The circuit
The 47\times496 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.
| wire | 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 |
|---|---|
| out 0 (228) | ·11·111··1·111·1111···1·1·1····1·1····1·1·1·1···1·111···1111···1·1111··1·1·11·······11111111··1·1··1·11·11111··111·1·····111··1111·1···11·11··1···1·11····1·1····1··1··111·1·111·1111····1·111111·······1·111·11···11·1·1·····111··11··1······1········11·111··11·1···11111·1·11·11·1·1····1··111·11·11·····1··1·1·1·1·1·1·1·····1··11··1·1··1··11·····111·····1·1·1·1····11111··11·11111··1·1·1·11111··1·1111·1111·1····111111·1111···1··1······1·1··1··1·11·1····11···11·11·1··1····1······1···11············· |
| out 1 (248) | 1·11··11······1·11·111··1111·1·1·1·1·1·1··1111·1111·1111·1111111111······111·1·1·111··1···1·1··1··1···1···11·1·····1·11·1·1··11··1··111·1111··1111·111111·11········1·1111·1111·11111·1·1··111·111111··1·1····11··1··11···111··111····1··1··1111111·11·11··1·····111111··11111·····111111··1·1·1··1·111·1·····1·11·1···1··111··11··1·1·11·1··111···111111··11·1111·1··11·1·1····11·1··11···111······1·1·1···1···1·1·1··1·11···11·11···11····1111111·1111·1·11······1·1·····1······11··11·1···11·1··············· |
| out 2 (254) | 11·111·1···11···11111·····1·····1···1111111··1······11·1··1111·1·11··1··11·····1·1··1····1·111······1111·11·111·1·111·1111·11···111·111·11··1·1111111··1·1··11·1·1111·1····1·111·11·111··1·····1·111·1111···1··1···1··1·1·11···11·1····11·1···1·1···1111·1111·1·111····1·1111··11·1·1111····11·11···11·1··111·1·111·1·111···1·1··1·11·1·11111··1··11····11111111·111·1··1··1·1··11·1·11·1··11···11·1···1···111·1111·11··111·111111··11·1111··11·1··1···1·1·····1·11·1··1··1·1·11111·1·111····11·1·1············· |
| out 3 (250) | ··1···111·11····11····1··11·1·11··1·1·11·11·1·1·111·1·111111111··111·1111111···11··111·1··11·11··1···1111··1111··1··11····1··11·1··111··11··1111···1·11·1·······1··11·111·111·1·1·1111·1·1··1·1·1··111·11··1··11·1·1·1·1·1111·11·111·11111··111·11··11····111·1·1··111··111······1·1···1·1111·1·1··1····1·····1··11·1··11111····1····11·1·1···11111·····11·····1··1·1··11·1····1·1111··11··11·111·111·1111·1·1···111··1·1··1··1·111···1·111·1··1·111··11··1···1·1··1···1·1·1··111··111·111···1·1·111··1········· |
| out 4 (242) | ·111····1·1111·1···1··1··1···1··11·1·1···1·11·11·1··1···11··11111111·1·11····1··11·1····111··111···111··1111··1·11111·1·1111···1·11·11·1·1111····1111·····11··111··11111·1····1·1··11···11·1····1·1··111··1·11·111·1······1····1··111·11··111·11··111···111·1·1·1·1··1·1···1·1··1··1······1·11111·1···11·1·11····11·1·11·11··1·····1·····111·11·111·1·1····1·11·····1111·1···1···11···1···111·1·111·111··1·1··1111···111·1·111···111·11···1·11·1·11·111·1··1·11·11·11·11111·11·11·1··111·····11··1·1············ |
| out 5 (236) | 1···········111·1·11·111····1··1·11·1··111······1·11··11·11····1··1·11·1·······11·1111··1···1····1·1···11·1·····1··11···11··1·1·111111111··1·111······11111·1··11·1111·111···11··111····111······11111····11···11···1···1·····1111·1111····1···1111·1·1····1··111·1·1111·1·1·1111111···11·11111·111111·11·1·1···1·1···1111·111·1·1····11·1·1·1·11··11·1···1·111··111···11·11··1111·····1·11···11·11··1111111···11·····1···1·11·11·1·1······11·1111··1···1···111·11·1·1·1111·······111···1·11·111······1········· |
| out 6 (242) | ·······1111·1·1·111·1111·11···11·11·11··11·1·11·1·1·111·1··111······1··11·11·1111····11·······1·······1·1····1·1···11·11·1111···1···11····111···111···1···1·1·1·1··1111···11·1·11·1··1····1111··1111··1·11111·11·1····1111111··1·11·11111·1111··111·1·111·111··1··1······11·11·1··111··1··1··11··1·1···1·11·1111·11··1··1··11··1·11·1·1111·1·1····11··1·1··1·11·11·1·11·111····1·····11·1··1···1·111·11·······1··1111·111··111·1111······11···111·11·11·1·11·1····1····1·11111··1··111·11····1111·1·1··········· |
| out 7 (238) | ···1··11·1··1·1····1·1·11·1··1··1··11···1·1·····11111··11·····1··11111111··11·11·1111·1··1·1·11··11·····11··111111··1·1·11·11·1·1··1·····111·1·1·1···1···11··11····1·1·1·11·111·11··1··1···11··1··11·1··1···11·11·1·1·1··1····111·11111·111··1·1··1·1····11111··11111·1·111··1·1111·11····1····111·11··11··1·1··1··1··1·1···1···111·1·1·11·1····1··11·111···1··1·········11111·111····11·1·1····11·1·11111·1·11···1·1··1·11·111·111···1·11···1·1111··1111··1···1··111·111·1·1··1··11111111····1·1···1··········· |
| out 8 (254) | ·1·1·1····1111·111·1·1·11·1·1·111······11111111·11·1····1·1·1····11111···111·1111·1·11111·111··1··1·1·11111··1111··1·1····111··1··1········111·11111·11111·11·111··1··1·1···11····1··111·111··11111·1··1···1·111···1·11·11·111··1·111···1···111111·1·1·1·11·1··11··1···11·11·1···1·1··1··11·111·111··11··11····1········1·1·1111·1·111···1···1··111·11111·1··1····111····1111··111·1··11·11·1····1·11···111·1····111·11·1·11·1···1··111111··11····11·1·1111··1·111·11·1·11·11111·1·1····1·11··1··1·············· |
| out 9 (252) | ·1·111·1·1·1···1·111···11··1···1·1·11·1··11··11·111··1··11··11111···1111··1·111·1·······1·1···111·1·11····11·1·1111··1111··1·1··1·1·1·11···11·1··1·1···1·11·11····1·····1·11······1·1·1···111·111·111·1····1·11··11···1··1···111·111··1·1·1·1····1··1·111111·11··111·1·11·111111·1··1·11·1···11·1·1··1·1111····11·1··111··111·1111··1···1··111·111111·111··1·1111·111·1··11··11·1·1·1·1········111··11·1···111·11·111·1·111··1·1111····111··1·1·111·11111··1·11··1111111·1····11·1··1·111··1·11·1··1············ |
| out 10 (220) | ·1·1··111111·11111···1···1·······111·1··11·1·1···1··111·······1·1·1····1111···111··1·1·1··11···1···111·····111·1·11····1··1·1····1··1·1···11··1···11·111·11···11·11···111111111·1··11··111··1····11·11······111·1····11·111···11·····11111·····11···11·1·1··1··11·1······11·111·111·11······111··1·1·1·11······11111·1·1·1·1·1···11······1·1·111···1···1··11111·11··111·····111···1··111··111···11··1····1···1111···1···111···········1···11·1··········1111·1····111·1111·1·1·1111··1·1·1·1··1·11111·1········· |
| out 11 (238) | ·11·111····11·1···1··1··11·1·1·111·11·1·11·11··1111···1··1····1·1····1··1·11·1····111·1··111·1·1··1·11·1·1·11·1·1·1·11·1·111111·1·1·······111·····1··11·111111·1·111···111··1··11··1·1··11·111··1···111·11··1·1···11·1··1···1····11···11111·11·1·11···1·111·1·1·1··11111·····1·11·11····1··11···1·1···111···111·1111111···1··11··1···111111···1··11···1·1··1·111·1111··111·1111111··1111·11·1··1·1·······1·1···1··11·1···11··11····1·1··1····1···111111···111···1······11···111··1·111···1···111·111············ |
| out 12 (248) | 11111111·1····1·11·1·1·1··1·1···11··1····1·11····1··1····1·11111···11·1·1····111·1·1··11·11·1····1··1·1··111·1·1111·11··1····11·1111111···1111······11·1111··111·11111111··11····111·111··11·111···11···111····1·····1····11··111·111··111·1····1·1·1···11111··1·1·111·11111·1··11···111·1·1···1111·1·1··1·1·1·11·11111···1··11·1111···1·111····1··1···1111····1·11111······1·1·111·······111111·111·1·111·1·1··1·111·1·1·1··1··111··111·1··1··1·1·1·1··1·11·1·····1··1·1··1·1111····11·1111·11···11············ |
| out 13 (240) | 11·1·1··11··1··1·111·11·11··11·1·11···1111·11·111···111·11111·1··111··1·111·····11··1·1111·1···1··1111·1··11·11·11·11·11····11···11··1······11111·1·11·1111···1··1··1····1··11··111·1·1111·····111····111··1·11·1··111·1111··11···1·11·11·1·1·1··1···11·111···111·1··111·1111··11····1····11·11···1··1·······1111·1·11·11·1····1··11··1···11·11·1····1111·111··11·11·111·11111··1·1·1·1111······1·1··111111···········11···1··1···111···1··1111·111······11·1····11··1·111·1····1·1···1111·1····1·1············· |
| out 14 (232) | ·1····1·1·1····11·····1·1·11·1······11111··1·1·1·1·1·111·111111····1··1·11·1···1·1······1·1··1····1·1·1·1··1··1·1·111······11·1·111·1·111·1····1···111111··1····11·1·····11·1··1····1·1·11····111····11····1·1····11111·11·11·11······11111·11·11·1·11·1·1··1··111··1111··1·11111···1···1··1·1·1·11·1········1····1111·1111111···1···111···111···1·111···1·111·1·1·11···111·1·11111·11···11·····1··11·1··1·1···111··1·1·1·1·1·1··1·11·1···1·11·1111···1·1111·11··11··111·11111111·1··1·1···1···11··1··1········· |
| out 15 (256) | 11··11·1111···111··1·11111····11··············1·111······11·111···1···111·1·1·····1·111··1··11··1·······11···111·····1··1··111111·11··1·111·1·1···111··1·1·····1·11·11111·1·1·111·11·1·11111·1·1·11····1···11··111···111·1111·11··11····11·111·1··1··1111·····11··11·1·1··1·1·11···111·1111··1·111·1·111111·1···1111·11111·111·1·1·1·1·111111·111·1111·111··111·1·1···1··1·1··1·1111····111········11111·1·····1111·1111·1·11···11111····1··1111·11·1··11·11·1·1···11··1111···11·1·111·····1·11111111·1········· |
