··11·1·111···1111···11·11··1·1··1·1··1·11··11·111·····1······1···11·11·111·1··1111··1·1·111···11···1·11···1··1·11··1·1·1····11·11·111·1·111·1·1·1··1····1···11·······1·11···1·1·111··11··111··111·1111·1·11·1111·1·1··111·111·1···1·1·11·1··1····1··111·1111··1·1·111·1·1111·111111··1···111·1111·1·····1111·1···1 |
| check 76 (166) | 1·1····1·1··11··1·1··1111·111··1··1···1·11··111111·····11111··11·1·1·1···11·1·11·1·1111·11·1···11111·11···1·1·1·1·1111··1··11··11····1111·11····11111·1··11··1··1·111··1·11·1···11···1·1···1···1··1·11··11·1111·1·11·1·1·11111····11··111··111·····111·1111·1·11···1·1111·111··111111·1·111·1111······111·1··11·1··11 |
| check 77 (168) | ·1·111·11··1111··1·1······11111·11·11·1····11111···111·11·11111111·1··11··11111·11·1··11·1·1·11111·1·11·1·1·111·1111·1·111·111111····1···11··1·····1·11··1·11·1·1·1111········11··1111·111·111111·1···1·111··1·11111111··11·11··1·······1··11··111·1·1···1·1·1·1··1·1··11·······1·1·1·1·1·1····1111·1111·11··11··1·1· |
| check 78 (150) | ·····1··1·1·111·1·111·11·······11111··1······1··1111·1··11·111·111·······11·1·11·111·1·111···111···1·······111·····1····111·1·111···1·111··1111·····111111·11····1··1·1·1····1·1111111······1···111····111·1···11·····1··1····11·1·1····1·11·1·11····1111·111111····111·1111111····11··11·1··1·111111··1··1111·111·1· |
| check 79 (158) | 1·1··11·11··1·1111·11111··111···11·1···1111111·11111···1···11·1···11·111·1··1·1····11·····11··11111·1·1·1·11·11·1·1··1··1·1·111·1···11·1·1··1·1··1111··11····1·1·1·1·11··1111·11··1111·111···111·····1··1··111·····11·1····1111111·1········11······11···1·1·1·1··1·1·1·1···1·11·11··1·1·11··11·1·1··11·1··11·1111111 |
| check 80 (132) | 1·1··11·1··1····1·1·······1·111·1·1·11·111·1111·11·111·11··1····1··11·····1111········1·1··1··1···1·1··1·1··11····11·1····1·1·111····1·1··1····111···1·1·1·1·1·1·1·1·1··1····1·1······1·1··11·111··1·11··11··1·1···1····1·11····1111···········1·1·1··1·1·1··1·111111··1111111·1·111·1··1·1···1·1···1··11··1·11···1·· |
| check 81 (144) | ··11··1···111···1·11····1···1··111··11····1··1·1··1···11111·1111·111·111·1·1··1··1·11·1·····1·····11··111·1··1··1·1···111·1·1··1·111·1··1111·11·111·111111111··11··1···111···1·11···1····1··111··11···11·11···1··111····11·111111·11······1·11·1····1···11··111···1···1·····1·1··1111·1··1···1·11··1·1·1·1······11·1· |
The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.
Figures of merit
inputs n309Noisy T states per run.
outputs k71
distance d3Exact, proved and witnessed here.
error coefficient A_{3}2,060Faults 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 N82
checks r11
V_{\mathrm{ex}}71T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3387Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3387Overhead 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 width71Rank of the output rows modulo the check rows.
