The circuit
The 81\times308 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 (123) | 1111·1··1·11····1·11·1·········1····111···1···11····1···11···1··1··11···1·1·····1··1·1·······111···1··1111·11··1···11111·····11·1····1·111·1··111··1·····11··11111···1·11····1·111··········1····111··1·11·1···11····1···11··1·1········1··1·1·1····111···1111····111·····1··11111····11·1··1·111··111111····11····· |
| out 1 (123) | ·1·1·1111···1·1·1··1·1··1·1·1·1111·1··1···1··1·1·····1··11·111111·········1·1······1··1····1···1·····1·111···1··1···1·111·····1····1··11·111···1·1·1·1·1·1··1·1·11·111···11··1··11··1··1·11·1111···1··11·1··1··11··11111·······1·1·········1··1···1···1··1·111········1····1··1·111····11····11·11·11·1·1·1·11·····1 |
| out 2 (115) | 1·1··1····1·1·1···1·1·····1·1·1··1·11········1·······1·11···1111···11···1···1·····11·11····1·11···11·11·1··11··111·1·1··1··1·1········1·1··1··1·11···1·1··1·11·1·1·····1·11····1·······1·11···11·1·····1····11·1····1111·11··1···1········11·11···1·11·1·11·1·····111·····1111·1··1··11·1····1·1···1·1·1··1·1·1····1 |
| out 3 (117) | ·11··1···1·1··1···1··1····11··1·1··1··1······1····1·11·11·····11···11···1·11·····1·1·11····11··1··11·11··1·····1····11··1111··1·1···11·11·1····1·····11··1··1·11·1····1·1·1····1·1·····11·1··1·1···1···1··1111·1······11·11··1111········1·1·11···11··11·11··1······1·····1···11··1111·1·1·11·11·1····1···11·1·····1 |
| out 4 (129) | ·····11·11111·1···11·1·····1··111···1·1·1·····1···1··1··1·······1··1·······111·1·1··111·1·····11···1···11111·1·1·1··1··11111····1····11111····11·1··1111····1····1·1·111111····1111·····1·1·11···1·11···1·1·1··1·········1······111····1·1··111·1····11····111··1·1·1·1···1·1·1··11111··11··11111···111··1111······1 |
| out 5 (109) | ·········11·······11·······1···111·11···1·1····1····1····1··1·1·········1·1····111111·········11··1111····111·1·1···1···1111·11·1·······1111········1111·11···········11·······11·······1···1111·1··1·1··1·1····11··1·1······1·1·······111111········11111······1·111···1··1··1···111111·1·····111·1·····111111····· |
| out 6 (129) | ·····11··1·11·1···11·1··1··1··111···1·1·1·····1···1··1··1··1·1··1··1·······1·111·1···1··1·····11···1··11·111·1·1·1··1··11111····1····1111111··11·1··1111···1·····1·1··1·111····111··1···1·1·11···1·11···1·1·1··1···1·1···1······1·1····1·1···1··1····11···11·1··1·1·1·1···1·1·1··11111··11··111111·1111··1111····1·· |
| out 7 (123) | 1111·1··111······111·1·········11···1·1·1·1··111····1···11···1··1··11···1·1·····1··1··········1····1··1111·111·1·1·1·111··1··11·1····1·111·1··111··1·····11··11111···111·······111··········11···1·11·1111·1···11····1···11··1·1········1··1·········1····1111····111·1···1·11·111··1·11·1··1·111··111111····11····· |
| out 8 (137) | ·······11·111·1·1·11·1··1··1··111···1·1·1·····1···1··1··1·······1··1·······111·111111·1·1··1·111···1··11·111·1·1·1··1··11111····1····11111····11·1··1111····1·······11·11111·1·111··1···1·1·11···1·11···1·1·1··1·········1······111····111111·1·1·1·111···11·1··1·1·1·1···1·1·1··11111··11··11111···111··1111······1 |
| out 9 (131) | 11···11·11·11···1·11·1··1···1··11··11·1·1····111··1·1···11·1··1·········1··1···1··11·1······1·1····111···11··11·11·1···11·1·····1···1·1·1111··1111··11···1·1·11··1·1·11·11···11111··1····1··11·1·1·11··11111···11··1··1······1··1······1··11·1·····1·1··11···1··1···1·1·1··111···11·1···11·1·1·111·1·111·11··1···1·· |
| out 10 (123) | 1·1··1·1··1·111···1·····1·1·1·1·11·111·······11·····11·11···1111···11···1···1·····1··11·1··1·11····1·11····111·11··1·1··1····1··1·····1·1··1··1·11···1·1··1·11·1·1··1··1·11····1····1··1·11··111·11····11··111·1····1111·11··1···1········1··11·1·1·11···11·······111·1···11·1·1··1···1·11···1·1···1·1·1··1·1·1····1 |
| out 11 (129) | ·11···1··11·1·····1·····1·11····11·11···1·1···11·······111·111·11···1········1··111·1·1·1··11··1···11··1····111··1···1·111·1·1··1···11111·1···1··1···11··111··11···1··11·1·····1····1··11····111·1··1·1·11···1·11··111·1··1·······1·····111·1·1·1·11··1·1··1·······11·1·11··1··1·111·11·11·11111·1··11····11·11··1·· |
| out 12 (115) | ·1·1··1·1···1·1····1·1····1·1··1·1·1··1·1·1··1111···11·1·1··1·111·········1·1···1·····1····1·1·1·····1·1·1··1···1·····111··1·11·1····111·1·····1·1·1·1·1·1··1·1·1··1·1···11·····11·····1·1··1·11···11·1111·111··1···1·11·······1·1······1·····1···1·1·1··1·1·1·····1·······1····111··11111··111·1···1·1·1·1·11·····1 |
| out 13 (127) | ·11··11··111··1·1··1·1··1·1····11·····1·1·1····1··1·11·1·1·111·1···11······11··11···1·1····1111·····1·1·1111·111·····1····1··1··1···1····11····1····1··1·1111·11·1·1··111·1··1··11··1··1····11·····11·1··11111··1··111·1·11·····11·····11···1·1···1111··1·1·11··1·1···111·1····1····1·1··1·1····11····1··1··111··1·1 |
| out 14 (129) | ·11···1··11·1·····1·····1·1··1··11········1··1·1····1··111·111·11···1········1··111·1·1·1··11··1···11··1··11111·11··11·1111··1······11111·1···1··1···11··111··11···1··11·1·····1····1··1·····11·······11·1·1·1·11··111·1··1·······1·····111·1·1·1·11··1·1··1····1·111·1·1··11·11·1111·1·1··11111·1··11····11·11··1·· |
| out 15 (119) | ··11··1·11····1·1····1······1·1··1··111···1··111····11·····111······1···1···11·11·11·1··1···1·11··1·····1111·1··1····11·1·1··········111···1··11···111···1·11··11··1·11···1··1···1·······11···1··111··1111·11·1····111····1··1···11····11·11·1··1··1·111····11··1·1···1····1···11·1·1·······111····1·11·111··1···1·1 |
| out 16 (107) | ·11··1··1·1·1······1····1·1····11··111········1·····1·11·1····111···1···1·1··1·11·111···1··11·1···1··1·1··11········11·1··1···1···1·1····11···1··1··1··1···1··11·1···1·1·1······1···1··1····11·1·11·····1··1·1··1·····11··1··1·1··1····11·111···1·11·1·1·1·1····1·1···········11·1··1··11·11····11··11···1··1····1·· |
| out 17 (121) | ······111··11·1·1·11·1··1·····111···111·1·1·······1··1··1·······1··1·······111·111·11···1····111···1··1··1·1·1·1····1···111·····1····11111····11·1··1111····1······111··111··1·111·11·····1·11···1111·1···1·1··1·········1······111····111·11···1···111···1··1····1·1·1···1···1···111···11··11111···111··1111······1 |
| out 18 (109) | ·····111··1·······11···········111·1····1·1··111····1····1··111·····1···1·1·1··1·1··11········11··1111·····11·1·····1···11···11·1······1111·······1·1111·111·····1·11··1·······11···········1111····1·1111·1····1···111···1··1·1·1·····1·1··11·······11111········111···1·····1···11··11·1····1111·······111111··1·· |
| out 19 (125) | ·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····111·111··1·1··111··1·········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···11···1···111·1···111·1·1··111·1·······1·····1··11·1·1······ |
| out 20 (123) | ·1·1····11··1·1·1··1·1··1·1····1·1·1·11·1·1···11····11·1·1··1·111·········1·1···1·1··11····1···1·····1·111··1···11····111·11··1·1····111·1·····1·1·1·1·1·1··1·1·1····11··11··1··11··1··1····1·11··111·1·11·111··1···1·11·······1·1······1·1··11···1···1··1·111···1·1·······11···111·11·111··111·1···1·1·1·1·11·····1 |
| out 21 (117) | 1111··1····11·1·1·····1····1··1·········1·1···11··1··1···1···1······1···1·1111·111·1111·1····1······1·····1·1······1·11·111··11·1·····1····1····11·11111·11·11111··1····111··1··········1·1·········1·1·111·1···1····1····1··1·1111····111·1111·1···1···1·······1··1·········1·11·111·1111···1·····1···11111111····1 |
| out 22 (125) | 1··1·11·····1·1·1··1·1··1·11···1·1··1·1·1···········1··1···11··1···1····1·1··1···111··1·11·1111·····1·1·11·1··111··11·1·11·1··1·····1·1··111···111·1·11····1·1··11·1·····11··1··11··1··11···1·1··1·11······1·1·····11··1·1···1·1··1······111··1·1·1111··1·1·11····1·····1·11·11·1·11·1·11··1·1··11·1··111·11·····1·· |
| out 23 (121) | ·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··11111111·····1·11·1···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···1·····1···1·····1·1·1111···1··1·11··111··1·111·1·1·····1·11·1··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 (123) | ··11·111··111·····11········1··111··11··1·1···11··1·1······111·1···11···1··1····11··1·1·····11····11··11··1····1·1··1111·11·····1···11··11·1·1···1·1··11·1·1···111·11··111·····11········1··111··11·1·1·1111·······111·1·11··1··1·······11··1·1····11··1··11····1···1·····1·1·1111·11···11·11··11··1····1··111···1·· |
| out 26 (137) | ·····1·111111·1·1·11·1·····1···11·1·1·1·······1···1·11··1·······1··1·······111·1·111111·1····111···1··1111111111·1·····11111·········11111····11·1··1111····1····1··1111111··1·111······1···11···1·1····1·111··1·········1······111····1·111111·1···111···1111··1·111·1·1·1·1····11111··1···11111···111··1111······1 |