| out 16 (244) | ···1·1·1··1·11·111·1·1·11··1·1··1·1111·1···1111·1··1··11··1··111·11·11·1·1·1·11·1·11··1·1·1·1·111·1··111·1··1·11111·······11·1·111··11····1··1··11··11·1··1111··1··111·1·1··1···111··111·····1··1111··1·11·····11······11111·····11···11····11··11·11·1···1111··1······1·111····1···11···1·11·11111111·1·11·1·1·111·11·1·11·1·1·11·1··1····1··1·111·11···1··11·111········1·1··1·1··1·1·1111··11·1111·1·11·1111····1·1·1·11·1·1···1·1·11111·11··11·1··1··11111·1··11···1111··111·1·111·1·····11·1··11··········· |
| out 17 (226) | ·1·1·1··11···111··111··1····1·····1·111···1·1·····1111·11·111·11·11··1··111···11··11·11·1·1·1··1··1··1·111··111·11111·1··1··11·1·1·1·····1·1·1······1111···1·11···1·1·1·1111·1·1·1····11··111············1111···11····11···11·11····1···11·1···1·11··11·1·11··1·11·1·11··1···11·11·1···11111·11·····1··1·111·11··11···1··111··1·1··11·11··1·1··1111·1111·1··111··1·1··1·····1··11·11·1·11··1····1·11·11··1··11····1·1····111·11·1111·······111·1··11··1·11·111·1·········1··1·1·111··11·1··1····11111··········· |
| out 18 (240) | ·1···1·1··1·11···1·1·1·1··1·1·11·11···1·11··111·1··1··11·11··111··11··1·1·1·1··1·1··11111·1·1·111·1··11·11··1·11··11·········11·1111·········1··11·1·1·1111111·1···11··1·····1·1·1·11···11111·11····11·1·11111··1·····1111·11·1·1··1··11·1··1···1····1··1111·11·····1··111··111·1··11····11·1··11·11111·11···11····1111·11111111111·11··1··1·1111·····1··1··1·1·11·····1·1·111111··11·1··1··1··111·1111·1·····11··1··11··1·······1·1··1····111·1·1111·1111···1·11·111··1·11··11·1·1··1·111······11111··········· |
| out 19 (236) | 11···111··11111·1·11···1·111··1·111·1···111·111111······11111···11·1··11·······1·1·111··111·····1·1····1··1·1·111·111·11··1··1····11111··111·1·11·111·1·1······1······1···111·1··111··1·····1··11·1·11111111····1··1··1·1111·11··11······1·11·1·11111·111··11·1··1··1···1111·11···1··1··1·····1·1···11·1·11·111111111·1·1·1···11··11··11·11·1111111····1·1111··111··1···11····11·1···1·111····11·1··1·1···11··1·····11·111····111·····1··111··1·1·11·11·111·1·1····1····11····1····1···11·1··111·1·11··········· |
| out 20 (226) | ·11··1···1111·1···1·1···1·11··11·····1·11··1··11·111·1·1·111·1··1··1···1·11··1·1111··1···1··111·1·111··1··1111·········11·1111····1·11·1·11··1···1·1·111··1··1·11··111····11111111·11·11111·1···11··1··1···1·1·11·1··111111··1·11··1·····1·1··11·111···111··11··1···1···1··1·1·····1·11··111·1·1·1111·111··1·11·11111·····1···11··11·11····1·11····1··1···1·11·1111······1·1···11·1··11···1·111····111··11·11··1·111·1··1·111··111·1·11·····1·1·····1·1···1111·1·1···11·1·1··1··11·1······1···1················· |
| out 21 (236) | ··111·1·11·111·1···111·111·111·11111·1··1111···111·1111111111··1111······1·1·111····11··11·111······1···1··1·1···1·1·111··11··111111·····11·11····1·1··1111·1·11·1·11·11··1111··11··1··1·1·····11··1··1·11111·1···11·111····111·1111··1·11111·1·1··1······111··1·111·1·11··11·1·1·····1··111·1··11··111······1··1·1·111·1··11111····11·111·111·111·1····1·111··1·······1·11······1·1··1·1·1·11·1·····1·1····1·1··11·1·1·1··1·1··11···1··1111···1·1··11··1111·1···1·······1111··1···1··1·1·····1·1··1············ |
| out 22 (228) | ···11·11·111···11···11··111··11···1111···1111·1·11·1·1··11111··1·1·11·11····1111··11111···1·1··1···11··1·1··1·1·····1···111111·1·1·111·1·1···1·1·1·1··111111111··11··1·111·1··1·1··11·11·····1·1·1·1··11··1·11·1·············1··111·1··111·11·1·111····111·1··11··1111111·1·1·1111·11··1111·1···1·11··1··1·111·11··11·1·1··1·····1··1111·1·1··1·1···1·1··1···1·111···11·11111·11·1·11·1···1···1·1···1111··1···1···1····1······1····111·1·······1··111·1··1···1····1···1111···1·······1··1111··1·······1········· |
| out 23 (252) | ·1··1···11·····11···111·11·1··1·11·1····11·1111111·······1··1········111········1··1111·1··111111·11111·1111·1·····1·1··11·11····11··11·111111·1·11·111··11···1···1······11·11·1·11·111·1·11·11···11···1·1·11·1·····11·11····111·····1··1111·1·1··1···111·1·1···1·111111111·11·111111···1··11·11111·111···1·1··111·11111····1····11·1···1·11··1··1····1··1·1111··1····11111·1··11···11111··1·1111·11·1111·1·111·1·1111··1111···111111··1111·1·1·1··1·11·11·1··1·111····11111··1111····1··11··11·1·1·1··········· |
| out 24 (244) | 1111··1·1·1·1111····111·11·1···1·1111·1··1··1··1···11·11·111······1·1111··1·111·1·····1··1·111···1·1··1··1··1·1·11··1····1·11····11·1···11···1··11·11···1···1····11·11111··111·111··1··1111··1·11·1·1111···1·111··1111·11···1··1·1··11111·1··111···111·1111·111·11·1111111·11··11····1·11·1··1·1····1·11··1·1·1·111·1·111·11·····111···1111111·1····111·1···11··11111·····1111····11·1·1111·11·11··11···11111··1··1········1·1·1·1··11··1·11111·1·111··11·1···11·1··1·1·······1·111····1·1·1·····11·1··········· |
| out 25 (238) | 1·11··11·1···1·1···11·1·1······111··11·1·1··11··1·11·1·111··11·····111·11··11··1·1···1111·1·111·1··11··11··1·111·11·1·111·1·1·11···11·111·11···11·1····11·111···1·11·11·····111111111··1··1··1·111··1·····111··1··1·1······11·1··11111··111·1·11······11·1···1····1···1··1····111·1··1··1·1···11··111····11··11·1·1··11·1111··111··11·11···1·1·1111·1111·111·1···1·111··1111···1·1··1·1··1·1···111··1····11··1·1········11····11··1111·1···1··1··1····11·1111···11111·1111111··11·111·1···1··1·111··1··········· |
| out 26 (240) | ·111·1··1······1·1···111·1·1····1···1·1··111·1·11··11·····1··11111·1·11·····11··1·····1··1·1111···11·11·1··1·1·11·11111·111·1·1·1·1··1·····11111·11111··1·1·1111·111·1·111·1··1··1···1···11·111·····1·1111···1·111·1··1··111··11·1·1·111111···11·1···1···1·····11·111···1·1···111·11···11····1·····11·1·1·····1·1·11·11··11·1··11·1··1··1·1···1·111··1··111··1····11·11··1·11·1···111·········111···1·1··11··1·111·11·1111·11·1·111···11·11111111111··1·1·111·11111·····1·1····111·11··1·111···111·11··········· |
| out 27 (248) | ·1·1·1·1··1·11·111·1·11··11·1·11·1····1·1111111·1··1··11··1··111·11·11·1·1·1·1··1·11····1·1·1·11··1··111·111·11·····11·····111·111·1·1·1·1·1····11·11·1···11······11·1·1··1··1·1·11·11··1111··1··11····1·1···1111·1111·111···111···11111·11···1·1·1·111·····111···1·111·1··1····11··111111·11·11·1·1111·11·11··11111··1·11··1·1···1··1·1··1·11111·1111·····11·1111··11·1··1··1··1·11····1···11··1······111··11·1··1111·1111·111·1·111···1·111·1·1····1·····11·····11111··11······1··11·11·11··1·1·111·1········· |
| out 28 (236) | 1··1···11·1···1····111·1·1·1111·1·1111·1·1·1·111·1···111····111·1····11·1·1··1111111········11··1·1·1·111······1111·11··1····1··1·11·111·1··11·1·11····111···1·····1··1···11111···1··1·1··11·····111···1·1····1·111·11····11···1·111···11111·111·111111·111··11·1·1··1···1111········11··11·11····11·1111·1111····111·1··11·111·1·1·11·111111·······1··11···11·111·11·11···1111···111·1·1··1··1·11111·11111···1·1·······1·1··1··1···11····11···1··1·11·111···1··1111··1·1·1·1···1······11··1·11·1111············ |
| out 29 (242) | ·1····11·1··1·111··1·1·1···11·11·1···111·111····11111··111····1···1······11··1··1····1·······11·11·1··1··1·1·1·····1···11·1····1·11··11·11·····1··1··1111·1··111···11··1··1·1·1111111·11·1111111·1111···11111111··1·111111·····1111·11·1··1·11·1··11·1111111·111····1·11·11·1·11···1111···1···11111·1·11·111·11···1··111·11···11···11·1·11·1·11·11·1·1·1··11··11··1·1·11·1111··1·1··1······1·11·11··11··1·111111111·1···111··1··11·1····11·1·1···1··111····11··1·1···1··1····1·11··1··1··1·1··1·11·1············ |
| out 30 (244) | ·11·11·1111·11··1··11···111··11··1·1·1·1111·111·1·1·11····1······1·····11··11··11·1··111····11··11·11·1·1··1111111111·1·····111·1··1·11·1111·11···1·1·1111··11·1·1·1···1·11111·11·1·1·11111·····1·11···111111·111·11·····1·····1111··1··11111···1·111···11··1·1·····11··11·1·1·1·11··11111·1·····1···1······111··1·1·1·1··1·1···11111··1··11···1111··11··1·111··1··1·1···1··1111··1···11·1·111·1·111··1111·1···1·1·······11··1·1·11··11··1·111··11··11·1·11111··11·11·1·····1···11···1·1··1··1·111··1·1········· |
