The circuit
The 83\times311 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.
| wire | 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 |
|---|---|
| out 0 (133) | ·11··11·1·111···1·1··1··1·1·····11···1··1·····11····1··111·111·11···1········1···11··11·1··111·1····1··1··1·1111·1····1··11·1···1···11111·1··1·1··1···11··111··11·1·1·1·111···1·1·1··1··1·····11···1·1···11·1·1·11··111·11··1·······1······11··1111·111·1··1··1····1··11·1·1··1···1··11·11·1··11111·1··11····11·11··1·· |
| out 1 (125) | ·1·1·111111·1·1·1·1··1··1·111·1·····1·1·······1······1·····1····1·······1···1··1111·1·1····1··1···111··111111111·····1·11·1·····1··1·11·1··1····1·1·11·1···1·1·1·11·11111·11··1·1·1··1··1111······1·1····1···1······1····1·····1···1·····1111·1·1···1··1·111··111··1·111·1·1·····1·11·1··1·1···11·1···1··1·11·1··1····1 |
| out 2 (119) | ··11·1··11111···1·1111··1···1··111··11····1··1·1··1·····1···1··11···1···1··11···1111·11·····1·········111·1··1··1·1···111·1·1···1···1···111·········1··11·1·····111···11111···1·111··1····1··111··11···11·11····1····1··11··1··1··11······1111·11····1·······111···1···1·····1·1··111·1·1··1··1···111······1··111······ |
| out 3 (119) | ·11··11·111·1···1··1······1····1···1·1··1·1···1·····1··1·1·1··111··11···1·1··1·11··111··1··1111···1··1·11·11··1··1····1····1··1·1···1····1···1·1·····1··1·1·1··11·1·1·111·1···1··1······1····1··1··1·1·1·1··1·1··1··1··111·11··111··1····11··111··1·1111·1··1·11···1·1···1····1···1····1··11··1····1···11···1··11···1·· |
| out 4 (125) | ·····1····1·····1·11·······1···111·1·1········11········1··11111···1····1·1·1··1·11111·······111··11111···1111·1··1·····1111··1······11111···1····1··1111·111·····1·····1·····1·11·1·····1···1111··1·····11·····1···11111··1···1·1·1·····1·11111······11111111·····1·111···1···1····1111·11····11111···1····111111··1·· |
| out 5 (127) | ······1·1·111·1·1·11·1·····1··111····11···1·······1·11···1·1·1·11··········1·1·111··1·1·1····111···1··111111·11·11·······111····1·······1111···11····1111···11······1·1·1111··1·111······1·1·11····11··1···111···11·1·1·11········1·1····111··1·1·1···111·1··1111··1·1·1·1···11······111···1······111·1·11··1111····1·1 |
| out 6 (125) | ·····1··1·······1·11····1··1···111·1·1········11········1···1·11···1····1·1···11·111·11······111··1111··1·1111·1··1·····1111··1······1111111·1····1··1111·11·1····1···1·······1·11···1···1···1111··1·····11·····1····1·11··1···1·1·······1·111·11·····1111111··1···1·111···1···1····1111·11····111111·11····111111····1 |
| out 7 (125) | ·11··11·111·1····11··1··1·1······1···········111····1··111·111·11···1········1···11···1·1··11·······1··1··1·11·1·11··11··1111···1···11111·1··1·1··1···11··111··11·1·1·111·1·····1·1··1··1······1········111·1·1·11··111·11··1·······1······11···1·1·11·····1··1····1··11···1··11·11··11111·1··11111·1··11····11·11··1·· |
| out 8 (125) | ······11·11·······11····1··1···111·1·1········11········1··11111···1····1·1·1··111··1······1··11··1111··1·1111·1··1·····1111··1······11111···1····1··1111·111·······11·11···1···11···1···1···1111··1·····11·····1···11111··1···1·1·1·····111··1·····1··111111··1···1·111···1···1····1111·11····11111···1····111111··1·· |