Output gate
71 T0 CS0 CCZon 71 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}
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 (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 79 single-wire gates and 789 \mathrm{CZ} gates: \mathrm{S} 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{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{Z} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23 and 844 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 868 correction gates
\mathrm{S} 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{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{Z} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{S} on output 17, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23, \mathrm{S} on output 24, \mathrm{Z} on output 25, \mathrm{Z} on output 26, \mathrm{Z} on output 27, \mathrm{S} on output 28, \mathrm{Z} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{Z} on output 32, \mathrm{S} on output 33, \mathrm{S} on output 34, \mathrm{Z} on output 35, \mathrm{S} on output 36, \mathrm{S} on output 37, \mathrm{Z} on output 38, \mathrm{S} on output 39, \mathrm{Z} on output 40, \mathrm{Z} on output 41, \mathrm{S} on output 42, \mathrm{Z} on output 43, \mathrm{Z} 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{S} on output 51, \mathrm{S} 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{S}^\dagger on output 59, \mathrm{S} on output 60, \mathrm{S} on output 61, \mathrm{S} on output 62, \mathrm{S} on output 63, \mathrm{S} on output 64, \mathrm{S} on output 65, \mathrm{Z} on output 66, \mathrm{Z} on output 67, \mathrm{S} on output 68, \mathrm{Z} on output 69, \mathrm{Z} on output 70, \mathrm{S} on check 71, \mathrm{S} on check 73, \mathrm{Z} on check 74, \mathrm{S} on check 75, \mathrm{S} on check 76, \mathrm{S} on check 78, \mathrm{S} on check 79, \mathrm{Z} on check 80, \mathrm{CZ} on output 1, output 5, \mathrm{CZ} on output 1, output 10, \mathrm{CZ} on output 1, output 11, \mathrm{CZ} on output 1, output 12, \mathrm{CZ} on output 1, output 15, \mathrm{CZ} on output 1, output 18, \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 25, \mathrm{CZ} on output 1, output 26, \mathrm{CZ} on output 1, output 27, \mathrm{CZ} on output 1, output 29, \mathrm{CZ} on output 1, output 32, \mathrm{CZ} on output 1, output 35, \mathrm{CZ} on output 1, output 38, \mathrm{CZ} on output 1, output 40, \mathrm{CZ} on output 1, output 41, \mathrm{CZ} on output 1, output 43, \mathrm{CZ} on output 1, output 44, \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 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 66, \mathrm{CZ} on output 1, output 67, \mathrm{CZ} on output 1, output 69, \mathrm{CZ} on output 1, output 70, \mathrm{CZ} on output 1, check 71, \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 80, \mathrm{CZ} on output 5, output 10, \mathrm{CZ} on output 5, output 11, \mathrm{CZ} on output 5, output 12, \mathrm{CZ} on output 5, output 15, \mathrm{CZ} on output 5, output 18, \mathrm{CZ} on output 5, output 21, \mathrm{CZ} on output 5, output 22, \mathrm{CZ} on output 5, output 23, \mathrm{CZ} on output 5, output 25, \mathrm{CZ} on output 5, output 26, \mathrm{CZ} on output 5, output 27, \mathrm{CZ} on output 5, output 29, \mathrm{CZ} on output 5, output 32, \mathrm{CZ} on output 5, output 35, \mathrm{CZ} on output 5, output 38, \mathrm{CZ} on output 5, output 40, \mathrm{CZ} on output 5, output 41, \mathrm{CZ} on output 5, output 43, \mathrm{CZ} on output 5, output 44, \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 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 66, \mathrm{CZ} on output 5, output 67, \mathrm{CZ} on output 5, output 69, \mathrm{CZ} on output 5, output 70, \mathrm{CZ} on output 5, check 71, \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 80, \mathrm{CZ} on output 10, output 11, \mathrm{CZ} on output 10, output 12, \mathrm{CZ} on output 10, output 15, \mathrm{CZ} on output 10, output 18, \mathrm{CZ} on output 