| out 31 (244) | ·1111··11··1·11··111········1·1·1··1·1111·11··1···1··11····11·111·1····11·1··111111··111··11····111·1·1····1111··1111····111····11··111········111·1·····1····1·11·11··11··1111111·11·111111·11·111··111·1···111···1·11···111·1·11·11·111···1·1111··111·11··1······1···1·1111··11111·····1··1··11·1···1·1·1··1·11·1111·1·1·1··1·1·1··11·····1·1·1·111····1·11·1··1·1·····11·1·11·111····11·1···1·1111111·1111···1·1·111······1·1·1·111·1···1111····11···1·1··1·11··1·1111·1·1·11·1·1·1··11·1··111111············ |
| out 32 (250) | ····1·11··11·11111··1··111·1··1·1····1····111·1·111··11111··11·1·11···1111··1·111111·1··11··1···1·1·111·1·1··11··1··11·111··11·111····1111·1···1··111··1··11·1·····11·1···11·1··111······11·11·11····1·11·11····1·1·111·1111·1·11··111·1··1··1111······1·1111·111···11·111···11111·1··1·11··1·1·····1·1·1·111111··1·1·1111·1·1···1·11··1···11··1·1·11·1·1·1···1·1··1··11·1····1···1·1·11·1····1·1·1··11·1·11··1···111···1·11·11···11··11·11···1··11·1··111111·111·1·····111·111·1111·1111111··1111··1·1········· |
| out 33 (240) | 1·111···1···1···11···111··1111··111··1·11··1111········1··1··111·1··1···1··111·····1111111···1··11·1·1··11·11·1·111111·1··1111··11····111·111·11111·111····11··1··1···1··11111····1····11······11····111··111·1·1·1····1111···11·1111··1111··11··11··111·······11·11··11··11··11····1··1·1··11····1·111·1···1·11·11·11·1·11·1··111111·1··1·111111·1·····1111·1·1·111·1111·11·1·······1111·11·1···111·1·1···111·1······1··1·11111··11··1··11·11····11·1111·····1···11···11··111··1···1··11·1···1·1·1···1········· |
| out 34 (244) | 1111·1·111·11···11··1111···1·1·11··1····1111·1111·11··1111·1··1········1·1··11··1··111······11·11····111111··1·······1·111111111·1·11·1···1···11··1111···1111····1···1··1··111·1·········1···1·1·1·1111111·1····1·1·11·1··1111·11··1·1·11··111··1111···1·11·111·1111·11111··111··11·1····1···1111·11·11·1111·1·1·1···1··1···111·1·1111·11···1··11·11·····1····1··11····1·1···11···11·11·11··111·11·1··1···1···1·11···1·111·1111·1·11···11·111·····1111·11·1···1111·11·····111·1·1111····11····111·····1········· |
| out 35 (244) | 1111··11····1·111·111·1··1·1·····1111111·····1·11··111········11111·······111···············1·11·11···111·1·1·1··11·1·1··1··1···11····111·111·111·1·1·1·1·11·1····1·1111··11·1···111·····1····1·111·111·1···11··1111111·111··1·1·1·1111··1·1·11·111··1·1·1··11·11·111··1··11·····11·1··1·11·111·1111·1·11·111··1····11·····1·1··1·1·11·11··11·1····11111····11·11111·11·11··1·1·11·1·····1··111····11·1··11·1··1·1111·1··11·11111···1·111··1·1·11·111··1·1·111·111·11111··1········1·1·1111···1·11·1··1········· |
| check 36 (240) | 1···········111··1··111111···1·1·1··11·11111··111·11··11·1·····1···1·11·······11111111·1·1111······11···11111·····1····1·1·····1··11·1···1·11·111·1···1·1111·1···11···1·1·111··11·1·1···11111··111····11111·111··1·1111·111111·1··1·1··1111··1·11·1··11111·111111·1·1·····1·1·····11111·11········1111·1·11·1·1···1···11·1·1··1···1111··1·1·11·1···1··1····1·11····1··111·111··111··1111··1··1·1·1·····111··11·1··1·1··111·1···1·11·····1····11111·1··1·1·11·11···1···1·1·11·1··1······1··11111··111·1·1·111···· |
| check 37 (240) | ·1····················111111111111111111111···································1·······1·········1······················1···········1·····1··1·····1···············1·1··11···1····························1····1········1···1··1·····1···111111111·1111111111111111111111111111111111·11111111111111111111111111111111111111111111111111111111111·111111111111111111111111111·11111111·1111111111111111···········1···········1·····1·············1·1·11······11·1··········11111111111111111·1111111111111111111 |
| check 38 (240) | ··1············1·1······111········11······1111111111111····1111·111·1·········111······1·······111····11·1·····1·········11····1··11·11·1·1·111··11··111111·111·1···1·····1·111·111·1111111111··········1·1···1111111··1···11··1·1·11111·1············1·11········1·····1·11111···1·1111111111111·1111111··11·1····1111········11········1······1111···1·1··1·1···11··111111·11111111···11··1··1·····1·111111111·11111111·11·11··11111·1········111·11··1·1111··11·1·1··1·1·11·1·1·111111111·11··111··111··1111 |
| check 39 (240) | ···1···········1·1111·111···11·······1········11·········11······11··1··111111111·11111·1111····11··1···11·11····11·1···1·111···111··1111·1··1··1··11··111·111···111··1·1·111·1··11··111111··11··1········1·····11·1·11··111··1111·11·1··1··1·1111·1···1·111··11111·1···1·111111·1··1···1······1··11·····1····1·1·····1·1····111·11··11111·11···1111·······11·111··111········11···1···1111·111··1··1···1····111·1····1111111111··1···1··111111·111··1·111·1·111111··11·111·11·1·1·1·111·111···1·1·1··11·1·11111 |
| check 40 (240) | ····1·····111·11·11····11···111·1·······111·1··1··1·11·1·1·11·11···111111··1·11······1·11···1111··11····11·111·1·1111·111·1·11·······11·111111··1·11·11·1····1·11·1·11···11·111···1····11·1111···1···11·111··1··11··11··1·1·111·111···111·11·1····1···1···1······11··11··11·11·1···11···1·1·····1·1····111···11111·11·1····1···11··11·1··1··1111111111··1111····1·1·11··1111·11·111·1·1111·····1··1··1·1·1··111···111·····1111··1·11·1·11·11··1111···1111111111··11········1·1·····111·11···1·1·1··1······1···11 |
| check 41 (240) | ·····1····1111···1·1·1·1···1·1···1·1111···1·111·11·1····111·1·····1···111···1····1·1··1·1·111··1··1·1·1··11··111·1···1······1·1····111····1111·1111·1111···11·1····1·11·11·····11··11···1···11·····1·11·1·1·1·1····1·11111····111··111·111··11111111·11···1·1··11······11···1·11··1···1··11·111·111·1··1···1111·111111·1·1·11···1·111·111··11·11···11···1·1····11··11·11···1·1·1··1·1··1··1··11······1···111·111111·1·1·1·1·1111·11111111·1····11··111······1111··11·1··111··1··1··1·111·1··111111···11··11··11· |
| check 42 (240) | ······1····111···1·1··11·1·1····111···11111····1111·····1111111·11··11··1·1·1··11·1·111111····11·1·1·11··1·········1··11111·1·····11···1111··11··11·11··1··1·1·11·1··11·11111··1·1·11·1····1··1·11·1111·1··1·111···1··1··1111·111·111·1·11··1··1····1····11111··1··1·111·1····11·11·1·1··1·1·11·11··1·11·1·1··11111·11·1·····1·111·1···1·1·1·1·111··11···11·1111·111·11···1·1·1111······11111···1····1···1·1··11·11·1···1··1·1·····11·11111····1·····1·11111··11111·1·1··1···1·11··1······11··1····1··11··1·1·11 |
| check 43 (240) | ·······1···1··········1111······11····11·········1····111···1111···1···1··1···11···11111···1··1·····11··1·1·11···111·1·1····11··111111···111···1···11·1·111··111··1··11··1··11··11·······111·111···11·111··1·1··1··1·11···11111·11·1··11·11111··11·11111111·11··1·11111·1···1···11·11·11······111111·1111111·11····1··1··11··11·1·1······1·1111111·····1·11··1···1·1···1··11······111·1·111·11·1··11··1····1··1··111·11111111·1·1111·11·11·11···1·11···11··1111·11·1·11111··111··111··1·1···1·1···111··1·11··11· |
| check 44 (240) | ········1·1111·1··1·1·1·11·1·111··11·1111·1··1111·11·1111·1·····111··1·1·1111···1·1·11··1··1·1111·11·1·11···1·1····1··11·1111··1·······111····111111··1····11···1········11··1111···1···11··1···111··111···1111·11111·1111··11···1···11···1·1111·1·1·111·····11·1·1···1·····1·11··111···1·1·111·1·11··11··1·1······11··1···111···1··1····111···1···111·1·1·1·111·111·1·1·1··1·11·111·1···1··11··1·111······11·1·····1·1··1·1·1·11·111·1·1111111·1·1·1·11···11·······1·1·11·11·1·1·11··1·111·1···111··1·1·1·11·1· |
| check 45 (256) | ·········1···111··11111·1·111···1·1111···1····1··1·11·1·1··1··1111···11·111·111··111·1···111·1111111··1·11111·1111···1··1····11·1·111·1··1···11·1·1·1·1111··1···111··111·11····1··11·1··1··11·1·1·11···11·1·111·11111····111·1·1····11·1···11·11··1·111·1··11111··111·111··1···1···1·1·11111·1·111·1·1·1·111··11111·1111·11·11··111111········1··11··11·1··111·11··1···11111·····11····11·11·1111··1·····1·1·1··11··111··1·1111·111··1·11··1··1·1·11·11··11·1·1·1·1·1·11·1··1·1····111111·1··11···1···1·······1· |
| check 46 (240) | ················11111···11··11····1··1····11··11··········1·······111·11······1··1·····11111·····1··1··1·1·11···1·111··11···1·1111··1·1111··11··1·1····1···111·111·11111·111111111·11······11··11·11111111·1111111·1·11··111111·1111·1111111·1···1··11·111··11·······111·111111111··1111·111111·11······11····1·1·······1···1111·111111111111···1···1·····111····11···1·····1·1·····1·111·1··11···11·111·11111···11···1111111···111·1·1111·····1···11·1···1·1······11··1·····1··1·1111··1···11111·1··1··1·11···· |
The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.