| out 9 (111) | ·1·1·1··11·1····1·1··1····1·1····1·1······1··111··1·1··111··1·11···1······11·1·111···11·1··1·········11·1··1·1··1·1··1·1··111·1·········1······1····11·1··1····1·11···11·1····111·1·····1·1····11······111111·1·11···1·11··1·····11·1····111···11·1·1·······11·1·····1·1·····1·1·1·1··111·1·······1·····1··11·1·1······ |
| out 10 (119) | ··11·111·1···11············11·1·11··111·1······1····11···1·11··1····1···1···11·1··1·11······1111··11····11·1·····1···11111··1·······11·1·····1·11···111···1·11··111·11·1···1·············111··11··1111····1·11···1··11··1···1··1···11····1··1·11·····111111····11····1········1··11111··1·····11·1·····111·111··1···1·1 |
| out 11 (117) | ·11·····11·1··1·1··1·1··1·1···11·1·1111······1·1··1··1·1····11·1····1······1···1··1········1111·····1·1·11111··1111··11·1···········1·1··1······1·1··1··1·11·1·11·····11·1·1··1··11··1··1··1·1·11·111···1·11·11······11·1···1·····1······1··1·······1111···1·1·11··1·11····11111·11·1····1····1·1··1·····1··1··111····1 |
| out 12 (117) | ·1·1······11····1·1·······111·1·11·1·1·········11·1·1··11··11·11··········1111·1·1··1···1··1··1····1·11·1·11111·1····1·11·1···1·······1·1·1····1··1·11·1··1·1··1·1······11····1·1·······1111··111··1······111·1·1···11·11········1111····1·1··1···1·1··1··1·11·1···1·111·1···1···1·11·1··11·····1·1·1···1··11·1·1···1·· |
| out 13 (111) | ·11··1··1·1·1······1····1·1···1111·111····1·········1··1·1····1·1··11···1·1·11·11·111···1··11·1···1··1·1··111········11····11·1·1···1····11····1·····1··1······11·1···1·1·1······1···1··1··1·1111·11···1····1·1··1·····1·1·11··1·1·11····11·111···1·11·1·1··1·1····1·11···1······11····11·11··1····11···1···1··1······· |
| out 14 (133) | ·11···1··11·1·····1·····1·1··1··11········1··1·1····1··111·111·11···1········1··111·1·1·1··11··1···11··1··111111·11··11·1111····1···11111·1··1·1··1···11··111··11···1··11·1·····1····1··1·····11·······11·1·1·1·11··111·11··1·······1·····111·1·1·1·11··1·11··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 (109) | ·11··1··11··1·····1·····1·11·····1···1····1··1·1····1·111···11··1···1········1···1······1··11··1···11··1····11·1·1···11·1111····1·1·11·11······1··1···11··111··11·1···11··1·····1····1··11·····1···1···11·1·1·1·1····11··1··1·······1······1······1·11··1·11··1·······11···1··1··11·1111·1·1·111·11·····1····11·11··1·· |
| out 17 (117) | ·······1·1········11····1······111·1······1····1········1··11111···1····1·1·1··1111·1·1·······11··1111·11··111·1·········1111·1······11111···1····1··1111·111········1·1········11··11·······1111······1··1·····1···11111··1···1·1·1·····1111·1·1······111111·11·····111···1·········111111····11111···1····111111··1·· |
| out 18 (135) | ·····1·111111·1·1·11·1········111···111···1··11···1·11···1·1···11···1······111·1·111111·1····111···1··1111·1·11·1········11·1···1······1111····11··1·1111····1····1··1111111··1·111········1·11···111··111·111···1··1···11··1·····111····1·111111·1···111·1··1111····1·1·1···1·······11·1··1·····1111···11··1111······1 |
| out 19 (127) | ·1·1··111··1······1·····111·1·1·11·11·····1··111··1·1··111··1·11···1······11·1·1·111··1·1··1·11····1·11····1111·111··1·1··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··1·11···1···111·1···111·1·1··111·1·······1·····1··11·1·1······ |