10, output 21, \mathrm{CZ} on output 10, output 22, \mathrm{CZ} on output 10, output 23, \mathrm{CZ} on output 10, output 25, \mathrm{CZ} on output 10, output 26, \mathrm{CZ} on output 10, output 27, \mathrm{CZ} on output 10, output 29, \mathrm{CZ} on output 10, output 32, \mathrm{CZ} on output 10, output 35, \mathrm{CZ} on output 10, output 38, \mathrm{CZ} on output 10, output 40, \mathrm{CZ} on output 10, output 41, \mathrm{CZ} on output 10, output 43, \mathrm{CZ} on output 10, output 44, \mathrm{CZ} on output 10, output 45, \mathrm{CZ} on output 10, output 46, \mathrm{CZ} on output 10, output 47, \mathrm{CZ} on output 10, output 50, \mathrm{CZ} on output 10, output 53, \mathrm{CZ} on output 10, output 54, \mathrm{CZ} on output 10, output 55, \mathrm{CZ} on output 10, output 56, \mathrm{CZ} on output 10, output 58, \mathrm{CZ} on output 10, output 59, \mathrm{CZ} on output 10, output 66, \mathrm{CZ} on output 10, output 67, \mathrm{CZ} on output 10, output 69, \mathrm{CZ} on output 10, output 70, \mathrm{CZ} on output 10, check 71, \mathrm{CZ} on output 10, check 73, \mathrm{CZ} on output 10, check 74, \mathrm{CZ} on output 10, check 76, \mathrm{CZ} on output 10, check 80, \mathrm{CZ} on output 11, output 12, \mathrm{CZ} on output 11, output 15, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 21, \mathrm{CZ} on output 11, output 22, \mathrm{CZ} on output 11, output 23, \mathrm{CZ} on output 11, output 25, \mathrm{CZ} on output 11, output 26, \mathrm{CZ} on output 11, output 27, \mathrm{CZ} on output 11, output 29, \mathrm{CZ} on output 11, output 32, \mathrm{CZ} on output 11, output 35, \mathrm{CZ} on output 11, output 38, \mathrm{CZ} on output 11, output 40, \mathrm{CZ} on output 11, output 41, \mathrm{CZ} on output 11, output 43, \mathrm{CZ} on output 11, output 44, \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 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 66, \mathrm{CZ} on output 11, output 67, \mathrm{CZ} on output 11, output 69, \mathrm{CZ} on output 11, output 70, \mathrm{CZ} on output 11, check 71, \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 80, \mathrm{CZ} on output 12, output 15, \mathrm{CZ} on output 12, output 18, \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 25, \mathrm{CZ} on output 12, output 26, \mathrm{CZ} on output 12, output 27, \mathrm{CZ} on output 12, output 29, \mathrm{CZ} on output 12, output 32, \mathrm{CZ} on output 12, output 35, \mathrm{CZ} on output 12, output 38, \mathrm{CZ} on output 12, output 40, \mathrm{CZ} on output 12, output 41, \mathrm{CZ} on output 12, output 43, \mathrm{CZ} on output 12, output 44, \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 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 66, \mathrm{CZ} on output 12, output 67, \mathrm{CZ} on output 12, output 69, \mathrm{CZ} on output 12, output 70, \mathrm{CZ} on output 12, check 71, \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 80, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 21, \mathrm{CZ} on output 15, output 22, \mathrm{CZ} on output 15, output 23, \mathrm{CZ} on output 15, output 25, \mathrm{CZ} on output 15, output 26, \mathrm{CZ} on output 15, output 27, \mathrm{CZ} on output 15, output 29, \mathrm{CZ} on output 15, output 32, \mathrm{CZ} on output 15, output 35, \mathrm{CZ} on output 15, output 38, \mathrm{CZ} on output 15, output 40, \mathrm{CZ} on output 15, output 41, \mathrm{CZ} on output 15, output 43, \mathrm{CZ} on output 15, output 44, \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 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 66, \mathrm{CZ} on output 15, output 67, \mathrm{CZ} on output 15, output 69, \mathrm{CZ} on output 15, output 70, \mathrm{CZ} on output 15, check 71, \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 80, \mathrm{CZ} on output 18, output 21, \mathrm{CZ} on output 18, output 22, \mathrm{CZ} on output 18, output 23, \mathrm{CZ} on output 18, output 25, \mathrm{CZ} on output 18, output 