Figures of merit
inputs n496Noisy T states per run.
outputs k36
distance d4Exact, proved and witnessed here.
error coefficient A_{4}2,434,503Faults of weight 4 in the circuit shown that pass every check and damage the output. The output error is A_{4}\,p^{4} to leading order.
wires N47
checks r11
V_{\mathrm{ex}}not definedUndefined, because the gate's terms overlap.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log dnot definedOverhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.8921Overhead 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 width36Rank of the output rows modulo the check rows.
Output gate
0 T0 CS3587 CCZon 36 output wires
As gates: CCZ0,1,2·CCZ0,1,7·CCZ0,1,8·CCZ0,1,9·CCZ0,1,11·CCZ0,1,12·CCZ0,1,13·CCZ0,1,14·CCZ0,1,15·CCZ0,1,17·CCZ0,1,18·CCZ0,1,21·CCZ0,1,22·CCZ0,1,25·CCZ0,1,26·CCZ0,1,27·CCZ0,1,28·CCZ0,1,30·CCZ0,1,33·CCZ0,1,35·CCZ0,2,6·CCZ0,2,7·CCZ0,2,11·CCZ0,2,14·CCZ0,2,17·CCZ0,2,18·CCZ0,2,21·CCZ0,2,24·CCZ0,2,25·CCZ0,2,26·CCZ0,2,27·CCZ0,2,28·CCZ0,2,31·CCZ0,3,5·CCZ0,3,6·CCZ0,3,7·CCZ0,3,8·CCZ0,3,9·CCZ0,3,10·CCZ0,3,16·CCZ0,3,17·CCZ0,3,18·CCZ0,3,19·CCZ0,3,20·CCZ0,3,22·CCZ0,3,23·CCZ0,3,25·CCZ0,3,26·CCZ0,3,29·CCZ0,3,33·CCZ0,4,5·CCZ0,4,6·CCZ0,4,7·CCZ0,4,8·CCZ0,4,10·CCZ0,4,11·CCZ0,4,14·CCZ0,4,15·CCZ0,4,18·CCZ0,4,19·CCZ0,4,20·CCZ0,4,22·CCZ0,4,23·CCZ0,4,25·CCZ0,4,26·CCZ0,4,27·CCZ0,4,28·CCZ0,4,29·CCZ0,4,31·CCZ0,4,32·CCZ0,4,35·CCZ0,5,6·CCZ0,5,7·CCZ0,5,8·CCZ0,5,9·CCZ0,5,10·CCZ0,5,12·CCZ0,5,13·CCZ0,5,15·CCZ0,5,16·CCZ0,5,19·CCZ0,5,21·CCZ0,5,24·CCZ0,5,26·CCZ0,5,27·CCZ0,5,30·CCZ0,5,31·CCZ0,5,33·CCZ0,6,11·CCZ0,6,12·CCZ0,6,13·CCZ0,6,14·CCZ0,6,17·CCZ0,6,18·CCZ0,6,20·CCZ0,6,21·CCZ0,6,25·CCZ0,6,27·CCZ0,6,28·CCZ0,6,30·CCZ0,6,31·CCZ0,6,34·CCZ0,6,35·CCZ0,7,13·CCZ0,7,14·CCZ0,7,15·CCZ0,7,16·CCZ0,7,19·CCZ0,7,20·CCZ0,7,21·CCZ0,7,22·CCZ0,7,25·CCZ0,7,29·CCZ0,7,31·CCZ0,7,32·CCZ0,7,33·CCZ0,7,35·CCZ0,8,12·CCZ0,8,13·CCZ0,8,18·CCZ0,8,20·CCZ0,8,23·CCZ0,8,24·CCZ0,8,25·CCZ0,8,27·CCZ0,8,34·CCZ0,8,35·CCZ0,9,11·CCZ0,9,12·CCZ0,9,13·CCZ0,9,14·CCZ0,9,15·CCZ0,9,21·CCZ0,9,24·CCZ0,9,25·CCZ0,9,26·CCZ0,9,28·CCZ0,9,29·CCZ0,9,30·CCZ0,9,33·CCZ0,9,35·CCZ0,10,12·CCZ0,10,13·CCZ0,10,15·CCZ0,10,17·CCZ0,10,18·CCZ0,10,20·CCZ0,10,21·CCZ0,10,22·CCZ0,10,23·CCZ0,10,24·CCZ0,10,25·CCZ0,10,27·CCZ0,10,29·CCZ0,10,30·CCZ0,10,31·CCZ0,11,14·CCZ0,11,15·CCZ0,11,16·CCZ0,11,17·CCZ0,11,19·CCZ0,11,20·CCZ0,11,23·CCZ0,11,24·CCZ0,11,25·CCZ0,11,27·CCZ0,11,29·CCZ0,11,32·CCZ0,12,14·CCZ0,12,15·CCZ0,12,16·CCZ0,12,17·CCZ0,12,18·CCZ0,12,20·CCZ0,12,21·CCZ0,12,22·CCZ0,12,24·CCZ0,12,25·CCZ0,12,26·CCZ0,12,29·CCZ0,12,31·CCZ0,12,33·CCZ0,12,34·CCZ0,12,35·CCZ0,13,15·CCZ0,13,16·CCZ0,13,18·CCZ0,13,19·CCZ0,13,20·CCZ0,13,21·CCZ0,13,23·CCZ0,13,25·CCZ0,13,26·CCZ0,13,30·CCZ0,13,31·CCZ0,13,33·CCZ0,13,34·CCZ0,13,35·CCZ0,14,15·CCZ0,14,18·CCZ0,14,19·CCZ0,14,20·CCZ0,14,21·CCZ0,14,22·CCZ0,14,25·CCZ0,14,28·CCZ0,14,30·CCZ0,14,31·CCZ0,14,33·CCZ0,14,35·CCZ0,15,19·CCZ0,15,21·CCZ0,15,22·CCZ0,15,23·CCZ0,15,25·CCZ0,15,28·CCZ0,15,29·CCZ0,15,32·CCZ0,15,35·CCZ0,16,19·CCZ0,16,23·CCZ0,16,25·CCZ0,16,26·CCZ0,16,28·CCZ0,16,29·CCZ0,16,30·CCZ0,16,31·CCZ0,16,33·CCZ0,16,34·CCZ0,17,18·CCZ0,17,20·CCZ0,17,21·CCZ0,17,23·CCZ0,17,24·CCZ0,17,25·CCZ0,17,26·CCZ0,17,28·CCZ0,17,31·CCZ0,17,32·CCZ0,17,35·CCZ0,18,22·CCZ0,18,24·CCZ0,18,26·CCZ0,18,29·CCZ0,18,30·CCZ0,18,31·CCZ0,18,32·CCZ0,18,35·CCZ0,19,20·CCZ0,19,25·CCZ0,19,28·CCZ0,19,32·CCZ0,19,33·CCZ0,19,35·CCZ0,20,21·CCZ0,20,24·CCZ0,20,26·CCZ0,20,28·CCZ0,20,30·CCZ0,20,32·CCZ0,20,35·CCZ0,21,24·CCZ0,21,29·CCZ0,21,30·CCZ0,21,32·CCZ0,21,33·CCZ0,21,34·CCZ0,21,35·CCZ0,22,23·CCZ0,22,24·CCZ0,22,26·CCZ0,22,29·CCZ0,22,31·CCZ0,22,32·CCZ0,22,33·CCZ0,22,34·CCZ0,22,35·CCZ0,23,25·CCZ0,23,28·CCZ0,23,29·CCZ0,23,31·CCZ0,23,33·CCZ0,23,34·CCZ0,23,35·CCZ0,24,28·CCZ0,24,29·CCZ0,24,30·CCZ0,24,31·CCZ0,24,32·CCZ0,24,35·CCZ0,25,26·CCZ0,25,27·CCZ0,25,28·CCZ0,25,33·CCZ0,26,29·CCZ0,26,31·CCZ0,26,32·CCZ0,26,33·CCZ0,26,35·CCZ0,27,28·CCZ0,27,29·CCZ0,27,30·CCZ0,27,32·CCZ0,27,33·CCZ0,27,34·CCZ0,27,35·CCZ0,28,29·CCZ0,28,32·CCZ0,29,30·CCZ0,29,31·CCZ0,29,35·CCZ0,30,31·CCZ0,30,35·CCZ0,31,33·CCZ0,31,34·CCZ0,31,35·CCZ0,32,33·CCZ0,32,34·CCZ1,2,3·CCZ1,2,4·CCZ1,2,6·CCZ1,2,11·CCZ1,2,12·CCZ1,2,13·CCZ1,2,15·CCZ1,2,16·CCZ1,2,18·CCZ1,2,19·CCZ1,2,20·CCZ1,2,22·CCZ1,2,23·CCZ1,2,24·CCZ1,2,25·CCZ1,2,26·CCZ1,2,27·CCZ1,2,28·CCZ1,2,30·CCZ1,2,31·CCZ1,2,32·CCZ1,3,4·CCZ1,3,6·CCZ1,3,9·CCZ1,3,11·CCZ1,3,12·CCZ1,3,14·CCZ1,3,18·CCZ1,3,20·CCZ1,3,22·CCZ1,3,23·CCZ1,3,24·CCZ1,3,25·CCZ1,3,28·CCZ1,3,30·CCZ1,3,33·CCZ1,3,34·CCZ1,4,8·CCZ1,4,9·CCZ1,4,10·CCZ1,4,11·CCZ1,4,12·CCZ1,4,14·CCZ1,4,15·CCZ1,4,16·CCZ1,4,17·CCZ1,4,19·CCZ1,4,21·CCZ1,4,24·CCZ1,4,25·CCZ1,4,27·CCZ1,4,31·CCZ1,4,32·CCZ1,4,35·CCZ1,5,6·CCZ1,5,8·CCZ1,5,9·CCZ1,5,11·CCZ1,5,12·CCZ1,5,14·CCZ1,5,20·CCZ1,5,22·CCZ1,5,23·CCZ1,5,26·CCZ1,5,29·CCZ1,5,30·CCZ1,5,32·CCZ1,5,33·CCZ1,5,34·CCZ1,6,7·CCZ1,6,9·CCZ1,6,10·CCZ1,6,11·CCZ1,6,12·CCZ1,6,20·CCZ1,6,23·CCZ1,6,27·CCZ1,6,29·CCZ1,6,34·CCZ1,6,35·CCZ1,7,9·CCZ1,7,10·CCZ1,7,13·CCZ1,7,14·CCZ1,7,17·CCZ1,7,20·CCZ1,7,21·CCZ1,7,22·CCZ1,7,23·CCZ1,7,24·CCZ1,7,25·CCZ1,7,29·CCZ1,7,30·CCZ1,7,32·CCZ1,7,35·CCZ1,8,9·CCZ1,8,10·CCZ1,8,16·CCZ1,8,17·CCZ1,8,19·CCZ1,8,20·CCZ1,8,21·CCZ1,8,22·CCZ1,8,23·CCZ1,8,24·CCZ1,8,26·CCZ1,8,27·CCZ1,8,30·CCZ1,8,31·CCZ1,9,11·CCZ1,9,12·CCZ1,9,13·CCZ1,9,14·CCZ1,9,17·CCZ1,9,18·CCZ1,9,21·CCZ1,9,22·CCZ1,9,26·CCZ1,9,27·CCZ1,9,28·CCZ1,9,29·CCZ1,9,30·CCZ1,9,34·CCZ1,10,13·CCZ1,10,15·CCZ1,10,17·CCZ1,10,20·CCZ1,10,21·CCZ1,10,23·CCZ1,10,24·CCZ1,10,26·CCZ1,10,27·CCZ1,10,34·CCZ1,10,35·CCZ1,11,15·CCZ1,11,25·CCZ1,11,29·CCZ1,11,33·CCZ1,11,34·CCZ1,11,35·CCZ1,12,15·CCZ1,12,25·CCZ1,12,29·CCZ1,12,33·CCZ1,12,34·CCZ1,12,35·CCZ1,13,14·CCZ1,13,15·CCZ1,13,18·CCZ1,13,22·CCZ1,13,24·CCZ1,13,27·CCZ1,13,28·CCZ1,13,30·CCZ1,13,34·CCZ1,14,17·CCZ1,14,18·CCZ1,14,20·CCZ1,14,21·CCZ1,14,23·CCZ1,14,27·CCZ1,14,28·CCZ1,14,32·CCZ1,14,33·CCZ1,15,17·CCZ1,15,18·CCZ1,15,21·CCZ1,15,28·CCZ1,15,29·CCZ1,15,32·CCZ1,15,33·CCZ1,15,34·CCZ1,15,35·CCZ1,16,18·CCZ1,16,24·CCZ1,16,25·CCZ1,16,26·CCZ1,16,28·CCZ1,16,29·CCZ1,16,32·CCZ1,17,22·CCZ1,17,25·CCZ1,17,26·CCZ1,17,27·CCZ1,17,29·CCZ1,17,30·CCZ1,17,32·CCZ1,17,34·CCZ1,18,19·CCZ1,18,26·CCZ1,18,27·CCZ1,18,31·CCZ1,18,32·CCZ1,18,33·CCZ1,18,34·CCZ1,19,24·CCZ1,19,25·CCZ1,19,26·CCZ1,19,28·CCZ1,19,29·CCZ1,19,32·CCZ1,20,22·CCZ1,20,26·CCZ1,20,27·CCZ1,20,30·CCZ1,20,32·CCZ1,20,33·CCZ1,20,35·CCZ1,21,22·CCZ1,21,25·CCZ1,21,26·CCZ1,21,27·CCZ1,21,29·CCZ1,21,30·CCZ1,21,32·CCZ1,21,34·CCZ1,22,23·CCZ1,22