| out 20 (109) | ·1·1··1····1·······1····1·1···11····1·····1···1···1·1··1·1·1·1··········1··111··1··1·1··1··1·1·1··1·1·1·······11111··1·111·1·········111·1···1·1··1·1·1·1··11··1·1··1····1·······1···1··1··1·1····1····1·1·11·1··1··1·1········1··111·····1··1·1··1·1·1·11·1·1······1····1·1·111·1·111·1·1·····111·1···11··1·1·1·1··1·· |
| out 21 (127) | ·11······111··1·1·1···1·1·1···1····1··1···1··1····1··1·11··1··1····11···1·111···11·1·1·····111·1··1·111·111··11·1····11·11111·1·····11·11····1··1·····11····11·11······111·1··1·1····1··1··1····1···1··11··1·11·1···1··1···11··1·111······11·1·1····111·11·111·11··1···1·1···1···11·11111·1···11·11····1·1···11·····1·1 |
| out 22 (119) | ·····11·1·111·····11··········11·····11·1····11···1·11··11·1····1··········1·1·1·1··1·1·11····11······1111·1·1··11···1··111·1···1····1·1111··1·11····1111···11····1·1·1·111·····11·········1·1·····111··11·111··11··1····1········1·1····1·1··1·1·1····11····1111····1·1·····11··1··111·1··1···1·1111··111··1111····1·1 |
| out 23 (125) | ·1·1····1·1·1·1·1·1··1··1·111·1·····1·1·······1······1·11··1···111······1···1··1·1·1111····1··1···111··111111111·····1·11·1·····1·····1·1··1·1·11·1·11·1···1·1·1·1····1·1·11··1·1·1··1··1111······1·1····1···11·1···1···11·····1···1·····1·1·1111···1··1·111··111··1·111·1·1·····1·11·1··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 (133) | ··11·1·1111···1·1·11·1······1·111··1··1···1···1·····11········1·1··11·····1··1··11111···1···1······111··111·1111··1···111·111·1·····11··11·1··111·1·1··11··1·1··111··1111··1··1·111·······11·11·1···1··1·1··11·········1·1·11····1··1·····11111···1··1····111··11··1··11·1·1···1··111·11111···11··11··1·11·1··11·1····1 |
| out 26 (117) | ·····1·11··11·1·1····1···········111··1···1··1·1··1·11···1··11111··1····1·1111··1····11·1····1····1·111111····1·111·····1··11·1·1·····1···1····11·1·······11·1····1··11··111··1···1············11···1··11·1111···1···11111·1···1·1111·····1····11·1···1··1·111111········1···111····1··11111····1···1···11······11····1 |
| out 27 (125) | ·····1·11··11·1·1····1·····1··1··1·11·1···1··1·1··1·11··1···11··1··1····1·1111··1····11·1····1····1·1111111·1·111·1·····1··11·1·1····1····1·11·11·1·······11·1····1··11··111··1···1······1·1···11·1·1··11·1111··1····11··1·1···1·1111·····1····11·1···1··1·111111··1··1··1·1·1·1····1··11111···1····1··111······11····1 |
| out 28 (31) | ·····1··1·······1··········1·········1····1···1·································1···1········1···········11·······1·····1···1·····································1···1·······1·······1··1·········1···1·1································1···1·······1·········1··1···········1····1···1······························ |
| out 29 (119) | ·1·1·1·1·11·1·1····1···1··1·1·1111·1111········1·····1·1···11·111··1······1·······1111·····1·1·1···1···1·1····1···1··1·1·1·1··1·1····1·1·11··1··1···1·1·1·1·11·1·11··1·11·11·····1······1·11·1111·111·····1··11·····11·111·1·····1··········1111····1·1·1·1···1·1········1·····1·1·1·1·1··11···1·1·11··1·1·1·1·11···1·1 |
| out 30 (111) | ·11··1··1·1·1······1····1·11···11··11·····1·········1··11··1··1·1··11···1·1·11·11·111···1··11·1···1··1·1···1······1··11····11·1·1···111··1·····11····1··1······11·1···1·1·1······1···1··11···11·1·1····1····1·1·1···1··1·1111··1·1·11····11·111···1·11·1·1··1·1······1·········1·11····11·11··111··1····11··1··1······· |