| out 27 (123) | ·····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····1·1111111·1111·1·····1··11·11······1····1·1·11·1·······11·1····1··11··111··1···1······1·1···11·1·1··11·1111··1····11···1···1·1111·····1····11·1···1··1111111··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 (115) | 11···1·111·11···1·11·1·11··11··11··1··1······111··1·····11·1··1·········1··1···1·····1······1······11····1···11··1·11··11·1·········1·1·1111··1111··11···1·1·11··1··111·11···1·111··1···11··11·1···1···1111····11··1··1······1··1······1·····1·····1····1····1······1·1·1···111··11·1···1··1·1·111·1·111·11··1···1·· |
| out 30 (135) | ·11··11··111··1·1··1·1··1·11··1111···11·1·1····1··1·11·11···11·1···11······11··11···1·1····1111·····1·1·11·11111·1···1····1··1··1···111··1··········1··1·1111·11·1·1··111·1··1··11··1··11·1·111···111·1··11111·1····11·1111·····11·····11···1·1···1111··1·1·11····11··1·1·1·1··1····1·1··1·111··1········1··111··1·1 |
| out 31 (125) | ·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···1111·1·11·1·1··111··1·········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···11·····1·111·1···1·1·1·1··111·1·······1·····1··11·1·1······ |
| out 32 (123) | ·····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····1·1111111·1111·1·····1··11·11······1·····1··11·1·······11·1····1····11111··1···1······1·1···11·1·1··11·1111··1···1··1··1···1·1111·····1··11···1···1··1111111··1··1··1·1·1·1····1··11111···1·····11111······11····1 |
| out 33 (125) | 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·····11·1·1111··1·1··11·11·············111··1·1·1··1·11·1·11···1··1··1··1···1···11·····11·1111·1··1111·1111······1···1·1·1··1···1·1·1·····11·1··1·11··1···111···1·1 |
| out 34 (125) | ·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···1111··1···1·1··111··1·········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···11·····1·111·1····1··1·1··111·1·······1·····1··11·1·1······ |
| out 35 (111) | ·1·1··1····1·······1····1·1·1··1····1·····1·······1····1·1·1···1···1····1··111··1··1·1··1··1·1·1··1·1·1·····111111··1·111·11·1··1····111·1·1··1····1·1····11··1·1··1····1·······1···1··1·1··1····1····1···1··1··1··1···1·1··11··111·····1··1·1··1·1·1·111·1········1··1·1·111·1·111·111··1··111·1··1·1··1·1···1··1·· |
| out 36 (129) | ······1·1·111·1·1·11·1····11··111···111·1····1····1··1··1·······1··1·······111·111··1·1·1····111···1··111111·1·1····1··111······1····11111····11·1··1111····1······1·1·1111··1·111·····11·1·11···1111··1··1·1··1·········1······111····111··1·1·1···111···1111·11·1·1·1···1···1··111····11··11111···111··1111······1 |
| out 37 (107) | ·1·1·1····1·1·1····1·1····1·1··1·1·1··1·1···11·1····11·1·1··1·111·········1·1·····1·1······1·1·1·····1·1·1··1···1·····1·11····1·1····111·1·····1·1·1·1·1·1··1·1·11·····1·11·····11·····1·1··1·11···11··1·1·111··1···1·11·······1·1········1·1·····1·1·1··1·1·1·····1·······1····1·11···111··111·1···1·1·1·1·11·····1 |
| out 38 (125) | 1··1·11··1··1·····11·1··1·11···111····1···1·········1··1···11··1···1····1·1··1···111·11·1··11·1·1···1·1·11·1·111···1··1111·1··1·····1·1··111···111·1·11····1·1··11·1··1··1·····111··1··11···111····1··1····1·1·····11··1·1···1·1··1······111·11·1·11·1··1·1·11····1···1·1·1··1··1111·1·11··1·1··11·1··111·11·····1·· |
| out 39 (129) | ······1·1·111·1·1·11·1········111·····1·1·1···1··11··1··1·······1··1·······111·111··1·1·1····111···1··1111·1·1·111··1···1111··1·1····11111····11·1··1111····1······1·1·1111··1·111········1·11·····11·1·1·1·1··1·········1······111····111··1·1·1···111···1111····1·1·1···111·1···1111·111··11111···111··1111······1 |
| out 40 (115) | ·1·1·1·111··1·1····1·1····1·1··1·1·1··1·1·11···1····11·1·1··1·111·········1·1·····11·11····1·1·1·····1·1·1··1···1·····11··1···1·1····111·1·····1·1·1·1·1·1··1·1·11··111··11·····11·····1·1··1·11···11·1··1·111··1···1·11·······1·1········11·11···1·1·1··1·1·1·····1·······1····11··1··111··111·1···1·1·1·1·11·····1 |
| out 41 (117) | 1·1··1·11··1····1····1····111··111·1··1···········1·1··1····11111···1···1··1·1·111··11··1··1···1·1···1·1·11·11··1··1·1·1·1·1·1·······1·1·1·1···11···1·1···1··1·1·1··11··1····1···1·····111··1111···1······11·1······1111··1··1··1·1····111··11··1·1···1··1·1·1··1··1··1····1·1·1·1·1·11·····1·1·1··11·11·1·1··1····· |
| out 42 (123) | ···1····1111··1···1·····1·11··1·11··1···1·····1···1··1·11··11··11·······1·111··1··1111·····11··1···11··1·····11··1·11·11··1···1·····11·11·11··1·1··11··1···11···1····1111·1····1····1··11·1··11··1··1···1·1·11·1···11··1·····1·111·1···1··1111····11··1·1··1········1·1·1···111·11··1··1···11·11·1·111·111··1····1·1 |
| out 43 (119) | ·11···11·111··1····1·1····11···1·1···11·1·····11··1····1·1·111·1···11······11··1···11·1····11·1·····1·1··1·1··11·1···1·1··11·1···1··1····11····1····1··1·1111·11···11·111·1·····11·····11···1·1···111···111··1··1··111·1·11·····11·····1···11·1···11·1··1·1··1····1·····1·1·1··1·1··111····1····11····1··1··111··1·1 |
| out 44 (133) | ··11·1·1111···1·1·11·1······1·11···11·1·1·····1·····11·····1··1·····1·1···1··1··11111···1···1······111··111·1·1·11··111··111·11·····11··1111··11···11·11··1·1··111··1111··1··1·111·······11·1··1·1·11···1··11······1··1···1····1··1·····11111···1··1····11··11··1··11···1··11·111··11111···11··111·1·11·11·11·1····1 |
| out 45 (121) | ·11···1··11·1·····1·····1·11·····1···1···1···111·······111·111·11···1········1··111·1·1·1··11··1···11··1····1·1·1···1···1111·1··1···11111·1···1··1···11··111··11···1··11·1·····1····1··11·····1···1····111···1·11··111·1··1·······1·····111·1·1·1·11··1·1··1·······11···1··1··1···11111·11·11111·1··11····11·11··1·· |
| out 46 (123) | 111··11111·11···1·11·1·····11··1···11·1·1·1··111··1·····11·1··1·········1··1···1··1··1······1······111··11····1·11·1····1·1·········1·1·1111··1111··11···1·1·111·1·1111·11···1·111······11··1··1·1·11·11111····11··1··1······1··1····1·1··1··1·····1····11··11······1···1··111····1·1···1··1·1·111·1·111·11··1···1·· |
| out 47 (107) | ········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··1111··········1··11······1····11··11·1·······1111········1··111······1··1·····1···11·111···111111··1····1·1··1···1·1··1········1·11·1······11111·1·····1··1·1·1·········1·111···1····1·1111······11·11·1 |
| out 48 (123) | 111··11···1·1·1···1·····1·1·1·1·11·111··1············1·11···1111···11···1···1······1·11····1·11····1·11····111·11··111··1·11·1········1·1··1··1·11···1·1··1·1111·1·1···1·11····1····1··1·11··111·11·1·······11·1····1111·11··1···1··1······1·11···1·11···11·······111·1···11·111··1·111·1····1·1···1·1·1··1·1·1····1 |
| out 49 (121) | ·····11··1111·1·1·11·1········111·····1·1····1····1··1··1·······1··1·······111·1·····11·1····111···1··1111·1·1·111··1··111······1····11111····11·1··1111····1····111··11111··1·111········1·11·····11··1··1·1··1·········1······111····1·····11·1···111···1111····1·1·1···111·1··111····11··11111···111··1111······1 |
| out 50 (115) | 1111··11··111·1·1····1·····1············1····111··1··1···1···1······1···1·1111·111··11··1····1·····1······1········1·11111···11·1·····1····1····11·11111·11·11111··11··1111··1···1······1··1········1··1111·1···1····1····1··1·1111····111··11··1···1···········1···1········1·11111··1111···1·····1···11111111····1 |
| out 51 (119) | ·11··1····11··1····1·1····11··11·1····1···1··1·1··1·11·111··11·1···11······1···11·1·111····11·1·····1·1··1·11·11····11·······1··1···11···1·····1····1·11·11·1·11·1·····11·1·····11·····11·1·1·1····1··11·11111·11···11·1·111····1······11·1·111···11·1··1·1··1····11····1·1···11······1··1·11···1·····1··1·1111····1 |
| out 52 (129) | ·11··11·1···1···1·1·······11··1·11···1·11····111····1··111·111·11···1········1···11··1··1··111·1···11··11····11·1··1·1··1111·1······11111·1···1··1···11··111··11·1·1·1···1···1·1·······11·1··11···1·1··111·1·1·11··111·1··1·······1······11··1··1·111·1·1··11·······1·1·1··1·1·1··11111·1··11111·1··11····11·11··1·· |
| out 53 (109) | ·····111··1·······11·······1···111·11···1·1····1····1····1·1111·········1·1····1·1··11········11··1111····111·1·1···1···1111·11·1······11···········1111·11······1·11··1·······11·······1···1111·1··1·1··1·1····1·11111······1·1·······1·1··11·······11111······1·111···1··1··1···111111·1····11·········111111····· |
| out 54 (115) | 111·····111·····1·11·1·········1····111·1·1··1·1········11···1··1··11···1·1········1·········111···1··1111·11··1···1·111··11·11······1·111·1··111··1·····11··111·····111·····1·111··········1····1111·11·1·····11····1···11··1·1······1····1········111···1111····111·····1··1·111··1111····1·111··111111····11····· |
| out 55 (115) | ·1·1·1111···1·1·1··1·1··1·1·1·11·1·11·1·1····1·1·····1·11··111111·······1·1········1··1····1···1·····1·111············1·1·····1········1·111···1·1·1·1·111·11·1·11·111···11··1··11··1··1·11·1·11·1·11··1·1··11·1···11111·····1·1···········1··1···1···1··1·111··················1·1····11·····1·11·11·1·1·1·11···1·1 |
| out 56 (131) | ·····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·········1·1111·11·1111·1·····1··11·11······11····1··1111·······1111····1·1···1111······1··1···1·1···11·1·1··11·1111··11··11·1··1···1·11·1·····1·1111··1······11111·1··1··1··1·1·1·1····1··11111···11·····11111·····11··1·1 |