,24·CCZ1,22,25·CCZ1,22,26·CCZ1,22,27·CCZ1,22,29·CCZ1,22,33·CCZ1,23,26·CCZ1,23,27·CCZ1,23,30·CCZ1,23,32·CCZ1,23,33·CCZ1,23,35·CCZ1,24,25·CCZ1,24,29·CCZ1,24,30·CCZ1,24,31·CCZ1,24,33·CCZ1,25,26·CCZ1,25,29·CCZ1,25,30·CCZ1,25,31·CCZ1,25,34·CCZ1,25,35·CCZ1,26,27·CCZ1,26,28·CCZ1,26,29·CCZ1,26,30·CCZ1,26,31·CCZ1,26,32·CCZ1,27,28·CCZ1,27,30·CCZ1,27,35·CCZ1,28,31·CCZ1,28,32·CCZ1,28,33·CCZ1,28,34·CCZ1,29,30·CCZ1,29,31·CCZ1,29,33·CCZ1,30,33·CCZ1,31,32·CCZ1,32,34·CCZ1,33,35·CCZ2,3,4·CCZ2,3,5·CCZ2,3,6·CCZ2,3,7·CCZ2,3,9·CCZ2,3,11·CCZ2,3,12·CCZ2,3,13·CCZ2,3,14·CCZ2,3,15·CCZ2,3,16·CCZ2,3,17·CCZ2,3,19·CCZ2,3,24·CCZ2,3,25·CCZ2,3,27·CCZ2,3,28·CCZ2,3,29·CCZ2,4,5·CCZ2,4,7·CCZ2,4,8·CCZ2,4,16·CCZ2,4,18·CCZ2,4,23·CCZ2,4,31·CCZ2,4,32·CCZ2,4,33·CCZ2,4,34·CCZ2,5,7·CCZ2,5,8·CCZ2,5,9·CCZ2,5,10·CCZ2,5,11·CCZ2,5,12·CCZ2,5,13·CCZ2,5,17·CCZ2,5,19·CCZ2,5,20·CCZ2,5,21·CCZ2,5,23·CCZ2,5,27·CCZ2,5,28·CCZ2,5,29·CCZ2,5,30·CCZ2,5,33·CCZ2,5,34·CCZ2,5,35·CCZ2,6,8·CCZ2,6,9·CCZ2,6,10·CCZ2,6,12·CCZ2,6,16·CCZ2,6,17·CCZ2,6,19·CCZ2,6,21·CCZ2,6,22·CCZ2,6,23·CCZ2,6,30·CCZ2,6,31·CCZ2,6,32·CCZ2,6,33·CCZ2,7,8·CCZ2,7,10·CCZ2,7,11·CCZ2,7,13·CCZ2,7,17·CCZ2,7,18·CCZ2,7,21·CCZ2,7,22·CCZ2,7,23·CCZ2,7,27·CCZ2,7,28·CCZ2,7,31·CCZ2,7,32·CCZ2,7,33·CCZ2,8,10·CCZ2,8,11·CCZ2,8,12·CCZ2,8,13·CCZ2,8,16·CCZ2,8,22·CCZ2,8,23·CCZ2,8,26·CCZ2,8,27·CCZ2,8,28·CCZ2,8,30·CCZ2,8,32·CCZ2,8,33·CCZ2,8,35·CCZ2,9,10·CCZ2,9,11·CCZ2,9,14·CCZ2,9,16·CCZ2,9,21·CCZ2,9,22·CCZ2,9,23·CCZ2,9,24·CCZ2,9,26·CCZ2,9,30·CCZ2,9,31·CCZ2,9,32·CCZ2,9,34·CCZ2,10,12·CCZ2,10,13·CCZ2,10,17·CCZ2,10,18·CCZ2,10,20·CCZ2,10,21·CCZ2,10,22·CCZ2,10,25·CCZ2,10,26·CCZ2,10,27·CCZ2,10,28·CCZ2,10,29·CCZ2,10,30·CCZ2,10,35·CCZ2,11,13·CCZ2,11,14·CCZ2,11,17·CCZ2,11,20·CCZ2,11,22·CCZ2,11,25·CCZ2,11,29·CCZ2,11,30·CCZ2,11,31·CCZ2,11,33·CCZ2,11,34·CCZ2,11,35·CCZ2,12,14·CCZ2,12,15·CCZ2,12,16·CCZ2,12,20·CCZ2,12,21·CCZ2,12,23·CCZ2,12,24·CCZ2,12,25·CCZ2,12,30·CCZ2,12,33·CCZ2,12,34·CCZ2,12,35·CCZ2,13,15·CCZ2,13,17·CCZ2,13,18·CCZ2,13,19·CCZ2,13,21·CCZ2,13,24·CCZ2,13,25·CCZ2,13,26·CCZ2,13,27·CCZ2,13,28·CCZ2,13,31·CCZ2,13,32·CCZ2,13,33·CCZ2,13,35·CCZ2,14,15·CCZ2,14,16·CCZ2,14,19·CCZ2,14,23·CCZ2,14,25·CCZ2,14,26·CCZ2,14,29·CCZ2,14,30·CCZ2,14,31·CCZ2,14,32·CCZ2,15,16·CCZ2,15,20·CCZ2,15,22·CCZ2,15,24·CCZ2,15,25·CCZ2,15,27·CCZ2,15,29·CCZ2,15,30·CCZ2,15,31·CCZ2,15,33·CCZ2,15,34·CCZ2,15,35·CCZ2,16,17·CCZ2,16,18·CCZ2,16,19·CCZ2,16,21·CCZ2,16,23·CCZ2,16,24·CCZ2,16,25·CCZ2,16,27·CCZ2,16,34·CCZ2,16,35·CCZ2,17,19·CCZ2,17,22·CCZ2,17,25·CCZ2,17,28·CCZ2,17,29·CCZ2,17,30·CCZ2,17,34·CCZ2,18,21·CCZ2,18,26·CCZ2,18,35·CCZ2,19,20·CCZ2,19,21·CCZ2,19,22·CCZ2,19,23·CCZ2,19,24·CCZ2,19,26·CCZ2,19,28·CCZ2,19,30·CCZ2,19,31·CCZ2,19,32·CCZ2,19,33·CCZ2,19,34·CCZ2,20,23·CCZ2,20,28·CCZ2,20,30·CCZ2,20,32·CCZ2,20,33·CCZ2,20,34·CCZ2,20,35·CCZ2,21,23·CCZ2,21,24·CCZ2,21,26·CCZ2,21,27·CCZ2,21,28·CCZ2,21,31·CCZ2,21,32·CCZ2,21,35·CCZ2,22,25·CCZ2,22,28·CCZ2,22,30·CCZ2,22,32·CCZ2,22,33·CCZ2,23,24·CCZ2,23,28·CCZ2,23,34·CCZ2,23,35·CCZ2,24,25·CCZ2,24,26·CCZ2,24,28·CCZ2,24,30·CCZ2,24,33·CCZ2,24,35·CCZ2,25,26·CCZ2,25,27·CCZ2,25,30·CCZ2,25,31·CCZ2,25,32·CCZ2,26,27·CCZ2,26,28·CCZ2,26,29·CCZ2,26,30·CCZ2,26,31·CCZ2,26,33·CCZ2,26,34·CCZ2,26,35·CCZ2,27,30·CCZ2,27,31·CCZ2,28,29·CCZ2,28,30·CCZ2,28,32·CCZ2,28,35·CCZ2,29,30·CCZ2,29,32·CCZ2,29,33·CCZ2,30,32·CCZ2,30,34·CCZ2,31,32·CCZ2,31,34·CCZ2,32,35·CCZ2,34,35·CCZ3,4,5·CCZ3,4,6·CCZ3,4,14·CCZ3,4,15·CCZ3,4,17·CCZ3,4,18·CCZ3,4,20·CCZ3,4,21·CCZ3,4,22·CCZ3,4,23·CCZ3,4,26·CCZ3,4,28·CCZ3,4,30·CCZ3,4,31·CCZ3,4,32·CCZ3,4,33·CCZ3,4,35·CCZ3,5,6·CCZ3,5,8·CCZ3,5,11·CCZ3,5,13·CCZ3,5,15·CCZ3,5,17·CCZ3,5,19·CCZ3,5,20·CCZ3,5,22·CCZ3,5,23·CCZ3,5,24·CCZ3,5,25·CCZ3,5,26·CCZ3,5,30·CCZ3,5,31·CCZ3,5,33·CCZ3,5,35·CCZ3,6,7·CCZ3,6,8·CCZ3,6,9·CCZ3,6,11·CCZ3,6,12·CCZ3,6,13·CCZ3,6,19·CCZ3,6,20·CCZ3,6,21·CCZ3,6,22·CCZ3,6,24·CCZ3,6,25·CCZ3,6,26·CCZ3,6,29·CCZ3,6,30·CCZ3,6,32·CCZ3,6,33·CCZ3,6,34·CCZ3,7,9·CCZ3,7,10·CCZ3,7,15·CCZ3,7,16·CCZ3,7,19·CCZ3,7,20·CCZ3,7,23·CCZ3,7,24·CCZ3,7,27·CCZ3,7,28·CCZ3,7,31·CCZ3,7,32·CCZ3,7,34·CCZ3,7,35·CCZ3,8,9·CCZ3,8,10·CCZ3,8,11·CCZ3,8,14·CCZ3,8,16·CCZ3,8,17·CCZ3,8,23·CCZ3,8,24·CCZ3,8,25·CCZ3,8,28·CCZ3,8,29·CCZ3,8,31·CCZ3,8,33·CCZ3,8,34·CCZ3,9,11·CCZ3,9,16·CCZ3,9,17·CCZ3,9,19·CCZ3,9,21·CCZ3,9,23·CCZ3,9,24·CCZ3,9,27·CCZ3,9,28·CCZ3,9,29·CCZ3,9,30·CCZ3,9,31·CCZ3,9,32·CCZ3,10,11·CCZ3,10,12·CCZ3,10,14·CCZ3,10,16·CCZ3,10,24·CCZ3,10,27·CCZ3,10,29·CCZ3,10,32·CCZ3,10,34·CCZ3,11,16·CCZ3,11,18·CCZ3,11,20·CCZ3,11,21·CCZ3,11,22·CCZ3,11,23·CCZ3,11,25·CCZ3,11,27·CCZ3,11,31·CCZ3,11,33·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32,34,35·CCZ33,34,35
As monomials: 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(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 labelling of the stored circuit.
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 27 single-wire gates and 525 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{S} on output 2, \mathrm{S}^\dagger on output 3, \mathrm{S}^\dagger on output 4, \mathrm{Z} on output 5, \mathrm{S}^\dagger on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{S} on output 11, \mathrm{Z} on output 16, \mathrm{S}^\dagger on output 17, \mathrm{Z} on output 19, \mathrm{S}^\dagger on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23, \mathrm{Z} on output 24, \mathrm{S} on output 25, \mathrm{Z} on output 28, \mathrm{S}^\dagger on output 29, \mathrm{Z} on output 30, \mathrm{Z} on output 31 and 528 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 552 correction gates