26, \mathrm{CZ} on output 18, output 27, \mathrm{CZ} on output 18, output 29, \mathrm{CZ} on output 18, output 32, \mathrm{CZ} on output 18, output 35, \mathrm{CZ} on output 18, output 38, \mathrm{CZ} on output 18, output 40, \mathrm{CZ} on output 18, output 41, \mathrm{CZ} on output 18, output 43, \mathrm{CZ} on output 18, output 44, \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 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 66, \mathrm{CZ} on output 18, output 67, \mathrm{CZ} on output 18, output 69, \mathrm{CZ} on output 18, output 70, \mathrm{CZ} on output 18, check 71, \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 80, \mathrm{CZ} on output 21, output 22, \mathrm{CZ} on output 21, output 23, \mathrm{CZ} on output 21, output 25, \mathrm{CZ} on output 21, output 26, \mathrm{CZ} on output 21, output 27, \mathrm{CZ} on output 21, output 29, \mathrm{CZ} on output 21, output 32, \mathrm{CZ} on output 21, output 35, \mathrm{CZ} on output 21, output 38, \mathrm{CZ} on output 21, output 40, \mathrm{CZ} on output 21, output 41, \mathrm{CZ} on output 21, output 43, \mathrm{CZ} on output 21, output 44, \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 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 66, \mathrm{CZ} on output 21, output 67, \mathrm{CZ} on output 21, output 69, \mathrm{CZ} on output 21, output 70, \mathrm{CZ} on output 21, check 71, \mathrm{CZ} on output 21, check 73, \mathrm{CZ} on output 21, check 74, \mathrm{CZ} on output 21, check 76, \mathrm{CZ} on output 21, check 80, \mathrm{CZ} on output 22, output 23, \mathrm{CZ} on output 22, output 25, \mathrm{CZ} on output 22, output 26, \mathrm{CZ} on output 22, output 27, \mathrm{CZ} on output 22, output 29, \mathrm{CZ} on output 22, output 32, \mathrm{CZ} on output 22, output 35, \mathrm{CZ} on output 22, output 38, \mathrm{CZ} on output 22, output 40, \mathrm{CZ} on output 22, output 41, \mathrm{CZ} on output 22, output 43, \mathrm{CZ} on output 22, output 44, \mathrm{CZ} on output 22, output 45, \mathrm{CZ} on output 22, output 46, \mathrm{CZ} on output 22, output 47, \mathrm{CZ} on output 22, output 50, \mathrm{CZ} on output 22, output 53, \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 58, \mathrm{CZ} on output 22, output 59, \mathrm{CZ} on output 22, output 66, \mathrm{CZ} on output 22, output 67, \mathrm{CZ} on output 22, output 69, \mathrm{CZ} on output 22, output 70, \mathrm{CZ} on output 22, check 71, \mathrm{CZ} on output 22, check 73, \mathrm{CZ} on output 22, check 74, \mathrm{CZ} on output 22, check 76, \mathrm{CZ} on output 22, check 80, \mathrm{CZ} on output 23, output 25, \mathrm{CZ} on output 23, output 26, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 29, \mathrm{CZ} on output 23, output 32, \mathrm{CZ} on output 23, output 35, \mathrm{CZ} on output 23, output 38, \mathrm{CZ} on output 23, output 40, \mathrm{CZ} on output 23, output 41, \mathrm{CZ} on output 23, output 43, \mathrm{CZ} on output 23, output 44, \mathrm{CZ} on output 23, output 45, \mathrm{CZ} on output 23, output 46, \mathrm{CZ} on output 23, output 47, \mathrm{CZ} on output 23, output 50, \mathrm{CZ} on output 23, output 53, \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 58, \mathrm{CZ} on output 23, output 59, \mathrm{CZ} on output 23, output 66, \mathrm{CZ} on output 23, output 67, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, output 70, \mathrm{CZ} on output 23, check 71, \mathrm{CZ} on output 23, check 73, \mathrm{CZ} on output 23, check 74, \mathrm{CZ} on output 23, check 76, \mathrm{CZ} on output 23, check 80, \mathrm{CZ} on output 25, output 26, \mathrm{CZ} on output 25, output 27, \mathrm{CZ} on output 25, output 29, \mathrm{CZ} on output 25, output 32, \mathrm{CZ} on output 25, output 35, \mathrm{CZ} on output 25, output 38, \mathrm{CZ} on output 25, output 40, \mathrm{CZ} on output 25, output 41, \mathrm{CZ} on output 25, output 43, \mathrm{CZ} on output 25, output 44, \mathrm{CZ} on output 25, output 