| out 57 (121) | ········11111·1···11·1··1··1··11······1···1···1···1··1···1······1··1·····1·1·1·1111·111·1·····11···1··11·111···111······1111····1······111····11·1··1111··111········111111····111··1···1·1·1······1··1·1·1·1···1········1······1·1····1111·111·1····11···11·1··1·1·1·····111·····1111··11····111···111··1111·1··1·1 |
| out 58 (119) | ··11··1·11····1·1····1······1·1·11··1·1·1·1···11····11···1·111······1···1·1··1·11·11·1··1···1·11··1·····1111····11··111·1···········11·1···1··11···111···1··1··11··1·11···1··1···1·······11··11··1·11·1·11·11···1··111····1··1·1··1····11·11·1··1··1·111····11··1·1········11·111·1········11·1····1·11·111··1·1···1 |
| out 59 (117) | ·1·1···111·1····1·1·······1·1·1·11·1·········11···1·1··111··1·11···1······11·1·1·1·1·11·1··1··1····1·11·1··111·1·1··1·11·1111·1·········1·····1····11·1··1····1·1···111·1····1·1·······1·11··111·······11·11·1·11···1·11·1·····11·1····1·1·1·11·1·1··1···11·1·····111·1···1·1·1·11·111·1·······1·····1··11·1·1······ |
| out 60 (115) | ·11···1··11·1·····1·····1·1······1······1·1··1·1···11··11···11·11··11·······11··111·1·1·1··11··1···11··1··1·1·1·11···1·1111··1······11·11·····1······11··11···11···1··11·1·····1····1··1······1·····1·11·1·1·1·1····11·1·11······11·····111·1·1·1·11··1·1··1····1··11···1··11··1·1111·1····11·11····11····11·11····· |
| out 61 (129) | ········1··11·1·1·11·1··1··1··111····11·1·1··11···1··1··1·······1··1·······111·1111·1···1···1111···1··11·111·1·11···1···11·1····1····11111····11·1··1111····1········1··111·11·111··1···1·1·11····111·111·1·1··1·········1······111····1111·1···1··1111···11·1··1·1·1·1···11··1···11·1··11··11111···111··1111······1 |
| out 62 (117) | ······1···1·····1·11····1··1···1·1·1····1····111········1···111········11·1·1··111·111·······111··1111··1·11111·····1··111···11······111111·········1·11·111·······1···1·····1·11···1···1···1·11····1··111·····1····111······1·1·1·····111·111······111111··1···1·111·1·1·····1··111··11····111111·······1·1111··1·· |
| out 63 (31) | ······1··1······1·······1·····1·1·······1·········1·······························1··1·······1··········1···11······1··········1···································1··1······1······1·····1··1······1·····1·······························1··1······1·······1······1··1·······1····································· |
| out 64 (121) | ····1··11··11·1·1·11·1········111·····1·1····1····1··1··1·······1··1·······111··11111···1····111···1··1111·1·1·111··1··111······1····11111····11·1··1111····1·······11··111··1·111········1·11·····11··1··1·1··1·········1······111·····11111···1···111···1111····1·1·1···111·1··111····11··11111···111··1111······1 |
| out 65 (31) | ·····11·1·1··············································111·1··················1·1·1·1···············································1·1·11·····················1·1·1·1········································1··1·1··················1·1·1·1··············································1·1·1·1················ |
| out 66 (31) | ·····1·1········1·······1·····1·1···················1···························1··1·········1··········1···11········1·········1································1··1········1······1·····1··1·······1·····1····························1··1········1·······1······1··1·········1········1·························· |
| out 67 (117) | ·····111··1·······11·······1···111·1·1··1····1·1····1······1111·········1·1·11·1·1··11········11··1111····111·1··1··1··111·1·11·1·····1111··········1111·111·····1·11··1·······11·······1···1111··1·1··1·1·1·······1111······1·1·11····1·1··11·······11111······1·111···1···1·1··111·111·1···1111········111111··11· |
| 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 (121) | ······1·1·111·1·1·11·1·····1··1·····1·1·······1···1·11··1·······1··1·······111·111··1·1·1····111···1··111111···1·1·····11111·········11111····11·1··1111····1······1·1·1111··1·111······1·1······1·1····1·111··1·········1······111····111··1·1·1···111···1111··1·1·11····1·1····11111··1···11111···111··1111······1 |
| check 70 (114) | 1111·1··111·····1·······1·····11·····11·1····11···1·11··1·······1··1·······111··1··1······111·····1111··1··1···11···1··111·1·········11111····11·1··1111····111111···111·····1······1·····1·1·····111··11·111··1·········1······111·····1··1·····111···111··1·····1·1·····11··1··111·1··1···11111···111··1111······1 |
| check 71 (124) | 1111··1111······1·11····111·1·1·11·11·····1··1····1··1··1··1·1··1···1···1·1·1·····1···1······111······11·11·1·1·1·······11······1····1111111··1111·1·····111·1111··1111······1·11···1·11·11··111·1····11··1·1··1···1·1····1··1·1·1········1···1·····111···11·1··1··1····1··1······11····11··111111·111111····11··1·· |
| check 72 (116) | ·····11··1·11·1···11·1··1··1··111···1·1······1····1·11·111·11·1·····1···1·1·1··1·1···1··1·····11···1··11·111·1·1·1·····111········1·1·1····1····11·1·····111·····1·1··1·111····111··1···1·1·11···1·1···1··1111·11··11·1···1··1·1·1·····1·1···1··1····11···11·1··1·1·1·1···1·1····111····1·11·1·····1···11····11··1·· |
| check 73 (154) | ···········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··1··1·1·1···1···111·1·1·1···111··11·111·11·11··11·1··111··11··111111111·1···11····1·1··11·1·11·111·1···11·····1·1··1···11··11··1·11·11·111·1···1·11·11·11111··111····1111·1··1··1·111·1··111··11·11··11·1 |
| check 74 (164) | ·11··1···11···1··111·1·11·11····11··1·1···11··1··1·1·1···1·11111····11·1····111··1··1·1111·11····1··11·1····111··11·11·1·1·1111·11·11·111·1·111··1·1··1··11·1··11··1·11··1·1·1·1···111··111·11·1····111111···1·11111·1·1111·1·11··1·1·1·111·····1··11·1·1····1·1·1··111111·11··11111111·11·111·1111·111···111·11·1·· |
| check 75 (152) | ··11··11·1···1··1·11·111···11···111·1····11·111111······111·1·1··1···1··11··11111·1·11···1··1·11111·11··11·11·1·111···1·111··11·11··1··11·1·1··1··1·11···111······1·1··1··1·1····1··11·····11111·111·11·11·11·1·1·1·11··1·1111·1·1···11111··1·1·1···1111········111111···1·1···1··1·········1·1·11·1·1··111111·1·111 |
| check 76 (150) | ·1·11111··1··1··111··1····1·11·1·1·111··1·111··1··111··1·11·1111·1·1··11··1·1·11···11··111·1····11···1·1·1·11····11···11·11···1111···11111·1·111···11··1·1····1·1·1·1··1111··11·111111·1·111··111··11··1·1··11···11·111·11·11··11·1·····11111··1··1··11··11·1·······11····11····1·1····11···1······1····1·11·1··1111 |
| check 77 (154) | 1··1·1···11111····1·11111·1···1··11··11···1··1·111·1···111·11·11·1·1·····1111·111·11·1·111·11··1··1··1·1··1·····1·11··1····111·1·1··11111·1111··11·11··11·11·1··11··11····1····1··11·1·1··1··1·111····111·1111·11····1··11···11···1····11·1·1·11··11··1·1·1·11··1···1·11111·11··1······1·1·11111··1··11111··11·11·11 |
| check 78 (160) | 1·1··11·1·1·1·11111·1111··1·1··1····1··111·11·1·1111···111·1·1·1··11·111111·1·11111·······11····11·1·11·1···111111··1··11··111·1·1····11·1····1··111·11·111··1·1·1·1·1·1·1111·1·1·1111·1·1··1····1···111·1·111·11··1·1·1··111·1·1·1····1111········111111··1·1·····1··1·1·1111·11··11··111···11·1····1·1·1··1··11111 |
| check 79 (134) | ··11·1··11111···1·······1··1111·1·111111·1·11··111·111···1···11·1···1·····111··1····1·······1·11····11111····1·1·111··11·1··1··111··11·1···········111····1····111···11111···1······1·11···11·1·1···11111·1·····1····11···1····111·····1····1······1·11·11111·11111111·111·1··11··1·11111··11·1·····1···111···1····· |
| check 80 (150) | ··11····111···1···11·1··1···1·111··1··1·1·1··1·······1111111····1111·111111··11··11·1···1···11·····111···11·111··1··1111·1···11·1·111·1··11111·1111·11111······11····111··1····111··1····11·11·1···11·11····1·1··11·11111·111·1·11·······11·1···1··11···11···1··1··11·1·1···1·1111·1··11·1··1·11··1·11··1····1111111 |
The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.
Figures of merit
inputs n308Noisy T states per run.
outputs k70
distance d3Exact, proved and witnessed here.
error coefficient A_{3}2,164Faults 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 N81
checks r11
V_{\mathrm{ex}}70T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3486Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3486Overhead per output qubit.
\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.
T-countnot computedMinimal T-count of the output gate. Not computable at this width.
phase-polynomial degreenot computedMinimised over changes of output basis.
effective width70Rank of the output rows modulo the check rows.
Output gate
70 T0 CS0 CCZon 70 output wires
As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}
As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69 (output wires per term, separated by +)
This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.