| out 31 (127) | ·1·1·1··11·1······1·····1·111·1·11·1··1···1··111··1·1··111··1·11···1······11·1·111···11·1··1·11····1·11···11111·1·11·1·1··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··1·11·····1·111·1···1·1·1·1··111·1·······1·····1··11·1·1······ |
| out 32 (125) | ·····1···1111·1·1····1·····1··1··1·11·1···1··1·1··1·11··1··1··1·1··1····1·1111··1··11···1····1····1·1111111·1·111·1·····1··11·1·1····1·····1·1·11·1·······11·1····1····11111··1···1······1·1···11·1·1··11·1111··1···1··1·1·1···1·1111·····1··11···1···1··1·111111··1··1··1·1·1·1····1··11111···1·····11111······11····1 |
| out 33 (125) | ·1·1·11·1·111···1··1·1··1·111··1····11··1····1····1·1··1·1·1·1··········1··111·····111111··1···1··111·1···1·1·1111·····1·1··1········111·1···1·1··1·1·1·1··11··1·11·1·1·111···1··11··1··111··1····11·1··1··11·1··1··1·1········1··111········1111·1·1···1111·1·····1··1··1·1·11····1·1··11·····111·1···11··1·1·1·1··1·· |
| out 34 (127) | ·1·1·1·1··11······1·····1·111·1·11·111····1··111··1·1··111··1·11···1······11·1·111·11···1··1·11····1·11···11111··1···1·1··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··1·11·····1·111·1····1··1·1··111·1·······1·····1··11·1·1······ |
| out 35 (119) | ·1·1····11··1·1·1··1·1··1·1·1·11·1·1·11·1·1····1·····1·1·1··111·1··1······1·1···1·1··11····1···1·····1·111·······11····111·1··1·1····111·1·1····1···1·1···1··1·1·1····11··11··1··11··1··1·11·1·11··111·1··1··11··1···111·1·1··1··1·1······1·1··11···1···1···1·111·············11···111·1··11···111·1··1··1·1·1··1·····1 |
| out 36 (117) | ·········11·······11······11···111·1·········1·1········1··11111···1····1·1·1··111111·········11··1111····1111·1········111·1·1······11111···1····1··1111·111··········11·······11······11···1111·······1·1·····1···11111··1···1·1·1·····111111········111111·····11·111···1········111·111····11111···1····111111··1·· |
| out 37 (117) | ·1·1·11·1111····1··1······1·1·11····11······11····1·1··1·1·1·1··········1··111·····11·1·1··1···1··1·1·1·1·····1111···1·1·11·1········111·1···1·1··1·1·1·1··11··1·11·1·1111····1··1······1·11·1····11····1··11·1··1··1·1········1··111········11·1·1·1···11·1·1·1·········1·1·11··1·1·11·11·····111·1···11··1·1·1·1··1·· |
| out 38 (127) | ·····11·11111·1·1··1··········111···111···1··11···1·11··11·1····1··········1·1·1·1··111·1····1111·····1111·1·11·1········11·1···1····1·1111··1·11····1111···11····1·1·111111··1··1·········1·11···111··111·111··11··1····1········1·1····1·1··111·1···111····1111····1·1·1···1·······11·1··1···1·1111··111··1111····1·1 |
| out 39 (117) | ·········11·······11···········111·111····1···11·1······1··11111···1····1·1·1··111111·········11··1111·····111·1·11······111·········11111···1····1··1111·111··········11·······11···········1111·11···1·11·····1···11111··1···1·1·1·····111111········111111········111···1··11·····111·1·····11111···1····111111··1·· |
| out 40 (109) | ·1·1·111···1····1··1······1·1·11····11····11······1·1··1·1·1·1··········1··111·······1··1··1···1··1·1·1·1·····1111···1·11··11········111·1···1·1··1·1·1·1··11··1·11·11···1····1··1······1·11·1····11···1···11·1··1··1·1········1··111··········1··1·1···11·1·1·1·········1·1·11··1·11··111·····111·1···11··1·1·1·1··1·· |