45, \mathrm{CZ} on output 25, output 46, \mathrm{CZ} on output 25, output 47, \mathrm{CZ} on output 25, output 50, \mathrm{CZ} on output 25, output 53, \mathrm{CZ} on output 25, output 54, \mathrm{CZ} on output 25, output 55, \mathrm{CZ} on output 25, output 56, \mathrm{CZ} on output 25, output 58, \mathrm{CZ} on output 25, output 59, \mathrm{CZ} on output 25, output 66, \mathrm{CZ} on output 25, output 67, \mathrm{CZ} on output 25, output 69, \mathrm{CZ} on output 25, output 70, \mathrm{CZ} on output 25, check 71, \mathrm{CZ} on output 25, check 73, \mathrm{CZ} on output 25, check 74, \mathrm{CZ} on output 25, check 76, \mathrm{CZ} on output 25, check 80, \mathrm{CZ} on output 26, output 27, \mathrm{CZ} on output 26, output 29, \mathrm{CZ} on output 26, output 32, \mathrm{CZ} on output 26, output 35, \mathrm{CZ} on output 26, output 38, \mathrm{CZ} on output 26, output 40, \mathrm{CZ} on output 26, output 41, \mathrm{CZ} on output 26, output 43, \mathrm{CZ} on output 26, output 44, \mathrm{CZ} on output 26, output 45, \mathrm{CZ} on output 26, output 46, \mathrm{CZ} on output 26, output 47, \mathrm{CZ} on output 26, output 50, \mathrm{CZ} on output 26, output 53, \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 58, \mathrm{CZ} on output 26, output 59, \mathrm{CZ} on output 26, output 66, \mathrm{CZ} on output 26, output 67, \mathrm{CZ} on output 26, output 69, \mathrm{CZ} on output 26, output 70, \mathrm{CZ} on output 26, check 71, \mathrm{CZ} on output 26, check 73, \mathrm{CZ} on output 26, check 74, \mathrm{CZ} on output 26, check 76, \mathrm{CZ} on output 26, check 80, \mathrm{CZ} on output 27, output 29, \mathrm{CZ} on output 27, output 32, \mathrm{CZ} on output 27, output 35, \mathrm{CZ} on output 27, output 38, \mathrm{CZ} on output 27, output 40, \mathrm{CZ} on output 27, output 41, \mathrm{CZ} on output 27, output 43, \mathrm{CZ} on output 27, output 44, \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 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 66, \mathrm{CZ} on output 27, output 67, \mathrm{CZ} on output 27, output 69, \mathrm{CZ} on output 27, output 70, \mathrm{CZ} on output 27, check 71, \mathrm{CZ} on output 27, check 73, \mathrm{CZ} on output 27, check 74, \mathrm{CZ} on output 27, check 76, \mathrm{CZ} on output 27, check 80, \mathrm{CZ} on output 29, output 32, \mathrm{CZ} on output 29, output 35, \mathrm{CZ} on output 29, output 38, \mathrm{CZ} on output 29, output 40, \mathrm{CZ} on output 29, output 41, \mathrm{CZ} on output 29, output 43, \mathrm{CZ} on output 29, output 44, \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 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 66, \mathrm{CZ} on output 29, output 67, \mathrm{CZ} on output 29, output 69, \mathrm{CZ} on output 29, output 70, \mathrm{CZ} on output 29, check 71, \mathrm{CZ} on output 29, check 73, \mathrm{CZ} on output 29, check 74, \mathrm{CZ} on output 29, check 76, \mathrm{CZ} on output 29, check 80, \mathrm{CZ} on output 32, output 35, \mathrm{CZ} on output 32, output 38, \mathrm{CZ} on output 32, output 40, \mathrm{CZ} on output 32, output 41, \mathrm{CZ} on output 32, output 43, \mathrm{CZ} on output 32, output 44, \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 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 66, \mathrm{CZ} on output 32, output 67, \mathrm{CZ} on output 32, output 69, \mathrm{CZ} on output 32, output 70, \mathrm{CZ} on output 32, check 71, \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 80, \mathrm{CZ} on output 35, output 38, \mathrm{CZ} on output 35, output 40, \mathrm{CZ} on output 35, output 41, \mathrm{CZ} on output 35, output 43, \mathrm{CZ} on output 35, output 44, \mathrm{CZ} on output 35, output 45, \mathrm{CZ} on output 35, output 46, \mathrm{CZ} on output 35, output 47, \mathrm{CZ} on output 35, output 50, \mathrm{CZ} on output 35, output 53, \mathrm{CZ} on output 35, output 54, \mathrm{CZ} on output 35, output 55, \mathrm{CZ} on output 35, output 