Clifford correction
With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 62 single-wire gates and 1194 \mathrm{CZ} gates: \mathrm{S}^\dagger on output 0, \mathrm{S}^\dagger on output 1, \mathrm{S}^\dagger on output 2, \mathrm{Z} on output 3, \mathrm{Z} on output 5, \mathrm{S}^\dagger on output 7, \mathrm{S}^\dagger on output 9, \mathrm{S}^\dagger on output 10, \mathrm{S}^\dagger on output 12, \mathrm{S} on output 13, \mathrm{S} on output 15, \mathrm{S}^\dagger on output 16, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{S}^\dagger on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{S} on output 24, \mathrm{S}^\dagger on output 25, \mathrm{S}^\dagger on output 27, \mathrm{S} on output 28, \mathrm{S}^\dagger on output 29, \mathrm{S} on output 30, \mathrm{Z} on output 31 and 1232 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 1256 correction gates
\mathrm{S}^\dagger on output 0, \mathrm{S}^\dagger on output 1, \mathrm{S}^\dagger on output 2, \mathrm{Z} on output 3, \mathrm{Z} on output 5, \mathrm{S}^\dagger on output 7, \mathrm{S}^\dagger on output 9, \mathrm{S}^\dagger on output 10, \mathrm{S}^\dagger on output 12, \mathrm{S} on output 13, \mathrm{S} on output 15, \mathrm{S}^\dagger on output 16, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{S}^\dagger on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{S} on output 24, \mathrm{S}^\dagger on output 25, \mathrm{S}^\dagger on output 27, \mathrm{S} on output 28, \mathrm{S}^\dagger on output 29, \mathrm{S} on output 30, \mathrm{Z} on output 31, \mathrm{S}^\dagger on output 32, \mathrm{Z} on output 33, \mathrm{Z} on output 34, \mathrm{S} on output 35, \mathrm{S}^\dagger on output 37, \mathrm{Z} on output 38, \mathrm{S}^\dagger on output 40, \mathrm{Z} on output 41, \mathrm{S}^\dagger on output 42, \mathrm{S} on output 43, \mathrm{Z} on output 44, \mathrm{S}^\dagger on output 46, \mathrm{S}^\dagger on output 47, \mathrm{S}^\dagger on output 48, \mathrm{S}^\dagger on output 50, \mathrm{S} on output 51, \mathrm{Z} on output 53, \mathrm{S}^\dagger on output 54, \mathrm{S}^\dagger on output 55, \mathrm{S}^\dagger on output 56, \mathrm{S} on output 58, \mathrm{Z} on output 59, \mathrm{S}^\dagger on output 60, \mathrm{Z} on output 62, \mathrm{S} on output 63, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{Z} on output 67, \mathrm{S} on output 68, \mathrm{S}^\dagger on check 70, \mathrm{Z} on check 71, \mathrm{Z} on check 72, \mathrm{S}^\dagger on check 73, \mathrm{Z} on check 74, \mathrm{S} on check 76, \mathrm{S}^\dagger on check 77, \mathrm{S} on check 79, \mathrm{S} on check 80, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 2, \mathrm{CZ} on output 0, output 3, \mathrm{CZ} on output 0, output 5, \mathrm{CZ} on output 0, output 9, \mathrm{CZ} on output 0, output 10, \mathrm{CZ} on output 0, output 12, \mathrm{CZ} on output 0, output 16, \mathrm{CZ} on output 0, output 18, \mathrm{CZ} on output 0, output 19, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 25, \mathrm{CZ} on output 0, output 27, \mathrm{CZ} on output 0, output 29, \mathrm{CZ} on output 0, output 31, \mathrm{CZ} on output 0, output 32, \mathrm{CZ} on output 0, output 33, \mathrm{CZ} on output 0, output 34, \mathrm{CZ} on output 0, output 37, \mathrm{CZ} on output 0, output 40, \mathrm{CZ} on output 0, output 41, \mathrm{CZ} on output 0, output 44, \mathrm{CZ} on output 0, output 46, \mathrm{CZ} on output 0, output 47, \mathrm{CZ} on output 0, output 48, \mathrm{CZ} on output 0, output 50, \mathrm{CZ} on output 0, output 53, \mathrm{CZ} on output 0, output 55, \mathrm{CZ} on output 0, output 56, \mathrm{CZ} on output 0, output 59, \mathrm{CZ} on output 0, output 62, \mathrm{CZ} on output 0, output 67, \mathrm{CZ} on output 0, check 71, \mathrm{CZ} on output 0, check 72, \mathrm{CZ} on output 0, check 76, \mathrm{CZ} on output 0, check 79, \mathrm{CZ} on output 0, check 80, \mathrm{CZ} on output 1, output 2, \mathrm{CZ} on output 1, output 7, \mathrm{CZ} on output 1, output 9, \mathrm{CZ} on output 1, output 10, \mathrm{CZ} on output 1, output 21, \mathrm{CZ} on output 1, output 22, \mathrm{CZ} on output 1, output 25, \mathrm{CZ} on output 1, output 29, \mathrm{CZ} on output 1, output 33, \mathrm{CZ} on output 1, output 38, \mathrm{CZ} on output 1, output 41, \mathrm{CZ} on output 1, output 42, \mathrm{CZ} on output 1, output 46, \mathrm{CZ} on output 1, output 48, \mathrm{CZ} on output 1, output 50, \mathrm{CZ} on output 1, output 54, \mathrm{CZ} on output 1, output 60, \mathrm{CZ} on output 1, check 72, \mathrm{CZ} on output 1, check 74, \mathrm{CZ} on output 1, check 76, \mathrm{CZ} on output 1, check 79, \mathrm{CZ} on output 2, output 3, \mathrm{CZ} on output 2, output 5, \mathrm{CZ} on output 2, output 7, \mathrm{CZ} on output 2, output 12, \mathrm{CZ} on output 2, output 16, \mathrm{CZ} on output 2, output 18, \mathrm{CZ} on output 2, output 19, \mathrm{CZ} on output 2, output 20, \mathrm{CZ} on output 2, output 21, \mathrm{CZ} on output 2, output 22, \mathrm{CZ} on output 2, output 27, \mathrm{CZ} on output 2, output 31, \mathrm{CZ} on output 2, output 32, \mathrm{CZ} on output 2, output 34, \mathrm{CZ} on output 2, output 37, \mathrm{CZ} on output 2, output 38, \mathrm{CZ} on output 2, output 40, \mathrm{CZ} on output 2, output 42, \mathrm{CZ} on output 2, output 44, \mathrm{CZ} on output 2, output 47, \mathrm{CZ} on output 2, output 53, \mathrm{CZ} on output 2, output 54, \mathrm{CZ} on output 2, output 55, \mathrm{CZ} on output 2, output 56, \mathrm{CZ} on output 2, output 59, \mathrm{CZ} on output 2, output 60, \mathrm{CZ} on output 2, output 62, \mathrm{CZ} on output 2, output 67, \mathrm{CZ} on output 2, check 71, \mathrm{CZ} on output 2, check 74, \mathrm{CZ} on output 2, check 80, \mathrm{CZ} on output 3, output 4, \mathrm{CZ} on output 3, output 5, \mathrm{CZ} on output 3, output 6, \mathrm{CZ} on output 3, output 7, \mathrm{CZ} on output 3, output 8, \mathrm{CZ} on output 3, output 9, \mathrm{CZ} on output 3, output 10, \mathrm{CZ} on output 3, output 11, \mathrm{CZ} on output 3, output 14, \mathrm{CZ} on output 3, output 17, \mathrm{CZ} on output 3, output 18, \mathrm{CZ} on output 3, output 19, \mathrm{CZ} on output 3, output 23, \mathrm{CZ} on output 3, output 25, \mathrm{CZ} on output 3, output 26, \mathrm{CZ} on output 3, output 29, \mathrm{CZ} on output 3, output 31, \mathrm{CZ} on output 3, output 34, \mathrm{CZ} on output 3, output 36, \mathrm{CZ} on output 3, output 39, \mathrm{CZ} on output 3, output 42, \mathrm{CZ} on output 3, output 44, \mathrm{CZ} on output 3, output 45, \mathrm{CZ} on output 3, output 46, \mathrm{CZ} on output 3, output 48, \mathrm{CZ} on output 3, output 49, \mathrm{CZ} on output 3, output 50, \mathrm{CZ} on output 3, output 52, \mathrm{CZ} on output 3, output 53, \mathrm{CZ} on output 3, output 54, \mathrm{CZ} on output 3, output 57, \mathrm{CZ} on output 3, output 59, \mathrm{CZ} on output 3, output 60, \mathrm{CZ} on output 3, output 61, \mathrm{CZ} on output 3, output 62, \mathrm{CZ} on output 3, output 64, \mathrm{CZ} on output 3, output 67, \mathrm{CZ} on output 3, output 69, \mathrm{CZ} on output 3, check 70, \mathrm{CZ} on output 3, check 72, \mathrm{CZ} on output 3, check 73, \mathrm{CZ} on output 3, check 74, \mathrm{CZ} on output 3, check 77, \mathrm{CZ} on output 3, check 80, \mathrm{CZ} on output 4, output 5, \mathrm{CZ} on output 4, output 6, \mathrm{CZ} on output 4, output 8, \mathrm{CZ} on output 4, output 11, \mathrm{CZ} on output 4, output 14, \mathrm{CZ} on output 4, output 17, \mathrm{CZ} on output 4, output 18, \mathrm{CZ} on output 4, output 19, \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 31, \mathrm{CZ} on output 4, output 33, \mathrm{CZ} on output 4, output 34, \mathrm{CZ} on output 4, output 36, \mathrm{CZ} on output 4, output 38, \mathrm{CZ} on output 4, output 39, \mathrm{CZ} on output 4, output 41, \mathrm{CZ} on output 4, output 44, \mathrm{CZ} on output 4, output 45, \mathrm{CZ} on output 4, output 49, \mathrm{CZ} on output 4, output 52, \mathrm{CZ} on output 4, output 53, \mathrm{CZ} on output 4, output 57, \mathrm{CZ} on output 4, output 59, \mathrm{CZ} on output 4, output 61, \mathrm{CZ} on output 4, output 62, \mathrm{CZ} on output 4, output 64, \mathrm{CZ} on output 4, output 67, \mathrm{CZ} on output 4, output 69, \mathrm{CZ} on output 4, check 70, \mathrm{CZ} on output 4, check 73, \mathrm{CZ} on output 4, check 76, \mathrm{CZ} on output 4, check 77, \mathrm{CZ} on output 4, check 79, \mathrm{CZ} on output 4, check 80, \mathrm{CZ} on output 5, output 6, \mathrm{CZ} on output 5, output 7, \mathrm{CZ} on output 5, output 8, \mathrm{CZ} on output 5, output 9, \mathrm{CZ} on output 5, output 10, \mathrm{CZ} on output 5, output 11, \mathrm{CZ} on output 5, output 14, \mathrm{CZ} on output 5, output 17, \mathrm{CZ} on output 5, output 18, \mathrm{CZ} on output 5, output 19, \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 29, \mathrm{CZ} on output 5, output 31, \mathrm{CZ} on output 5, output 34, \mathrm{CZ} on output 5, output 36, \mathrm{CZ} on output 5, output 39, \mathrm{CZ} on output 5, output 42, \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 48, \mathrm{CZ} on output 5, output 