\mathrm{Z} on output 0, \mathrm{S} on output 2, \mathrm{S}^\dagger on output 3, \mathrm{S}^\dagger on output 4, \mathrm{Z} on output 5, \mathrm{S}^\dagger on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{S} on output 11, \mathrm{Z} on output 16, \mathrm{S}^\dagger on output 17, \mathrm{Z} on output 19, \mathrm{S}^\dagger on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{Z} on output 23, \mathrm{Z} on output 24, \mathrm{S} on output 25, \mathrm{Z} on output 28, \mathrm{S}^\dagger on output 29, \mathrm{Z} on output 30, \mathrm{Z} on output 31, \mathrm{S}^\dagger on output 32, \mathrm{Z} on output 34, \mathrm{Z} on output 35, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 3, \mathrm{CZ} on output 0, output 6, \mathrm{CZ} on output 0, output 7, \mathrm{CZ} on output 0, output 8, \mathrm{CZ} on output 0, output 13, \mathrm{CZ} on output 0, output 15, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 21, \mathrm{CZ} on output 0, output 27, \mathrm{CZ} on output 0, output 29, \mathrm{CZ} on output 0, output 30, \mathrm{CZ} on output 0, output 32, \mathrm{CZ} on output 0, output 34, \mathrm{CZ} on output 0, check 37, \mathrm{CZ} on output 0, check 38, \mathrm{CZ} on output 0, check 40, \mathrm{CZ} on output 0, check 41, \mathrm{CZ} on output 0, check 42, \mathrm{CZ} on output 0, check 43, \mathrm{CZ} on output 1, output 2, \mathrm{CZ} on output 1, output 3, \mathrm{CZ} on output 1, output 7, \mathrm{CZ} on output 1, output 8, \mathrm{CZ} on output 1, output 10, \mathrm{CZ} on output 1, output 12, \mathrm{CZ} on output 1, output 13, \mathrm{CZ} on output 1, output 14, \mathrm{CZ} on output 1, output 16, \mathrm{CZ} on output 1, output 20, \mathrm{CZ} on output 1, output 25, \mathrm{CZ} on output 1, output 26, \mathrm{CZ} on output 1, output 28, \mathrm{CZ} on output 1, output 31, \mathrm{CZ} on output 1, output 32, \mathrm{CZ} on output 1, output 33, \mathrm{CZ} on output 1, output 34, \mathrm{CZ} on output 1, output 35, \mathrm{CZ} on output 1, check 39, \mathrm{CZ} on output 1, check 41, \mathrm{CZ} on output 1, check 42, \mathrm{CZ} on output 1, check 43, \mathrm{CZ} on output 2, output 3, \mathrm{CZ} on output 2, output 7, \mathrm{CZ} on output 2, output 8, \mathrm{CZ} on output 2, output 9, \mathrm{CZ} on output 2, output 10, \mathrm{CZ} on output 2, output 11, \mathrm{CZ} on output 2, output 14, \mathrm{CZ} on output 2, output 17, \mathrm{CZ} on output 2, output 21, \mathrm{CZ} on output 2, output 23, \mathrm{CZ} on output 2, output 24, \mathrm{CZ} on output 2, output 26, \mathrm{CZ} on output 2, output 29, \mathrm{CZ} on output 2, output 31, \mathrm{CZ} on output 2, output 33, \mathrm{CZ} on output 2, output 34, \mathrm{CZ} on output 2, output 35, \mathrm{CZ} on output 2, check 36, \mathrm{CZ} on output 2, check 37, \mathrm{CZ} on output 2, check 45, \mathrm{CZ} on output 3, output 4, \mathrm{CZ} on output 3, output 6, \mathrm{CZ} on output 3, output 14, \mathrm{CZ} on output 3, output 15, \mathrm{CZ} on output 3, output 16, \mathrm{CZ} on output 3, output 20, \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 27, \mathrm{CZ} on output 3, output 29, \mathrm{CZ} on output 3, output 30, \mathrm{CZ} on output 3, output 32, \mathrm{CZ} on output 3, output 34, \mathrm{CZ} on output 3, check 36, \mathrm{CZ} on output 3, check 38, \mathrm{CZ} on output 3, check 39, \mathrm{CZ} on output 3, check 40, \mathrm{CZ} on output 3, check 46, \mathrm{CZ} on output 4, output 6, \mathrm{CZ} on output 4, output 7, \mathrm{CZ} on output 4, output 9, \mathrm{CZ} on output 4, output 11, \mathrm{CZ} on output 4, output 13, \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 24, \mathrm{CZ} on output 4, output 25, \mathrm{CZ} on output 4, output 27, \mathrm{CZ} on output 4, output 32, \mathrm{CZ} on output 4, output 34, \mathrm{CZ} on output 4, check 41, \mathrm{CZ} on output 4, check 43, \mathrm{CZ} on output 4, check 46, \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 18, \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 30, \mathrm{CZ} on output 5, check 38, \mathrm{CZ} on output 5, check 39, \mathrm{CZ} on output 5, check 41, \mathrm{CZ} on output 5, check 42, \mathrm{CZ} on output 5, check 45, \mathrm{CZ} on output 5, check 46, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 13, \mathrm{CZ} on output 6, output 14, \mathrm{CZ} on output 6, output 15, \mathrm{CZ} on output 6, output 17, \mathrm{CZ} on output 6, output 25, \mathrm{CZ} on output 6, output 28, \mathrm{CZ} on output 6, output 29, \mathrm{CZ} on output 6, output 30, \mathrm{CZ} on output 6, output 31, \mathrm{CZ} on output 6, output 32, \mathrm{CZ} on output 6, output 33, \mathrm{CZ} on output 6, output 34, \mathrm{CZ} on output 6, check 36, \mathrm{CZ} on output 6, check 38, \mathrm{CZ} on output 6, check 42, \mathrm{CZ} on output 6, check 43, \mathrm{CZ} on output 6, check 45, \mathrm{CZ} on output 7, output 8, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, output 10, \mathrm{CZ} on output 7, output 11, \mathrm{CZ} on output 7, output 13, \mathrm{CZ} on output 7, output 15, \mathrm{CZ} on output 7, output 19, \mathrm{CZ} on output 7, output 21, \mathrm{CZ} on output 7, output 22, \mathrm{CZ} on output 7, output 23, \mathrm{CZ} on output 7, output 25, \mathrm{CZ} on output 7, output 28, \mathrm{CZ} on output 7, output 29, \mathrm{CZ} on output 7, output 30, \mathrm{CZ} on output 7, output 34, \mathrm{CZ} on output 7, output 35, \mathrm{CZ} on output 7, check 36, \mathrm{CZ} on output 7, check 37, \mathrm{CZ} on output 7, check 38, \mathrm{CZ} on output 7, check 39, \mathrm{CZ} on output 7, check 42, \mathrm{CZ} on output 7, check 43, \mathrm{CZ} on output 7, check 46, \mathrm{CZ} on output 8, output 12, \mathrm{CZ} on output 8, output 13, \mathrm{CZ} on output 8, output 14, \mathrm{CZ} on output 8, output 15, \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 20, \mathrm{CZ} on output 8, output 21, \mathrm{CZ} on output 8, output 22, \mathrm{CZ} on output 8, output 24, \mathrm{CZ} on output 8, output 25, \mathrm{CZ} on output 8, output 28, \mathrm{CZ} on output 8, output 32, \mathrm{CZ} on output 8, output 33, \mathrm{CZ} on output 8, output 34, \mathrm{CZ} on output 8, check 36, \mathrm{CZ} on output 8, check 37, \mathrm{CZ} on output 8, check 38, \mathrm{CZ} on output 8, check 39, \mathrm{CZ} on output 8, check 40, \mathrm{CZ} on output 8, check 41, \mathrm{CZ} on output 8, check 42, \mathrm{CZ} on output 9, output 13, \mathrm{CZ} on output 9, output 17, \mathrm{CZ} on output 9, output 21, \mathrm{CZ} on output 9, output 31, \mathrm{CZ} on output 9, output 32, \mathrm{CZ} on output 9, output 33, \mathrm{CZ} on output 9, output 35, \mathrm{CZ} on output 9, check 37, \mathrm{CZ} on output 9, check 39, \mathrm{CZ} on output 9, check 40, \mathrm{CZ} on output 9, check 41, \mathrm{CZ} on output 9, check 42, \mathrm{CZ} on output 9, check 43, \mathrm{CZ} on output 9, check 45, \mathrm{CZ} on output 9, check 46, \mathrm{CZ} on output 10, output 12, \mathrm{CZ} on output 10, output 13, \mathrm{CZ} on output 10, output 14, \mathrm{CZ} on output 10, output 20, \mathrm{CZ} on output 10, output 21, \mathrm{CZ} on output 10, output 24, \mathrm{CZ} on