| out 41 (125) | ··11·1·1··1···1···1·····1···1·111··1111······11·····11··11···11····11·····1··1··1111·1··1···11···1··11···11·1111·1····11··1·1·1·····1·1·11·····11·1·1··11··1·1··111··1··1··1····1····1····11·11·1·111···11··11··11····11···11····1··1·····1111·1··1··11····11···1··1··11·1·1··1···11··1·111···1·1·11····11·1··11·1····1 |
| out 42 (133) | 1·········1·····1·11·1·····1···1·1·111··1·1···11········1··11111···1····1·1·1··1111111·······111··1·11····111111·11··1···111··1······11111···1····1··1111·111·1·········1·····1·111······1···1·11·11·1·1·11·····1···11111··1···1·1·1·1···1111111······1111·11······1·111·1·1··11·1···111·11····11111···1····111111··1·· |
| out 43 (127) | ·11···11···1··1···1··1····1·····1··1111·1·1··1····1····11··1··1····11···1·111···111···1····11··1··11·11··11·11··111···1·11111·1··1··11·11····1··1·····11····11·11···11···1·1····1·1·····1·····1·1·1111·11··1··1·1···1··1···11··1·111······111···1···11··111·11··1··1··11·····111··1·11111·1···11·11····1·1···11·····1·1 |
| out 44 (111) | ··11·1·11·····1·1····1·····11·1·11····1·1·1··1·1····11··11·111·1····1·1·1····1·1········1···1·11··1·····11·1······1··111·1·11·······1··1···1·1·11···1·1···1··1··111··11····1··1···1······111··11····11·11·1·11··11··111·1···1··1····1····1········1··1·111·····11····1·········1·111·1·11·····1··1····1111·1·1··1·····1 |
| out 45 (109) | ·11·····11·1··1·1··1·1··1·1···1111····1·111····1··1··1·1····11·1····1······1···1··1········1111·····1·1·11111·111··········1········1·1··1······1·1··1··1·11·1·11·····11·1·1··1··11··1··1··1·111····11·1··11·11······11·1···1·····1······1··1·······1111···1·1·11··1·11··1·1·1·········1·1····1·1··1·····1··1··111····1 |
| out 46 (127) | ·111·111·11·1·1····1····1·1·1·11·1·1·11·1·1····1·····1·1···11·111··1······1········111·····1·1·1···1·1·111·······11····111·1··1·1····1·1·11··1··1···1·1·1·1·11·1111·11·11·11·····1···1··1·11·1·11··111·1··1··11·····11·111·1·····1·····1·····111····1·1·1·1·1·111·············11···111·1··11···1·1·11··1·1·1·1·11···1·1 |
| out 47 (109) | ········1··11·1······1··1·····1··1·1111······111··1·11··1···1·1·1··1····1·1··1·····1·11·1·········1·1111·1··1·111··········1··1·1····1····11·1·11·1·······1111········1··111······1··1·····1···11·111···111111··1····1·1·1·1···1·1··1········1·11·1······1·1111·1·····1··1·1·1·········1·111···1····1·1111······11·11·1 |
| out 48 (119) | ·111·11·11111···1·11·1······1··1·1··1···1·1····1··1·····1···1··11···1···1··11···11·1·11·····1·····1···11··1··11·1····1111·111···1···1···111·········1··11·1····1111·1·11111···1·111·······1··1·1··1··1·1··11····1····1··11··1··1··11··1···11·1·11····1···1···11····1···1·1···1···1111·111··1··1···111······1··111······ |
| out 49 (117) | ·····1··1·1·······11···········111·111·······1·1········1··11111···1····1·1·1··1··11·1········11··1111·····111·1·11·····111·1·1······11111···1····1··1111·111·····11··1·1·······11···········1111·11····1·1·····1···11111··1···1·1·1·····1··11·1·······111111········111···1··11····111·111····11111···1····111111··1·· |
| out 50 (119) | ·11····1·1·1··1·1·1··1··1·1········1··1···········1··1·11··1··1····11···1·111···11···11····111·1··11·11·111·1·1·1····11··11·1·1·····11·11····1··1·····11····11·11····1·1·1·1··1·1·1··1··1···1···1···1······1·11·1···1··1···11··1·111······11···11···111·111·11·11··1··1··1···1···11··11·1·1···11·11····1·1···11·····1·1 |