49, \mathrm{CZ} on output 5, output 50, \mathrm{CZ} on output 5, output 52, \mathrm{CZ} on output 5, output 53, \mathrm{CZ} on output 5, output 54, \mathrm{CZ} on output 5, output 57, \mathrm{CZ} on output 5, output 59, \mathrm{CZ} on output 5, output 60, \mathrm{CZ} on output 5, output 61, \mathrm{CZ} on output 5, output 62, \mathrm{CZ} on output 5, output 64, \mathrm{CZ} on output 5, output 67, \mathrm{CZ} on output 5, output 69, \mathrm{CZ} on output 5, check 70, \mathrm{CZ} on output 5, check 72, \mathrm{CZ} on output 5, check 73, \mathrm{CZ} on output 5, check 74, \mathrm{CZ} on output 5, check 77, \mathrm{CZ} on output 5, check 80, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 11, \mathrm{CZ} on output 6, output 14, \mathrm{CZ} on output 6, output 17, \mathrm{CZ} on output 6, output 18, \mathrm{CZ} on output 6, output 19, \mathrm{CZ} on output 6, output 21, \mathrm{CZ} on output 6, output 22, \mathrm{CZ} on output 6, output 23, \mathrm{CZ} on output 6, output 26, \mathrm{CZ} on output 6, output 31, \mathrm{CZ} on output 6, output 33, \mathrm{CZ} on output 6, output 34, \mathrm{CZ} on output 6, output 36, \mathrm{CZ} on output 6, output 38, \mathrm{CZ} on output 6, output 39, \mathrm{CZ} on output 6, output 41, \mathrm{CZ} on output 6, output 44, \mathrm{CZ} on output 6, output 45, \mathrm{CZ} on output 6, output 49, \mathrm{CZ} on output 6, output 52, \mathrm{CZ} on output 6, output 53, \mathrm{CZ} on output 6, output 57, \mathrm{CZ} on output 6, output 59, \mathrm{CZ} on output 6, output 61, \mathrm{CZ} on output 6, output 62, \mathrm{CZ} on output 6, output 64, \mathrm{CZ} on output 6, output 67, \mathrm{CZ} on output 6, output 69, \mathrm{CZ} on output 6, check 70, \mathrm{CZ} on output 6, check 73, \mathrm{CZ} on output 6, check 76, \mathrm{CZ} on output 6, check 77, \mathrm{CZ} on output 6, check 79, \mathrm{CZ} on output 6, check 80, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, output 10, \mathrm{CZ} on output 7, output 12, \mathrm{CZ} on output 7, output 16, \mathrm{CZ} on output 7, output 18, \mathrm{CZ} on output 7, output 19, \mathrm{CZ} on output 7, output 20, \mathrm{CZ} on output 7, output 25, \mathrm{CZ} on output 7, output 27, \mathrm{CZ} on output 7, output 29, \mathrm{CZ} on output 7, output 31, \mathrm{CZ} on output 7, output 32, \mathrm{CZ} on output 7, output 33, \mathrm{CZ} on output 7, output 34, \mathrm{CZ} on output 7, output 37, \mathrm{CZ} on output 7, output 40, \mathrm{CZ} on output 7, output 41, \mathrm{CZ} on output 7, output 44, \mathrm{CZ} on output 7, output 46, \mathrm{CZ} on output 7, output 47, \mathrm{CZ} on output 7, output 48, \mathrm{CZ} on output 7, output 50, \mathrm{CZ} on output 7, output 53, \mathrm{CZ} on output 7, output 55, \mathrm{CZ} on output 7, output 56, \mathrm{CZ} on output 7, output 59, \mathrm{CZ} on output 7, output 62, \mathrm{CZ} on output 7, output 67, \mathrm{CZ} on output 7, check 71, \mathrm{CZ} on output 7, check 72, \mathrm{CZ} on output 7, check 76, \mathrm{CZ} on output 7, check 79, \mathrm{CZ} on output 7, check 80, \mathrm{CZ} on output 8, output 11, \mathrm{CZ} on output 8, output 14, \mathrm{CZ} on output 8, output 17, \mathrm{CZ} on output 8, output 18, \mathrm{CZ} on output 8, output 19, \mathrm{CZ} on output 8, output 21, \mathrm{CZ} on output 8, output 22, \mathrm{CZ} on output 8, output 23, \mathrm{CZ} on output 8, output 26, \mathrm{CZ} on output 8, output 31, \mathrm{CZ} on output 8, output 33, \mathrm{CZ} on output 8, output 34, \mathrm{CZ} on output 8, output 36, \mathrm{CZ} on output 8, output 38, \mathrm{CZ} on output 8, output 39, \mathrm{CZ} on output 8, output 41, \mathrm{CZ} on output 8, output 44, \mathrm{CZ} on output 8, output 45, \mathrm{CZ} on output 8, output 49, \mathrm{CZ} on output 8, output 52, \mathrm{CZ} on output 8, output 53, \mathrm{CZ} on output 8, output 57, \mathrm{CZ} on output 8, output 59, \mathrm{CZ} on output 8, output 61, \mathrm{CZ} on output 8, output 62, \mathrm{CZ} on output 8, output 64, \mathrm{CZ} on output 8, output 67, \mathrm{CZ} on output 8, output 69, \mathrm{CZ} on output 8, check 70, \mathrm{CZ} on output 8, check 73, \mathrm{CZ} on output 8, check 76, \mathrm{CZ} on output 8, check 77, \mathrm{CZ} on output 8, check 79, \mathrm{CZ} on output 8, check 80, \mathrm{CZ} on output 9, output 12, \mathrm{CZ} on output 9, output 16, \mathrm{CZ} on output 9, output 18, \mathrm{CZ} on output 9, output 19, \mathrm{CZ} on output 9, output 20, \mathrm{CZ} on output 9, output 21, \mathrm{CZ} on output 9, output 22, \mathrm{CZ} on output 9, output 27, \mathrm{CZ} on output 9, output 31, \mathrm{CZ} on output 9, output 32, \mathrm{CZ} on output 9, output 34, \mathrm{CZ} on output 9, output 37, \mathrm{CZ} on output 9, output 38, \mathrm{CZ} on output 9, output 40, \mathrm{CZ} on output 9, output 42, \mathrm{CZ} on output 9, output 44, \mathrm{CZ} on output 9, output 47, \mathrm{CZ} on output 9, output 53, \mathrm{CZ} on output 9, output 54, \mathrm{CZ} on output 9, output 55, \mathrm{CZ} on output 9, output 56, \mathrm{CZ} on output 9, output 59, \mathrm{CZ} on output 9, output 60, \mathrm{CZ} on output 9, output 62, \mathrm{CZ} on output 9, output 67, \mathrm{CZ} on output 9, check 71, \mathrm{CZ} on output 9, check 74, \mathrm{CZ} on output 9, check 80, \mathrm{CZ} on output 10, output 12, \mathrm{CZ} on output 10, output 16, \mathrm{CZ} on output 10, output 18, \mathrm{CZ} on output 10, output 19, \mathrm{CZ} on output 10, output 20, \mathrm{CZ} on output 10, output 21, \mathrm{CZ} on output 10, output 22, \mathrm{CZ} on output 10, output 27, \mathrm{CZ} on output 10, output 31, \mathrm{CZ} on output 10, output 32, \mathrm{CZ} on output 10, output 34, \mathrm{CZ} on output 10, output 37, \mathrm{CZ} on output 10, output 38, \mathrm{CZ} on output 10, output 40, \mathrm{CZ} on output 10, output 42, \mathrm{CZ} on output 10, output 44, \mathrm{CZ} on output 10, output 47, \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 59, \mathrm{CZ} on output 10, output 60, \mathrm{CZ} on output 10, output 62, \mathrm{CZ} on output 10, output 67, \mathrm{CZ} on output 10, check 71, \mathrm{CZ} on output 10, check 74, \mathrm{CZ} on output 10, check 80, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 17, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 19, \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 26, \mathrm{CZ} on output 11, output 31, \mathrm{CZ} on output 11, output 33, \mathrm{CZ} on output 11, output 34, \mathrm{CZ} on output 11, output 36, \mathrm{CZ} on output 11, output 38, \mathrm{CZ} on output 11, output 39, \mathrm{CZ} on output 11, output 41, \mathrm{CZ} on output 11, output 44, \mathrm{CZ} on output 11, output 45, \mathrm{CZ} on output 11, output 49, \mathrm{CZ} on output 11, output 52, \mathrm{CZ} on output 11, output 53, \mathrm{CZ} on output 11, output 57, \mathrm{CZ} on output 11, output 59, \mathrm{CZ} on output 11, output 61, \mathrm{CZ} on output 11, output 62, \mathrm{CZ} on output 11, output 64, \mathrm{CZ} on output 11, output 67, \mathrm{CZ} on output 11, output 69, \mathrm{CZ} on output 11, check 70, \mathrm{CZ} on output 11, check 73, \mathrm{CZ} on output 11, check 76, \mathrm{CZ} on output 11, check 77, \mathrm{CZ} on output 11, check 79, \mathrm{CZ} on output 11, check 80, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, output 22, \mathrm{CZ} on output 12, output 25, \mathrm{CZ} on output 12, output 29, \mathrm{CZ} on output 12, output 33, \mathrm{CZ} on output 12, output 38, \mathrm{CZ} on output 12, output 41, \mathrm{CZ} on output 12, output 42, \mathrm{CZ} on output 12, output 46, \mathrm{CZ} on output 12, output 48, \mathrm{CZ} on output 12, output 50, \mathrm{CZ} on output 12, output 54, \mathrm{CZ} on output 12, output 60, \mathrm{CZ} on output 12, check 72, \mathrm{CZ} on output 12, check 74, \mathrm{CZ} on output 12, check 76, \mathrm{CZ} on output 12, check 79, \mathrm{CZ} on output 14, output 17, \mathrm{CZ} on output 14, output 18, \mathrm{CZ} on output 14, output 19, \mathrm{CZ} on output 14, output 21, \mathrm{CZ} on output 14, output 22, \mathrm{CZ} on output 14, output 23, \mathrm{CZ} on output 14, output 26, \mathrm{CZ} on output 14, output 31, \mathrm{CZ} on output 14, output 33, \mathrm{CZ} on output 14, output 34, \mathrm{CZ} on output 14, output 36, \mathrm{CZ} on output 14, output 38, \mathrm{CZ} on output 14, output 39, \mathrm{CZ} on output 14, output 41, \mathrm{CZ} on output 14, output 44, \mathrm{CZ} on output 14, output 45, \mathrm{CZ} on output 14, output 49, \mathrm{CZ} on output 14, output 52, \mathrm{CZ} on output 14, output 53, \mathrm{CZ} on output 14, output 57, \mathrm{CZ} on output 14, output 59, \mathrm{CZ} on output 14, output 61, \mathrm{CZ} on output 14, output 62, \mathrm{CZ} on output 14, output 64, \mathrm{CZ} on output 14, output 67, \mathrm{CZ} on output 14, output 69, \mathrm{CZ} on output 14, check 70, \mathrm{CZ} on output 14, check 73, \mathrm{CZ} on output 14, check 76, \mathrm{CZ} on output 14, check 77, \mathrm{CZ} on output 14, check 79, \mathrm{CZ} on output 14, check 80, \mathrm{CZ} on output 16, output 21, \mathrm{CZ} on output 16, output 22, \mathrm{CZ} on output 16, output 25, \mathrm{CZ} on output 