56, \mathrm{CZ} on output 35, output 58, \mathrm{CZ} on output 35, output 59, \mathrm{CZ} on output 35, output 66, \mathrm{CZ} on output 35, output 67, \mathrm{CZ} on output 35, output 69, \mathrm{CZ} on output 35, output 70, \mathrm{CZ} on output 35, check 71, \mathrm{CZ} on output 35, check 73, \mathrm{CZ} on output 35, check 74, \mathrm{CZ} on output 35, check 76, \mathrm{CZ} on output 35, check 80, \mathrm{CZ} on output 38, output 40, \mathrm{CZ} on output 38, output 41, \mathrm{CZ} on output 38, output 43, \mathrm{CZ} on output 38, output 44, \mathrm{CZ} on output 38, output 45, \mathrm{CZ} on output 38, output 46, \mathrm{CZ} on output 38, output 47, \mathrm{CZ} on output 38, output 50, \mathrm{CZ} on output 38, output 53, \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 58, \mathrm{CZ} on output 38, output 59, \mathrm{CZ} on output 38, output 66, \mathrm{CZ} on output 38, output 67, \mathrm{CZ} on output 38, output 69, \mathrm{CZ} on output 38, output 70, \mathrm{CZ} on output 38, check 71, \mathrm{CZ} on output 38, check 73, \mathrm{CZ} on output 38, check 74, \mathrm{CZ} on output 38, check 76, \mathrm{CZ} on output 38, check 80, \mathrm{CZ} on output 40, output 41, \mathrm{CZ} on output 40, output 43, \mathrm{CZ} on output 40, output 44, \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 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 66, \mathrm{CZ} on output 40, output 67, \mathrm{CZ} on output 40, output 69, \mathrm{CZ} on output 40, output 70, \mathrm{CZ} on output 40, check 71, \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 80, \mathrm{CZ} on output 41, output 43, \mathrm{CZ} on output 41, output 44, \mathrm{CZ} on output 41, output 45, \mathrm{CZ} on output 41, output 46, \mathrm{CZ} on output 41, output 47, \mathrm{CZ} on output 41, output 50, \mathrm{CZ} on output 41, output 53, \mathrm{CZ} on output 41, output 54, \mathrm{CZ} on output 41, output 55, \mathrm{CZ} on output 41, output 56, \mathrm{CZ} on output 41, output 58, \mathrm{CZ} on output 41, output 59, \mathrm{CZ} on output 41, output 66, \mathrm{CZ} on output 41, output 67, \mathrm{CZ} on output 41, output 69, \mathrm{CZ} on output 41, output 70, \mathrm{CZ} on output 41, check 71, \mathrm{CZ} on output 41, check 73, \mathrm{CZ} on output 41, check 74, \mathrm{CZ} on output 41, check 76, \mathrm{CZ} on output 41, check 80, \mathrm{CZ} on output 43, output 44, \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 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 66, \mathrm{CZ} on output 43, output 67, \mathrm{CZ} on output 43, output 69, \mathrm{CZ} on output 43, output 70, \mathrm{CZ} on output 43, check 71, \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 80, \mathrm{CZ} on output 44, output 45, \mathrm{CZ} on output 44, output 46, \mathrm{CZ} on output 44, output 47, \mathrm{CZ} on output 44, output 50, \mathrm{CZ} on output 44, output 53, \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 58, \mathrm{CZ} on output 44, output 59, \mathrm{CZ} on output 44, output 66, \mathrm{CZ} on output 44, output 67, \mathrm{CZ} on output 44, output 69, \mathrm{CZ} on output 44, output 70, \mathrm{CZ} on output 44, check 71, \mathrm{CZ} on output 44, check 73, \mathrm{CZ} on output 44, check 74, \mathrm{CZ} on output 44, check 76, \mathrm{CZ} on output 44, 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 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 66, \mathrm{CZ} on output 45, output 67, \mathrm{CZ} on output 45, output 69, \mathrm{CZ} on output 45, output 70, \mathrm{CZ} on output 45, check 71, \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 80, \mathrm{CZ} on output 46, output 47, \mathrm{CZ} on output 46, output 50, \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 66, \mathrm{CZ} on output 46, output 67, \mathrm{CZ} on output 46, output 69, \mathrm{CZ} on output 46, output 70, \mathrm{CZ} on output 46, check 71, \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 80, \mathrm{CZ} on