| out 51 (119) | ·11··11·111·1···1··1······11···1···111··1·1··1······1··111·1··1·1··11···1·1··1·11··111··1··1111···1··1·11··1··1·······1·····1·1·1···11···1·····1·····1·11···1··11·1·1·111·1···1··1······11···1··1·11·1·11···1·1·11··1··1·1·111·1·1··1····11··111··1·1111·1··1·11·····1···1········1·····1·11··11···1····1···1·11····1·· |
| out 52 (133) | ·11··11·1···1···1·1·······11··1·11···1·11····111····1··111·111·11···1········1···11··1··1··111·1···11··11····111·1··1·1··1111···1···11111·1··1·1··1···11··111··11·1·1·1···1···1·1·······11·1··11···1·1··111·1·1·11··111·11··1·······1······11··1··1·111·1·11··11·······1·1·1··1·1·1··11111·1··11111·1··11····11·11··1·· |
| out 53 (127) | ·····1·111111·1·1·11·1·····1··111····11···1·······1·11···1·····11··········1·1·1·111111·1····111···1··111111·11·11·······111····1······11······11····1111···11····1··1111111··1·111······1·1·11····11··1···111···1·1····11········1·1····1·111111·1···111·1··1111··1·1·1·1···11······111···1·····11·····11··1111····1·1 |
| out 54 (109) | ·111·····1·1··1····1····1·11··11·1····1·1·1···11··1··1·1····11·1····1······1···1··1·1······11·1····11·1·11·11··11·····1····11·······1·1··1······1·1··1··1·11·1·111·····1·1·1·····1···1··11·1·1·1····11·1·111·11······11·1···1·····1·····11··1·1·····11·1··11·1·11····11····1·1····1····111····1·1··1·····1··1··111····1 |
| out 55 (125) | ·1·1·111111·1·1·1·1··1··1·111·1·1·····1·1·1···1······1·1·1·1····1··············1111·1·1····1··1···111··1111111·1·1·····1··1·····1····1··1··1····1·1·11·1·1·111·1·11·11111·11··1·1·1··1··1111··1·····11·1·1···11··1··1····1···············1111·1·1···1··1·111··111··1·111···1··1····1··1··1·1···1··1···1··1·11·1··1··1·1 |
| out 56 (133) | ·····11···111·1······1··1··1··1··1·11·1···1··1·1··1·11··11·11·1·1·11····1·11·1··1·1111··1·········1·1111·11·1·111·1·····1··11·1·1····11····1·1·1111·······1111····1·1···1111······1··1···1·1···11·1·1··11·1111··11··11·1·1·1···1·11·1·····1·1111··1······1·1111·1··1··1··1·1·1·1····1··11111···11·····11111·····11··1·1 |
| out 57 (125) | ······1···1·····1·11····1··1···1·1·111··1·1···11·········1·11111···1····111····111·111·······111··1111··1·111111·11··1···111··1········111···1····1··1111·1·········1···1·····1·11···1···1···1·11·11·1·1·11······1··11111··1···1·1·······111·111······1111111··1···1·111·1·1··11·1···111·11······111···1····11111······ |
| 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 (119) | ·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··1111·1·1··1·11·11111·········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··1·11·1·····111·1···1·1·1·11·111·1·······1·····1··11·1·1······ |
| out 60 (95) | ·11···1·····1······1····1·11···11··11···1·····1····11··1·1····1·1··11···1·1·11·1···1··1·1··11·1···1··1·1···1······1···1·1··1··1·····1····11····1·····1··1······11···1·····1······1···1··11···11·1·1··1···1··1·1··1·····1·1·11··1·1·11····1···1··1·1·11·1·1··1·1······1·········1··1·1··1··1···1····11···1···1··1······· |
| out 61 (125) | ······1··1········11····1··1···111·11·····1··111········1··11111···1····1·1·1··111·11·1·····1·11··1111··1·1111·1·1·······11···1······11111···1····1··1111·111·······1··1·····1··11···1···1···1111·1····1111·····1···11111··1···1·1·1·····111·11·1····1·111111··1···1·111···1··1······11··11····11111···1····111111··1·· |