16, output 29, \mathrm{CZ} on output 16, output 33, \mathrm{CZ} on output 16, output 38, \mathrm{CZ} on output 16, output 41, \mathrm{CZ} on output 16, output 42, \mathrm{CZ} on output 16, output 46, \mathrm{CZ} on output 16, output 48, \mathrm{CZ} on output 16, output 50, \mathrm{CZ} on output 16, output 54, \mathrm{CZ} on output 16, output 60, \mathrm{CZ} on output 16, check 72, \mathrm{CZ} on output 16, check 74, \mathrm{CZ} on output 16, check 76, \mathrm{CZ} on output 16, check 79, \mathrm{CZ} on output 17, output 18, \mathrm{CZ} on output 17, output 19, \mathrm{CZ} on output 17, output 21, \mathrm{CZ} on output 17, output 22, \mathrm{CZ} on output 17, output 23, \mathrm{CZ} on output 17, output 26, \mathrm{CZ} on output 17, output 31, \mathrm{CZ} on output 17, output 33, \mathrm{CZ} on output 17, output 34, \mathrm{CZ} on output 17, output 36, \mathrm{CZ} on output 17, output 38, \mathrm{CZ} on output 17, output 39, \mathrm{CZ} on output 17, output 41, \mathrm{CZ} on output 17, output 44, \mathrm{CZ} on output 17, output 45, \mathrm{CZ} on output 17, output 49, \mathrm{CZ} on output 17, output 52, \mathrm{CZ} on output 17, output 53, \mathrm{CZ} on output 17, output 57, \mathrm{CZ} on output 17, output 59, \mathrm{CZ} on output 17, output 61, \mathrm{CZ} on output 17, output 62, \mathrm{CZ} on output 17, output 64, \mathrm{CZ} on output 17, output 67, \mathrm{CZ} on output 17, output 69, \mathrm{CZ} on output 17, check 70, \mathrm{CZ} on output 17, check 73, \mathrm{CZ} on output 17, check 76, \mathrm{CZ} on output 17, check 77, \mathrm{CZ} on output 17, check 79, \mathrm{CZ} on output 17, check 80, \mathrm{CZ} on output 18, output 19, \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 29, \mathrm{CZ} on output 18, output 31, \mathrm{CZ} on output 18, output 34, \mathrm{CZ} on output 18, output 36, \mathrm{CZ} on output 18, output 39, \mathrm{CZ} on output 18, output 42, \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 48, \mathrm{CZ} on output 18, output 49, \mathrm{CZ} on output 18, output 50, \mathrm{CZ} on output 18, output 52, \mathrm{CZ} on output 18, output 53, \mathrm{CZ} on output 18, output 54, \mathrm{CZ} on output 18, output 57, \mathrm{CZ} on output 18, output 59, \mathrm{CZ} on output 18, output 60, \mathrm{CZ} on output 18, output 61, \mathrm{CZ} on output 18, output 62, \mathrm{CZ} on output 18, output 64, \mathrm{CZ} on output 18, output 67, \mathrm{CZ} on output 18, output 69, \mathrm{CZ} on output 18, check 70, \mathrm{CZ} on output 18, check 72, \mathrm{CZ} on output 18, check 73, \mathrm{CZ} on output 18, check 74, \mathrm{CZ} on output 18, check 77, \mathrm{CZ} on output 18, check 80, \mathrm{CZ} on output 19, output 23, \mathrm{CZ} on output 19, output 25, \mathrm{CZ} on output 19, output 26, \mathrm{CZ} on output 19, output 29, \mathrm{CZ} on output 19, output 31, \mathrm{CZ} on output 19, output 34, \mathrm{CZ} on output 19, output 36, \mathrm{CZ} on output 19, output 39, \mathrm{CZ} on output 19, output 42, \mathrm{CZ} on output 19, output 44, \mathrm{CZ} on output 19, output 45, \mathrm{CZ} on output 19, output 46, \mathrm{CZ} on output 19, output 48, \mathrm{CZ} on output 19, output 49, \mathrm{CZ} on output 19, output 50, \mathrm{CZ} on output 19, output 52, \mathrm{CZ} on output 19, output 53, \mathrm{CZ} on output 19, output 54, \mathrm{CZ} on output 19, output 57, \mathrm{CZ} on output 19, output 59, \mathrm{CZ} on output 19, output 60, \mathrm{CZ} on output 19, output 61, \mathrm{CZ} on output 19, output 62, \mathrm{CZ} on output 19, output 64, \mathrm{CZ} on output 19, output 67, \mathrm{CZ} on output 19, output 69, \mathrm{CZ} on output 19, check 70, \mathrm{CZ} on output 19, check 72, \mathrm{CZ} on output 19, check 73, \mathrm{CZ} on output 19, check 74, \mathrm{CZ} on output 19, check 77, \mathrm{CZ} on output 19, check 80, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 22, \mathrm{CZ} on output 20, output 25, \mathrm{CZ} on output 20, output 29, \mathrm{CZ} on output 20, output 33, \mathrm{CZ} on output 20, output 38, \mathrm{CZ} on output 20, output 41, \mathrm{CZ} on output 20, output 42, \mathrm{CZ} on output 20, output 46, \mathrm{CZ} on output 20, output 48, \mathrm{CZ} on output 20, output 50, \mathrm{CZ} on output 20, output 54, \mathrm{CZ} on output 20, output 60, \mathrm{CZ} on output 20, check 72, \mathrm{CZ} on output 20, check 74, \mathrm{CZ} on output 20, check 76, \mathrm{CZ} on output 20, check 79, \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 36, \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 45, \mathrm{CZ} on output 21, output 46, \mathrm{CZ} on output 21, output 47, \mathrm{CZ} on output 21, output 48, \mathrm{CZ} on output 21, output 49, \mathrm{CZ} on output 21, output 50, \mathrm{CZ} on output 21, output 52, \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 61, \mathrm{CZ} on output 21, output 64, \mathrm{CZ} on output 21, output 69, \mathrm{CZ} on output 21, check 70, \mathrm{CZ} on output 21, check 71, \mathrm{CZ} on output 21, check 72, \mathrm{CZ} on output 21, check 73, \mathrm{CZ} on output 21, check 77, \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 36, \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 45, \mathrm{CZ} on output 22, output 46, \mathrm{CZ} on output 22, output 47, \mathrm{CZ} on output 22, output 48, \mathrm{CZ} on output 22, output 49, \mathrm{CZ} on output 22, output 50, \mathrm{CZ} on output 22, output 52, \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 61, \mathrm{CZ} on output 22, output 64, \mathrm{CZ} on output 22, output 69, \mathrm{CZ} on output 22, check 70, \mathrm{CZ} on output 22, check 71, \mathrm{CZ} on output 22, check 72, \mathrm{CZ} on output 22, check 73, \mathrm{CZ} on output 22, check 77, \mathrm{CZ} on output 23, output 26, \mathrm{CZ} on output 23, output 31, \mathrm{CZ} on output 23, output 33, \mathrm{CZ} on output 23, output 34, \mathrm{CZ} on output 23, output 36, \mathrm{CZ} on output 23, output 38, \mathrm{CZ} on output 23, output 39, \mathrm{CZ} on output 23, output 41, \mathrm{CZ} on output 23, output 44, \mathrm{CZ} on output 23, output 45, \mathrm{CZ} on output 23, output 49, \mathrm{CZ} on output 23, output 52, \mathrm{CZ} on output 23, output 53, \mathrm{CZ} on output 23, output 57, \mathrm{CZ} on output 23, output 59, \mathrm{CZ} on output 23, output 61, \mathrm{CZ} on output 23, output 62, \mathrm{CZ} on output 23, output 64, \mathrm{CZ} on output 23, output 67, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, check 70, \mathrm{CZ} on output 23, check 73, \mathrm{CZ} on output 23, check 76, \mathrm{CZ} on output 23, check 77, \mathrm{CZ} on output 23, check 79, \mathrm{CZ} on output 23, check 80, \mathrm{CZ} on output 25, output 27, \mathrm{CZ} on output 25, output 31, \mathrm{CZ} on output 25, output 32, \mathrm{CZ} on output 25, output 34, \mathrm{CZ} on output 25, output 37, \mathrm{CZ} on output 25, output 38, \mathrm{CZ} on output 25, output 40, \mathrm{CZ} on output 25, output 42, \mathrm{CZ} on output 25, output 44, \mathrm{CZ} on output 25, output 47, \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 59, \mathrm{CZ} on output 25, output 60, \mathrm{CZ} on output 25, output 62, \mathrm{CZ} on output 25, output 67, \mathrm{CZ} on output 25, check 71, \mathrm{CZ} on output 25, check 74, \mathrm{CZ} on output 25, check 80, \mathrm{CZ} on output 26, output 31, \mathrm{CZ} on output 26, output 33, \mathrm{CZ} on output 26, output 34, \mathrm{CZ} on output 26, output 36, \mathrm{CZ} on output 26, output 38, \mathrm{CZ} on output 26, output 39, \mathrm{CZ} on output 26, output 41, \mathrm{CZ} on output 26, output 44, \mathrm{CZ} on output 26, output 45, \mathrm{CZ} on output 26, output 49, \mathrm{CZ} on output 26, output 52, \mathrm{CZ} on output 26, output 53, \mathrm{CZ} on output 26, output 57, \mathrm{CZ} on output 26, output 59, \mathrm{CZ} on output 26, output 61, \mathrm{CZ} on output 26, output 62, \mathrm{CZ} on output 26, output 64, \mathrm{CZ} on output 26, output 67, \mathrm{CZ} on output 26, output 69, \mathrm{CZ} on output 26, check 70, \mathrm{CZ} on output 26, check 73, \mathrm{CZ} on output 26, check 76, \mathrm{CZ} on output 26, check 77, \mathrm{CZ} on output 26, check 79, \mathrm{CZ} on output 26, check 80, \mathrm{CZ} on output 27, output 29, \mathrm{CZ} on output 27, output 33, \mathrm{CZ} on output 27, output 38, \mathrm{CZ} on output 27, output 41, \mathrm{CZ} on output 27, output 42, \mathrm{CZ} on output 27, output 46, \mathrm{CZ} on output 27, output 48, \mathrm{CZ} on output 27, output 50, \mathrm{CZ} on output 27, output 54, \mathrm{CZ} on output 27, output 60, \mathrm{CZ} on output 27, check 72, \mathrm{CZ} on output 27, check 74, \mathrm{CZ} on output 27, check 76, \mathrm{CZ} on output 27, check 79, \mathrm{CZ} on output 29, output 31, \mathrm{CZ} on output 29, output 32, \mathrm{CZ} on output 29, output 34, \mathrm{CZ} on output 29, output 37, \mathrm{CZ} on output 29, output 38, \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 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 59, \mathrm{CZ} on output 29, output 60, \mathrm{CZ} on output 29, output 62, \mathrm{CZ} on output 29, output 67, \mathrm{CZ} on