output 10, output 28, \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 35, \mathrm{CZ} on output 10, check 36, \mathrm{CZ} on output 10, check 39, \mathrm{CZ} on output 10, check 40, \mathrm{CZ} on output 10, check 41, \mathrm{CZ} on output 10, check 43, \mathrm{CZ} on output 10, check 46, \mathrm{CZ} on output 11, output 15, \mathrm{CZ} on output 11, output 16, \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 24, \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 28, \mathrm{CZ} on output 11, output 29, \mathrm{CZ} on output 11, output 30, \mathrm{CZ} on output 11, output 34, \mathrm{CZ} on output 11, output 35, \mathrm{CZ} on output 11, check 36, \mathrm{CZ} on output 11, check 37, \mathrm{CZ} on output 11, check 39, \mathrm{CZ} on output 11, check 40, \mathrm{CZ} on output 11, check 41, \mathrm{CZ} on output 11, check 42, \mathrm{CZ} on output 11, check 44, \mathrm{CZ} on output 11, check 45, \mathrm{CZ} on output 11, check 46, \mathrm{CZ} on output 12, output 13, \mathrm{CZ} on output 12, output 14, \mathrm{CZ} on output 12, output 16, \mathrm{CZ} on output 12, output 17, \mathrm{CZ} on output 12, output 18, \mathrm{CZ} on output 12, output 19, \mathrm{CZ} on output 12, output 20, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, output 22, \mathrm{CZ} on output 12, output 24, \mathrm{CZ} on output 12, output 26, \mathrm{CZ} on output 12, output 30, \mathrm{CZ} on output 12, output 31, \mathrm{CZ} on output 12, output 33, \mathrm{CZ} on output 12, check 36, \mathrm{CZ} on output 12, check 37, \mathrm{CZ} on output 12, check 38, \mathrm{CZ} on output 12, check 42, \mathrm{CZ} on output 12, check 43, \mathrm{CZ} on output 12, check 44, \mathrm{CZ} on output 12, check 45, \mathrm{CZ} on output 12, check 46, \mathrm{CZ} on output 13, output 14, \mathrm{CZ} on output 13, output 15, \mathrm{CZ} on output 13, output 16, \mathrm{CZ} on output 13, output 17, \mathrm{CZ} on output 13, output 24, \mathrm{CZ} on output 13, output 26, \mathrm{CZ} on output 13, output 32, \mathrm{CZ} on output 13, output 35, \mathrm{CZ} on output 13, check 37, \mathrm{CZ} on output 13, check 38, \mathrm{CZ} on output 14, output 16, \mathrm{CZ} on output 14, output 17, \mathrm{CZ} on output 14, output 18, \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 24, \mathrm{CZ} on output 14, output 26, \mathrm{CZ} on output 14, output 27, \mathrm{CZ} on output 14, output 31, \mathrm{CZ} on output 14, output 33, \mathrm{CZ} on output 14, check 38, \mathrm{CZ} on output 14, check 39, \mathrm{CZ} on output 14, check 41, \mathrm{CZ} on output 14, check 43, \mathrm{CZ} on output 14, check 44, \mathrm{CZ} on output 14, check 45, \mathrm{CZ} on output 15, output 16, \mathrm{CZ} on output 15, output 19, \mathrm{CZ} on output 15, output 20, \mathrm{CZ} on output 15, output 22, \mathrm{CZ} on output 15, output 24, \mathrm{CZ} on output 15, output 25, \mathrm{CZ} on output 15, output 26, \mathrm{CZ} on output 15, output 28, \mathrm{CZ} on output 15, output 29, \mathrm{CZ} on output 15, output 30, \mathrm{CZ} on output 15, output 35, \mathrm{CZ} on output 15, check 37, \mathrm{CZ} on output 15, check 40, \mathrm{CZ} on output 15, check 42, \mathrm{CZ} on output 15, check 45, \mathrm{CZ} on output 16, output 18, \mathrm{CZ} on output 16, output 19, \mathrm{CZ} on output 16, output 21, \mathrm{CZ} on output 16, output 23, \mathrm{CZ} on output 16, output 24, \mathrm{CZ} on output 16, output 25, \mathrm{CZ} on output 16, output 26, \mathrm{CZ} on output 16, output 35, \mathrm{CZ} on output 16, check 36, \mathrm{CZ} on output 16, check 37, \mathrm{CZ} on output 16, check 41, \mathrm{CZ} on output 16, check 43, \mathrm{CZ} on output 16, check 44, \mathrm{CZ} on output 16, check 46, \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 26, \mathrm{CZ} on output 17, output 27, \mathrm{CZ} on output 17, output 29, \mathrm{CZ} on output 17, output 32, \mathrm{CZ} on output 17, output 34, \mathrm{CZ} on output 17, output 35, \mathrm{CZ} on output 17, check 37, \mathrm{CZ} on output 17, check 38, \mathrm{CZ} on output 17, check 39, \mathrm{CZ} on output 17, check 41, \mathrm{CZ} on output 17, check 44, \mathrm{CZ} on output 17, check 45, \mathrm{CZ} on output 17, check 46, \mathrm{CZ} on output 18, output 19, \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 24, \mathrm{CZ} on output 18, output 27, \mathrm{CZ} on output 18, output 30, \mathrm{CZ} on output 18, output 31, \mathrm{CZ} on output 18, output 32, \mathrm{CZ} on output 18, output 33, \mathrm{CZ} on output 18, output 34, \mathrm{CZ} on output 18, check 37, \mathrm{CZ} on output 18, check 38, \mathrm{CZ} on output 18, check 39, \mathrm{CZ} on output 18, check 41, \mathrm{CZ} on output 18, check 45, \mathrm{CZ} on output 18, check 46, \mathrm{CZ} on output 19, output 20, \mathrm{CZ} on output 19, output 21, \mathrm{CZ} on output 19, output 23, \mathrm{CZ} on output 19, output 27, \mathrm{CZ} on output 19, output 28, \mathrm{CZ} on output 19, output 30, \mathrm{CZ} on output 19, output 32, \mathrm{CZ} on output 19, output 35, \mathrm{CZ} on output 19, check 38, \mathrm{CZ} on output 19, check 40, \mathrm{CZ} on output 19, check 41, \mathrm{CZ} on output 19, check 43, \mathrm{CZ} on output 19, check 45, \mathrm{CZ} on output 19, check 46, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 22, \mathrm{CZ} on output 20, output 23, \mathrm{CZ} on output 20, output 24, \mathrm{CZ} on output 20, output 25, \mathrm{CZ} on output 20, output 26, \mathrm{CZ} on output 20, output 27, \mathrm{CZ} on output 20, output 28, \mathrm{CZ} on output 20, output 29, \mathrm{CZ} on output 20, output 30, \mathrm{CZ} on output 20, output 32, \mathrm{CZ} on output 20, check 38, \mathrm{CZ} on output 20, check 42, \mathrm{CZ} on output 20, check 43, \mathrm{CZ} on output 21, output 22, \mathrm{CZ} on output 21, output 24, \mathrm{CZ} on output 21, output 33, \mathrm{CZ} on output 21, output 35, \mathrm{CZ} on output 21, check 36, \mathrm{CZ} on output 21, check 37, \mathrm{CZ} on output 21, check 39, \mathrm{CZ} on output 21, check 44, \mathrm{CZ} on output 21, check 45, \mathrm{CZ} on output 21, check 46, \mathrm{CZ} on output 22, output 24, \mathrm{CZ} on output 22, output 26, \mathrm{CZ} on output 22, output 27, \mathrm{CZ} on output 