output 47, output 50, \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 66, \mathrm{CZ} on output 47, output 67, \mathrm{CZ} on output 47, output 69, \mathrm{CZ} on output 47, output 70, \mathrm{CZ} on output 47, check 71, \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 80, \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 66, \mathrm{CZ} on output 50, output 67, \mathrm{CZ} on output 50, output 69, \mathrm{CZ} on output 50, output 70, \mathrm{CZ} on output 50, check 71, \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 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 66, \mathrm{CZ} on output 53, output 67, \mathrm{CZ} on output 53, output 69, \mathrm{CZ} on output 53, output 70, \mathrm{CZ} on output 53, check 71, \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 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 66, \mathrm{CZ} on output 54, output 67, \mathrm{CZ} on output 54, output 69, \mathrm{CZ} on output 54, output 70, \mathrm{CZ} on output 54, check 71, \mathrm{CZ} on output 54, check 73, \mathrm{CZ} on output 54, check 74, \mathrm{CZ} on output 54, check 76, \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 66, \mathrm{CZ} on output 55, output 67, \mathrm{CZ} on output 55, output 69, \mathrm{CZ} on output 55, output 70, \mathrm{CZ} on output 55, check 71, \mathrm{CZ} on output 55, check 73, \mathrm{CZ} on output 55, check 74, \mathrm{CZ} on output 55, check 76, \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 66, \mathrm{CZ} on output 56, output 67, \mathrm{CZ} on output 56, output 69, \mathrm{CZ} on output 56, output 70, \mathrm{CZ} on output 56, check 71, \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 80, \mathrm{CZ} on output 58, output 59, \mathrm{CZ} on output 58, output 66, \mathrm{CZ} on output 58, output 67, \mathrm{CZ} on output 58, output 69, \mathrm{CZ} on output 58, output 70, \mathrm{CZ} on output 58, check 71, \mathrm{CZ} on output 58, check 73, \mathrm{CZ} on output 58, check 74, \mathrm{CZ} on output 58, check 76, \mathrm{CZ} on output 58, check 80, \mathrm{CZ} on output 59, output 66, \mathrm{CZ} on output 59, output 67, \mathrm{CZ} on output 59, output 69, \mathrm{CZ} on output 59, output 70, \mathrm{CZ} on output 59, check 71, \mathrm{CZ} on output 59, check 73, \mathrm{CZ} on output 59, check 75, \mathrm{CZ} on output 59, check 76, \mathrm{CZ} on output 59, check 78, \mathrm{CZ} on output 59, check 79, \mathrm{CZ} on output 66, output 67, \mathrm{CZ} on output 66, output 69, \mathrm{CZ} on output 66, output 70, \mathrm{CZ} on output 66, check 71, \mathrm{CZ} on output 66, check 73, \mathrm{CZ} on output 66, check 74, \mathrm{CZ} on output 66, check 76, \mathrm{CZ} on output 66, check 80, \mathrm{CZ} on output 67, output 69, \mathrm{CZ} on output 67, output 70, \mathrm{CZ} on output 67, check 71, \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 80, \mathrm{CZ} on output 69, output 70, \mathrm{CZ} on output 69, check 71, \mathrm{CZ} on output 69, check 73, \mathrm{CZ} on output 69, check 74, \mathrm{CZ} on output 69, check 76, \mathrm{CZ} on output 69, check 80, \mathrm{CZ} on output 70, check 71, \mathrm{CZ} on output 70, check 73, \mathrm{CZ} on output 70, check 74, \mathrm{CZ} on output 70, check 76, \mathrm{CZ} on output 70, check 80, \mathrm{CZ} on check 71, check 73, \mathrm{CZ} on check 71, check 74, \mathrm{CZ} on check 71, check 76, \mathrm{CZ} on check 71, check 80, \mathrm{CZ} on check 73, check 74, \mathrm{CZ} on check 73, check 76, \mathrm{CZ} on check 73, check 80, \mathrm{CZ} on check 74, check 75, \mathrm{CZ} on check 74, check 76, \mathrm{CZ} on check 74, check 78, \mathrm{CZ} on check 74, check 79, \mathrm{CZ} on check 75, check 78, \mathrm{CZ} on check 75, check 79, \mathrm{CZ} on check 75, check 80, \mathrm{CZ} on check 76, check 80, \mathrm{CZ} on check 78, check 79, \mathrm{CZ} on check 78, check 80, \mathrm{CZ} on check 79, check 80