output 29, check 71, \mathrm{CZ} on output 29, check 74, \mathrm{CZ} on output 29, check 80, \mathrm{CZ} on output 31, output 34, \mathrm{CZ} on output 31, output 36, \mathrm{CZ} on output 31, output 39, \mathrm{CZ} on output 31, output 42, \mathrm{CZ} on output 31, output 44, \mathrm{CZ} on output 31, output 45, \mathrm{CZ} on output 31, output 46, \mathrm{CZ} on output 31, output 48, \mathrm{CZ} on output 31, output 49, \mathrm{CZ} on output 31, output 50, \mathrm{CZ} on output 31, output 52, \mathrm{CZ} on output 31, output 53, \mathrm{CZ} on output 31, output 54, \mathrm{CZ} on output 31, output 57, \mathrm{CZ} on output 31, output 59, \mathrm{CZ} on output 31, output 60, \mathrm{CZ} on output 31, output 61, \mathrm{CZ} on output 31, output 62, \mathrm{CZ} on output 31, output 64, \mathrm{CZ} on output 31, output 67, \mathrm{CZ} on output 31, output 69, \mathrm{CZ} on output 31, check 70, \mathrm{CZ} on output 31, check 72, \mathrm{CZ} on output 31, check 73, \mathrm{CZ} on output 31, check 74, \mathrm{CZ} on output 31, check 77, \mathrm{CZ} on output 31, check 80, \mathrm{CZ} on output 32, output 33, \mathrm{CZ} on output 32, output 38, \mathrm{CZ} on output 32, output 41, \mathrm{CZ} on output 32, output 42, \mathrm{CZ} on output 32, output 46, \mathrm{CZ} on output 32, output 48, \mathrm{CZ} on output 32, output 50, \mathrm{CZ} on output 32, output 54, \mathrm{CZ} on output 32, output 60, \mathrm{CZ} on output 32, check 72, \mathrm{CZ} on output 32, check 74, \mathrm{CZ} on output 32, check 76, \mathrm{CZ} on output 32, check 79, \mathrm{CZ} on output 33, output 36, \mathrm{CZ} on output 33, output 37, \mathrm{CZ} on output 33, output 39, \mathrm{CZ} on output 33, output 40, \mathrm{CZ} on output 33, output 41, \mathrm{CZ} on output 33, output 42, \mathrm{CZ} on output 33, output 45, \mathrm{CZ} on output 33, output 47, \mathrm{CZ} on output 33, output 49, \mathrm{CZ} on output 33, output 52, \mathrm{CZ} on output 33, output 54, \mathrm{CZ} on output 33, output 55, \mathrm{CZ} on output 33, output 56, \mathrm{CZ} on output 33, output 57, \mathrm{CZ} on output 33, output 60, \mathrm{CZ} on output 33, output 61, \mathrm{CZ} on output 33, output 64, \mathrm{CZ} on output 33, output 69, \mathrm{CZ} on output 33, check 70, \mathrm{CZ} on output 33, check 71, \mathrm{CZ} on output 33, check 73, \mathrm{CZ} on output 33, check 74, \mathrm{CZ} on output 33, check 76, \mathrm{CZ} on output 33, check 77, \mathrm{CZ} on output 33, check 79, \mathrm{CZ} on output 34, output 36, \mathrm{CZ} on output 34, output 39, \mathrm{CZ} on output 34, output 42, \mathrm{CZ} on output 34, output 44, \mathrm{CZ} on output 34, output 45, \mathrm{CZ} on output 34, output 46, \mathrm{CZ} on output 34, output 48, \mathrm{CZ} on output 34, output 49, \mathrm{CZ} on output 34, output 50, \mathrm{CZ} on output 34, output 52, \mathrm{CZ} on output 34, output 53, \mathrm{CZ} on output 34, output 54, \mathrm{CZ} on output 34, output 57, \mathrm{CZ} on output 34, output 59, \mathrm{CZ} on output 34, output 60, \mathrm{CZ} on output 34, output 61, \mathrm{CZ} on output 34, output 62, \mathrm{CZ} on output 34, output 64, \mathrm{CZ} on output 34, output 67, \mathrm{CZ} on output 34, output 69, \mathrm{CZ} on output 34, check 70, \mathrm{CZ} on output 34, check 72, \mathrm{CZ} on output 34, check 73, \mathrm{CZ} on output 34, check 74, \mathrm{CZ} on output 34, check 77, \mathrm{CZ} on output 34, check 80, \mathrm{CZ} on output 36, output 38, \mathrm{CZ} on output 36, output 39, \mathrm{CZ} on output 36, output 41, \mathrm{CZ} on output 36, output 44, \mathrm{CZ} on output 36, output 45, \mathrm{CZ} on output 36, output 49, \mathrm{CZ} on output 36, output 52, \mathrm{CZ} on output 36, output 53, \mathrm{CZ} on output 36, output 57, \mathrm{CZ} on output 36, output 59, \mathrm{CZ} on output 36, output 61, \mathrm{CZ} on output 36, output 62, \mathrm{CZ} on output 36, output 64, \mathrm{CZ} on output 36, output 67, \mathrm{CZ} on output 36, output 69, \mathrm{CZ} on output 36, check 70, \mathrm{CZ} on output 36, check 73, \mathrm{CZ} on output 36, check 76, \mathrm{CZ} on output 36, check 77, \mathrm{CZ} on output 36, check 79, \mathrm{CZ} on output 36, check 80, \mathrm{CZ} on output 37, output 38, \mathrm{CZ} on output 37, output 41, \mathrm{CZ} on output 37, output 42, \mathrm{CZ} on output 37, output 46, \mathrm{CZ} on output 37, output 48, \mathrm{CZ} on output 37, output 50, \mathrm{CZ} on output 37, output 54, \mathrm{CZ} on output 37, output 60, \mathrm{CZ} on output 37, check 72, \mathrm{CZ} on output 37, check 74, \mathrm{CZ} on output 37, check 76, \mathrm{CZ} on output 37, check 79, \mathrm{CZ} on output 38, output 39, \mathrm{CZ} on output 38, output 40, \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 48, \mathrm{CZ} on output 38, output 49, \mathrm{CZ} on output 38, output 50, \mathrm{CZ} on output 38, output 52, \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 61, \mathrm{CZ} on output 38, output 64, \mathrm{CZ} on output 38, output 69, \mathrm{CZ} on output 38, check 70, \mathrm{CZ} on output 38, check 71, \mathrm{CZ} on output 38, check 72, \mathrm{CZ} on output 38, check 73, \mathrm{CZ} on output 38, check 77, \mathrm{CZ} on output 39, output 41, \mathrm{CZ} on output 39, output 44, \mathrm{CZ} on output 39, output 45, \mathrm{CZ} on output 39, output 49, \mathrm{CZ} on output 39, output 52, \mathrm{CZ} on output 39, output 53, \mathrm{CZ} on output 39, output 57, \mathrm{CZ} on output 39, output 59, \mathrm{CZ} on output 39, output 61, \mathrm{CZ} on output 39, output 62, \mathrm{CZ} on output 39, output 64, \mathrm{CZ} on output 39, output 67, \mathrm{CZ} on output 39, output 69, \mathrm{CZ} on output 39, check 70, \mathrm{CZ} on output 39, check 73, \mathrm{CZ} on output 39, check 76, \mathrm{CZ} on output 39, check 77, \mathrm{CZ} on output 39, check 79, \mathrm{CZ} on output 39, check 80, \mathrm{CZ} on output 40, output 41, \mathrm{CZ} on output 40, output 42, \mathrm{CZ} on output 40, output 46, \mathrm{CZ} on output 40, output 48, \mathrm{CZ} on output 40, output 50, \mathrm{CZ} on output 40, output 54, \mathrm{CZ} on output 40, output 60, \mathrm{CZ} on output 40, check 72, \mathrm{CZ} on output 40, check 74, \mathrm{CZ} on output 40, check 76, \mathrm{CZ} on output 40, check 79, \mathrm{CZ} on output 41, output 42, \mathrm{CZ} on output 41, output 45, \mathrm{CZ} on output 41, output 47, \mathrm{CZ} on output 41, output 49, \mathrm{CZ} on output 41, output 52, \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 57, \mathrm{CZ} on output 41, output 60, \mathrm{CZ} on output 41, output 61, \mathrm{CZ} on output 41, output 64, \mathrm{CZ} on output 41, output 69, \mathrm{CZ} on output 41, check 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 77, \mathrm{CZ} on output 41, check 79, \mathrm{CZ} on output 42, output 44, \mathrm{CZ} on output 42, output 46, \mathrm{CZ} on output 42, output 47, \mathrm{CZ} on output 42, output 48, \mathrm{CZ} on output 42, output 50, \mathrm{CZ} on output 42, output 53, \mathrm{CZ} on output 42, output 55, \mathrm{CZ} on output 42, output 56, \mathrm{CZ} on output 42, output 59, \mathrm{CZ} on output 42, output 62, \mathrm{CZ} on output 42, output 67, \mathrm{CZ} on output 42, check 71, \mathrm{CZ} on output 42, check 72, \mathrm{CZ} on output 42, check 76, \mathrm{CZ} on output 42, check 79, \mathrm{CZ} on output 42, check 80, \mathrm{CZ} on output 44, output 45, \mathrm{CZ} on output 44, output 46, \mathrm{CZ} on output 44, output 48, \mathrm{CZ} on output 44, output 49, \mathrm{CZ} on output 44, output 50, \mathrm{CZ} on output 44, output 52, \mathrm{CZ} on output 44, output 53, \mathrm{CZ} on output 44, output 54, \mathrm{CZ} on output 44, output 57, \mathrm{CZ} on output 44, output 59, \mathrm{CZ} on output 44, output 60, \mathrm{CZ} on output 44, output 61, \mathrm{CZ} on output 44, output 62, \mathrm{CZ} on output 44, output 64, \mathrm{CZ} on output 44, output 67, \mathrm{CZ} on output 44, output 69, \mathrm{CZ} on output 44, check 70, \mathrm{CZ} on output 44, check 72, \mathrm{CZ} on output 44, check 73, \mathrm{CZ} on output 44, check 74, \mathrm{CZ} on output 44, check 77, \mathrm{CZ} on output 44, check 80, \mathrm{CZ} on output 45, output 49, \mathrm{CZ} on output 45, output 52, \mathrm{CZ} on output 45, output 53, \mathrm{CZ} on output 45, output 57, \mathrm{CZ} on output 45, output 59, \mathrm{CZ} on output 45, output 61, \mathrm{CZ} on output 45, output 62, \mathrm{CZ} on output 45, output 64, \mathrm{CZ} on output 45, output 67, \mathrm{CZ} on output 45, output 69, \mathrm{CZ} on output 45, check 70, \mathrm{CZ} on output 45, check 73, \mathrm{CZ} on output 45, check 76, \mathrm{CZ} on output 45, check 77, \mathrm{CZ} on output 45, check 79, \mathrm{CZ} on output 45, check 80, \mathrm{CZ} on output 46, output 47, \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 59, \mathrm{CZ} on output 46, output 60, \mathrm{CZ} on output 46, output 62, \mathrm{CZ} on output 46, output 67, \mathrm{CZ} on output 46, check 71, \mathrm{CZ} on output 46, check 74, \mathrm{CZ} on output 46, check 80, \mathrm{CZ} on output 47, output 48, \mathrm{CZ} on output 47, output 50, \mathrm{CZ} on