22, output 30, \mathrm{CZ} on output 22, output 31, \mathrm{CZ} on output 22, output 33, \mathrm{CZ} on output 22, output 35, \mathrm{CZ} on output 22, check 36, \mathrm{CZ} on output 22, check 37, \mathrm{CZ} on output 22, check 39, \mathrm{CZ} on output 22, check 40, \mathrm{CZ} on output 22, check 41, \mathrm{CZ} on output 22, check 43, \mathrm{CZ} on output 22, check 44, \mathrm{CZ} on output 22, check 46, \mathrm{CZ} on output 23, output 24, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 28, \mathrm{CZ} on output 23, output 29, \mathrm{CZ} on output 23, output 30, \mathrm{CZ} on output 23, output 33, \mathrm{CZ} on output 23, output 35, \mathrm{CZ} on output 23, check 37, \mathrm{CZ} on output 23, check 38, \mathrm{CZ} on output 23, check 40, \mathrm{CZ} on output 23, check 44, \mathrm{CZ} on output 23, check 45, \mathrm{CZ} on output 23, check 46, \mathrm{CZ} on output 24, output 26, \mathrm{CZ} on output 24, output 29, \mathrm{CZ} on output 24, output 30, \mathrm{CZ} on output 24, output 31, \mathrm{CZ} on output 24, output 32, \mathrm{CZ} on output 24, output 33, \mathrm{CZ} on output 24, output 34, \mathrm{CZ} on output 24, output 35, \mathrm{CZ} on output 24, check 37, \mathrm{CZ} on output 24, check 39, \mathrm{CZ} on output 24, check 40, \mathrm{CZ} on output 24, check 41, \mathrm{CZ} on output 24, check 44, \mathrm{CZ} on output 24, check 45, \mathrm{CZ} on output 25, output 26, \mathrm{CZ} on output 25, output 27, \mathrm{CZ} on output 25, output 28, \mathrm{CZ} on output 25, output 30, \mathrm{CZ} on output 25, output 31, \mathrm{CZ} on output 25, output 32, \mathrm{CZ} on output 25, output 33, \mathrm{CZ} on output 25, check 36, \mathrm{CZ} on output 25, check 39, \mathrm{CZ} on output 25, check 40, \mathrm{CZ} on output 25, check 41, \mathrm{CZ} on output 25, check 42, \mathrm{CZ} on output 25, check 43, \mathrm{CZ} on output 25, check 45, \mathrm{CZ} on output 26, output 27, \mathrm{CZ} on output 26, output 31, \mathrm{CZ} on output 26, check 37, \mathrm{CZ} on output 26, check 39, \mathrm{CZ} on output 26, check 42, \mathrm{CZ} on output 26, check 44, \mathrm{CZ} on output 26, check 45, \mathrm{CZ} on output 26, check 46, \mathrm{CZ} on output 27, output 29, \mathrm{CZ} on output 27, output 33, \mathrm{CZ} on output 27, output 35, \mathrm{CZ} on output 27, check 36, \mathrm{CZ} on output 27, check 37, \mathrm{CZ} on output 27, check 38, \mathrm{CZ} on output 27, check 39, \mathrm{CZ} on output 27, check 42, \mathrm{CZ} on output 27, check 45, \mathrm{CZ} on output 28, output 31, \mathrm{CZ} on output 28, output 33, \mathrm{CZ} on output 28, output 34, \mathrm{CZ} on output 28, output 35, \mathrm{CZ} on output 28, check 39, \mathrm{CZ} on output 28, check 42, \mathrm{CZ} on output 28, check 44, \mathrm{CZ} on output 28, check 46, \mathrm{CZ} on output 29, output 30, \mathrm{CZ} on output 29, check 37, \mathrm{CZ} on output 29, check 41, \mathrm{CZ} on output 29, check 42, \mathrm{CZ} on output 29, check 43, \mathrm{CZ} on output 29, check 44, \mathrm{CZ} on output 30, output 31, \mathrm{CZ} on output 30, output 32, \mathrm{CZ} on output 30, output 33, \mathrm{CZ} on output 30, output 35, \mathrm{CZ} on output 30, check 36, \mathrm{CZ} on output 30, check 37, \mathrm{CZ} on output 30, check 38, \mathrm{CZ} on output 30, check 40, \mathrm{CZ} on output 30, check 41, \mathrm{CZ} on output 30, check 42, \mathrm{CZ} on output 31, output 32, \mathrm{CZ} on output 31, output 33, \mathrm{CZ} on output 31, check 36, \mathrm{CZ} on output 31, check 37, \mathrm{CZ} on output 31, check 38, \mathrm{CZ} on output 31, check 40, \mathrm{CZ} on output 31, check 41, \mathrm{CZ} on output 31, check 43, \mathrm{CZ} on output 31, check 45, \mathrm{CZ} on output 31, check 46, \mathrm{CZ} on output 32, output 34, \mathrm{CZ} on output 32, output 35, \mathrm{CZ} on output 32, check 38, \mathrm{CZ} on output 32, check 39, \mathrm{CZ} on output 32, check 40, \mathrm{CZ} on output 32, check 42, \mathrm{CZ} on output 32, check 43, \mathrm{CZ} on output 32, check 45, \mathrm{CZ} on output 32, check 46, \mathrm{CZ} on output 33, output 35, \mathrm{CZ} on output 33, check 39, \mathrm{CZ} on output 33, check 40, \mathrm{CZ} on output 33, check 41, \mathrm{CZ} on output 33, check 43, \mathrm{CZ} on output 33, check 44, \mathrm{CZ} on output 33, check 46, \mathrm{CZ} on output 34, output 35, \mathrm{CZ} on output 34, check 37, \mathrm{CZ} on output 34, check 38, \mathrm{CZ} on output 34, check 39, \mathrm{CZ} on output 34, check 40, \mathrm{CZ} on output 34, check 41, \mathrm{CZ} on output 34, check 42, \mathrm{CZ} on output 34, check 45, \mathrm{CZ} on output 34, check 46, \mathrm{CZ} on output 35, check 36, \mathrm{CZ} on output 35, check 37, \mathrm{CZ} on output 35, check 38, \mathrm{CZ} on output 35, check 41, \mathrm{CZ} on output 35, check 43, \mathrm{CZ} on output 35, check 44, \mathrm{CZ} on output 35, check 45, \mathrm{CZ} on output 35, check 46
These Clifford gates cannot be avoided. No choice of \mathrm{T}, \mathrm{T}^3, \mathrm{T}^5 or \mathrm{T}^\dagger for each rotation removes them; the catalogue proves this by showing that the linear system over \mathbb{Z}_4 the powers would have to solve has no solution.
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/496.36.4.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-496.36.4.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=4, exact. No fault of weight below 4 is both undetectable and damaging. One of weight 4 is.
Exactly 2,434,503 faults of weight 4 are undetectable and damaging, so A_{4}=2{,}434{,}503. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{4}\,p^{4}+O(p^{5}).
A damaging fault of weight 4 sits on columns [0,1,3,385].
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
found by an AI search campaign; a verified witness, not a maximum
Found by: AI search
Discovery: AI search
1 recorded source
[
{
"regime": "AI search",
"file": "master_catalog/catalogue_new",
"label": 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"N": 47,
"d": 4,
"d_is_exact": true,
"origin": "frontier_campaign",
"provenance": "frontier_campaign \u00b7 catalogue.jsonl:342"
}
]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/496.36.4.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[1073].