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 0, 7, 8, 17, 20, 22, 27, 28, 31, 32, 33, 36, 38, 40, 42, 63, 64, 68, 77, 79, 84, 86, 87, 88 and 104 more (listed below); \mathrm{T}^5 on rotations 6, 9, 11, 21, 37, 43, 45, 46, 48, 50, 54, 55, 56, 60, 66, 67, 71, 81, 90, 106, 158, 161; \mathrm{T}^\dagger on rotations 3, 4, 12, 13, 15, 18, 23, 25, 47, 59, 61, 72, 80, 129, 157, 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 128 rotations at T³
0, 7, 8, 17, 20, 22, 27, 28, 31, 32, 33, 36, 38, 40, 42, 63, 64, 68, 77, 79, 84, 86, 87, 88, 89, 91, 92, 93, 95, 96, 97, 98, 99, 101, 102, 104, 105, 108, 113, 116, 117, 123, 127, 131, 132, 133, 134, 137, 140, 142, 143, 145, 149, 151, 153, 156, 160, 162, 164, 165, 169, 171, 172, 174, 175, 178, 179, 181, 183, 186, 191, 194, 199, 200, 202, 203, 204, 205, 207, 208, 212, 214, 218, 224, 225, 226, 228, 229, 230, 231, 232, 233, 237, 239, 240, 241, 243, 244, 245, 247, 248, 249, 251, 252, 254, 255, 258, 260, 262, 264, 266, 268, 270, 273, 274, 275, 276, 278, 280, 288, 289, 292, 296, 297, 298, 300, 303, 306
Rotations are numbered by matrix column, from 0. The correction comes from the columns by the weight expansion of Bravyi and Haah (2012). verify_catalog.py re-derives it, checks the corrected circuit's phase input by input against the gate, and on small circuits simulates it gate by gate.
Convert the output with CNOT and S
A CNOT circuit on the outputs, followed by S, Z and CZ gates, turns this factory's gate into other gates that prepare the same magic state. Type a target gate to check whether it is reachable. If it is, you get the circuit, checked on every basis state.
Or list every gate it reaches. The list is built in your browser and saved as a text file, one gate per line.
Python code that writes the same list
import json, urllib.request
NAMES = {1: "T", 2: "CS", 3: "CCZ"}
def equivalent_gates(k, terms, limit=1_000_000):
"""Every gate a CNOT circuit and S, Z, CZ gates reach from this one.
A gate is its set of terms mod Clifford: {a} is T, {a,b} is CS and
{a,b,c} is CCZ on those outputs. CNOT c->t sends x_t to
x_c + x_t - 2 x_c x_t, so a term on t but not c adds the term with t
replaced by c, and, below CCZ, the term with c added.
"""
start = frozenset(frozenset(m) for m in terms)
seen, queue = {start}, [start]
for gate in queue:
for c in range(k):
for t in range(k):
if c == t:
continue
new = set(gate)
for m in gate:
if t in m and c not in m:
new ^= {(m - {t}) | {c}}
if len(m) < 3:
new ^= {m | {c}}
new = frozenset(new)
if new not in seen:
seen.add(new)
queue.append(new)
if len(seen) > limit:
raise RuntimeError(f"more than {limit} equivalent gates")
return seen
def name(gate, k):
sep = "," if k > 10 else ""
terms = sorted((sorted(m) for m in gate), key=lambda m: (len(m), m))
return "·".join(NAMES[len(m)] + sep.join(map(str, m)) for m in terms) or "I"
url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/309.71.3.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-309.71.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 2,060 faults of weight 3 are undetectable and damaging, so A_{3}=2{,}060. 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 [0,11,47].
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_309_71_3_2e205c5d61b9.json",
"label": "paired_column_contraction_309_71_3_2e205c5d61b9",
"N": 82,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=96), with searched graph punctures; 2 paired-column contractions",
"provenance": "gamma frontier release record paired_column_contraction_309_71_3_2e205c5d61b9 (source catalogue id paired_column_contraction_309_71_3_2e205c5d61b9); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=96), with searched graph punctures; 2 paired-column contractions; matrix 2e205c5d61b9d4a1...; the release states d=3 (exact), gamma=1.3386536952352588 (exact)",
"notes": "matrix gamma_frontier_release/matrices/2e205c5d61b9d4a161ddb7707a0a3053f678713bfbfd57bca4e7eda92fc4c487.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/309.71.3.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[959].