output 47, output 54, \mathrm{CZ} on output 47, output 60, \mathrm{CZ} on output 47, check 72, \mathrm{CZ} on output 47, check 74, \mathrm{CZ} on output 47, check 76, \mathrm{CZ} on output 47, check 79, \mathrm{CZ} on output 48, output 53, \mathrm{CZ} on output 48, output 54, \mathrm{CZ} on output 48, output 55, \mathrm{CZ} on output 48, output 56, \mathrm{CZ} on output 48, output 59, \mathrm{CZ} on output 48, output 60, \mathrm{CZ} on output 48, output 62, \mathrm{CZ} on output 48, output 67, \mathrm{CZ} on output 48, check 71, \mathrm{CZ} on output 48, check 74, \mathrm{CZ} on output 48, check 80, \mathrm{CZ} on output 49, output 52, \mathrm{CZ} on output 49, output 53, \mathrm{CZ} on output 49, output 57, \mathrm{CZ} on output 49, output 59, \mathrm{CZ} on output 49, output 61, \mathrm{CZ} on output 49, output 62, \mathrm{CZ} on output 49, output 64, \mathrm{CZ} on output 49, output 67, \mathrm{CZ} on output 49, output 69, \mathrm{CZ} on output 49, check 70, \mathrm{CZ} on output 49, check 73, \mathrm{CZ} on output 49, check 76, \mathrm{CZ} on output 49, check 77, \mathrm{CZ} on output 49, check 79, \mathrm{CZ} on output 49, 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 59, \mathrm{CZ} on output 50, output 60, \mathrm{CZ} on output 50, output 62, \mathrm{CZ} on output 50, output 67, \mathrm{CZ} on output 50, check 71, \mathrm{CZ} on output 50, check 74, \mathrm{CZ} on output 50, check 80, \mathrm{CZ} on output 52, output 53, \mathrm{CZ} on output 52, output 57, \mathrm{CZ} on output 52, output 59, \mathrm{CZ} on output 52, output 61, \mathrm{CZ} on output 52, output 62, \mathrm{CZ} on output 52, output 64, \mathrm{CZ} on output 52, output 67, \mathrm{CZ} on output 52, output 69, \mathrm{CZ} on output 52, check 70, \mathrm{CZ} on output 52, check 73, \mathrm{CZ} on output 52, check 76, \mathrm{CZ} on output 52, check 77, \mathrm{CZ} on output 52, check 79, \mathrm{CZ} on output 52, check 80, \mathrm{CZ} on output 53, output 54, \mathrm{CZ} on output 53, output 57, \mathrm{CZ} on output 53, output 59, \mathrm{CZ} on output 53, output 60, \mathrm{CZ} on output 53, output 61, \mathrm{CZ} on output 53, output 62, \mathrm{CZ} on output 53, output 64, \mathrm{CZ} on output 53, output 67, \mathrm{CZ} on output 53, output 69, \mathrm{CZ} on output 53, check 70, \mathrm{CZ} on output 53, check 72, \mathrm{CZ} on output 53, check 73, \mathrm{CZ} on output 53, check 74, \mathrm{CZ} on output 53, check 77, \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 59, \mathrm{CZ} on output 54, output 62, \mathrm{CZ} on output 54, output 67, \mathrm{CZ} on output 54, check 71, \mathrm{CZ} on output 54, check 72, \mathrm{CZ} on output 54, check 76, \mathrm{CZ} on output 54, check 79, \mathrm{CZ} on output 54, check 80, \mathrm{CZ} on output 55, output 60, \mathrm{CZ} on output 55, check 72, \mathrm{CZ} on output 55, check 74, \mathrm{CZ} on output 55, check 76, \mathrm{CZ} on output 55, check 79, \mathrm{CZ} on output 56, output 60, \mathrm{CZ} on output 56, check 72, \mathrm{CZ} on output 56, check 74, \mathrm{CZ} on output 56, check 76, \mathrm{CZ} on output 56, check 79, \mathrm{CZ} on output 57, output 59, \mathrm{CZ} on output 57, output 61, \mathrm{CZ} on output 57, output 62, \mathrm{CZ} on output 57, output 64, \mathrm{CZ} on output 57, output 67, \mathrm{CZ} on output 57, output 69, \mathrm{CZ} on output 57, check 70, \mathrm{CZ} on output 57, check 73, \mathrm{CZ} on output 57, check 76, \mathrm{CZ} on output 57, check 77, \mathrm{CZ} on output 57, check 79, \mathrm{CZ} on output 57, check 80, \mathrm{CZ} on output 59, output 60, \mathrm{CZ} on output 59, output 61, \mathrm{CZ} on output 59, output 62, \mathrm{CZ} on output 59, output 64, \mathrm{CZ} on output 59, output 67, \mathrm{CZ} on output 59, output 69, \mathrm{CZ} on output 59, check 70, \mathrm{CZ} on output 59, check 72, \mathrm{CZ} on output 59, check 73, \mathrm{CZ} on output 59, check 74, \mathrm{CZ} on output 59, check 77, \mathrm{CZ} on output 59, check 80, \mathrm{CZ} on output 60, output 62, \mathrm{CZ} on output 60, output 67, \mathrm{CZ} on output 60, check 71, \mathrm{CZ} on output 60, check 72, \mathrm{CZ} on output 60, check 76, \mathrm{CZ} on output 60, check 79, \mathrm{CZ} on output 60, check 80, \mathrm{CZ} on output 61, output 62, \mathrm{CZ} on output 61, output 64, \mathrm{CZ} on output 61, output 67, \mathrm{CZ} on output 61, output 69, \mathrm{CZ} on output 61, check 70, \mathrm{CZ} on output 61, check 73, \mathrm{CZ} on output 61, check 76, \mathrm{CZ} on output 61, check 77, \mathrm{CZ} on output 61, check 79, \mathrm{CZ} on output 61, check 80, \mathrm{CZ} on output 62, output 64, \mathrm{CZ} on output 62, output 67, \mathrm{CZ} on output 62, output 69, \mathrm{CZ} on output 62, check 70, \mathrm{CZ} on output 62, check 72, \mathrm{CZ} on output 62, check 73, \mathrm{CZ} on output 62, check 74, \mathrm{CZ} on output 62, check 77, \mathrm{CZ} on output 62, check 80, \mathrm{CZ} on output 64, output 67, \mathrm{CZ} on output 64, output 69, \mathrm{CZ} on output 64, check 70, \mathrm{CZ} on output 64, check 73, \mathrm{CZ} on output 64, check 76, \mathrm{CZ} on output 64, check 77, \mathrm{CZ} on output 64, check 79, \mathrm{CZ} on output 64, check 80, \mathrm{CZ} on output 67, output 69, \mathrm{CZ} on output 67, check 70, \mathrm{CZ} on output 67, check 72, \mathrm{CZ} on output 67, check 73, \mathrm{CZ} on output 67, check 74, \mathrm{CZ} on output 67, check 77, \mathrm{CZ} on output 67, check 80, \mathrm{CZ} on output 69, check 70, \mathrm{CZ} on output 69, check 73, \mathrm{CZ} on output 69, check 76, \mathrm{CZ} on output 69, check 77, \mathrm{CZ} on output 69, check 79, \mathrm{CZ} on output 69, check 80, \mathrm{CZ} on check 70, check 73, \mathrm{CZ} on check 70, check 76, \mathrm{CZ} on check 70, check 77, \mathrm{CZ} on check 70, check 79, \mathrm{CZ} on check 70, check 80, \mathrm{CZ} on check 71, check 72, \mathrm{CZ} on check 71, check 74, \mathrm{CZ} on check 71, check 76, \mathrm{CZ} on check 71, check 79, \mathrm{CZ} on check 72, check 74, \mathrm{CZ} on check 72, check 80, \mathrm{CZ} on check 73, check 76, \mathrm{CZ} on check 73, check 77, \mathrm{CZ} on check 73, check 79, \mathrm{CZ} on check 73, check 80, \mathrm{CZ} on check 74, check 76, \mathrm{CZ} on check 74, check 79, \mathrm{CZ} on check 74, check 80, \mathrm{CZ} on check 76, check 77, \mathrm{CZ} on check 76, check 79, \mathrm{CZ} on check 77, check 79, \mathrm{CZ} on check 77, check 80
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 0, 2, 8, 10, 14, 16, 22, 25, 34, 38, 44, 45, 46, 48, 54, 70, 85, 89, 90, 91, 93, 94, 95, 96 and 98 more (listed below); \mathrm{T}^5 on rotations 1, 3, 5, 6, 7, 11, 26, 27, 29, 35, 40, 47, 50, 61, 80, 81, 87, 106, 157, 182; \mathrm{T}^\dagger on rotations 9, 13, 18, 23, 31, 32, 36, 41, 42, 49, 55, 56, 59, 60, 63, 66, 67, 71, 72, 79, 164, 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 122 rotations at T³
0, 2, 8, 10, 14, 16, 22, 25, 34, 38, 44, 45, 46, 48, 54, 70, 85, 89, 90, 91, 93, 94, 95, 96, 97, 98, 101, 102, 107, 109, 110, 112, 113, 114, 115, 118, 119, 120, 121, 126, 129, 131, 133, 139, 141, 144, 147, 149, 151, 152, 158, 159, 161, 162, 166, 167, 168, 169, 170, 172, 173, 175, 177, 181, 183, 186, 187, 188, 190, 195, 196, 197, 199, 201, 202, 205, 209, 211, 212, 213, 214, 215, 217, 218, 221, 222, 223, 226, 229, 230, 232, 235, 236, 237, 244, 249, 251, 257, 259, 261, 264, 265, 266, 268, 270, 272, 275, 277, 279, 283, 287, 288, 290, 292, 293, 294, 295, 298, 299, 302, 304, 307
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/308.70.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-308.70.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 2,164 faults of weight 3 are undetectable and damaging, so A_{3}=2{,}164. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).
A damaging fault of weight 3 sits on columns [0,1,63].
A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.
Original source
S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535
Provenance
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_308_70_3_cf4a3978731c.json",
"label": "paired_column_contraction_308_70_3_cf4a3978731c",
"N": 81,
"d": 3,
"d_is_exact": true,
"origin": "Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=96), with searched graph punctures; 3 paired-column contractions",
"provenance": "gamma frontier release record paired_column_contraction_308_70_3_cf4a3978731c (source catalogue id paired_column_contraction_308_70_3_cf4a3978731c); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=96), with searched graph punctures; 3 paired-column contractions; matrix cf4a3978731c7946...; the release states d=3 (exact), gamma=1.3486145714976683 (exact)",
"notes": "matrix gamma_frontier_release/matrices/cf4a3978731c79461e234dda7bd2988016d7b1ecea383521795d787bca5cc05e.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/308.70.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]
facts, problems = VC.derive(columns, k, N) # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N) # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
problems or "verified")
Raw record
Show the JSON this page is built from
Source: master_catalog.json, factories[958].