| out 62 (47) | ······1··1······1·······1·······1···1···1·1··············1·····1·······1····1·····1··1·······1··········1·····1··1···1··1·············1······1········1·····1·······1··1······1······1········1···1··1·1·········1······1··········1········1··1······1········1·········1····1··1··1···········1······1·····1······1·· |
| out 63 (31) | ······1··1······1·······1·····1·1·······1·········1·······························1··1·······1··········1···1·1······1·········1····································1··1······1······1·····1··1······1·····1································1··1······1········1······1··1·······1····································· |
| out 64 (117) | ····1·11·1········11···········111·111·······1·1········1··11111···1····1·1·1···11··1·1·······11··1111·····111·1·11·····111·1·1······11111···1····1··1111·111·······11·1········11···········1111·11····1·1·····1···11111··1···1·1·1······11··1·1······111111········111···1··11····111·111····11111···1····111111··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 (135) | ·····1111·111·1···11·1··1··1···1·····11·1·1··11···1·11··11·1····1··········1·1·1·1·11·1·1·····11···1··11·11111··11···1·1·11·1···1····1·1111··1·11····1111···11····1·111·1111····111··1···1···1·····1111111·111··11··1····1········1·1····1·1·11·1·1····11·1··11·1··1·111·····11··1·1·11·1··1···1·1111··111··1111····1·1 |
| out 67 (127) | ·····1·111111·1·1·11·1·····1··111···1·1······1····1·11·········11··········11··1·111111·1····111···1··111111·11·1·1·····111·····1·····1111·····11····1111····1····1··1111111··1·111······1·1·11···1·1···1··111··········11········11·····1·111111·1···111·1··1111··1·1·1·1···1·1····111····1····1111····11··1111·····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 (125) | ······1·11·11·1·1····1········1111·1··1···1··1·1··1·11···1··11111··1····1·1111····11··1·1····1····1·111111··1··1111·····1··11·1·1·····1···1····11·1·······11·1······1·11·111··1···1········1·1111···1··11·1111···1···11111·1···1·1111·······11··1·1···1··1·111111·····1·1··1·111····1··11111····1···1···11······11····1 |
| out 70 (135) | ······1·1·111·1·1·11·1·····1··111····11·1·1··11···1··1··11·1····1··········1·1·111··1·1·1····111···1··111111·11·11···1···11·1···1····1·1111··1·11····1111···11······1·1·1111··1·111······1·1·11····111·111·1·1··11··1····1········1·1····111··1·1·1···111·1··1111··1·1·1·1···11··1···11·1··11··1·1111··111··1111····1·1 |
| check 71 (118) | 1··1····11·1··1·1··1·1··1·1···111··1·1····1····1··1··1·1·····11·1··1·······1····11·········1111···11·1·1··111····1··1··1111·········1·1··111···1·11·1·11··11·11··1····11·1·1··1··11··1··1··1·11·1··1···1··11·11·······11·1·1······1·······11········1111·11·1·1····1·11·······1·1··1111··1····1·1··11·1·1·11·11·11····1 |
| check 72 (112) | ·11··1···1·1··1···1··1····11···1·1··1·1·1···········1··1·1··1··1········1·1·11·11·1·1·····1··1·1··11·1·11··1···111··11·1·11·1·1·1···1····1·1····11··1·11·······11·1····1·1·1····1·1·····11···1·1··1·11······1·1··1···1··1······1·1·11····11·1·1····1··1·111·1·11·····1·····1·11·11·1·11·1·11··1····1··1··111·11········ |
| check 73 (120) | ·11····111··1···1·1······1··1·11···1··1·1····1····1··1·11···11·11··11·······11··11·1····1··111·1···11··11··11·1·1···11·11···1·1·····11·11····1·1······11··11···11····111··1···1·1······1··11·1··1···11··1··1·11·1····11·11·11······11·····11·1····1·111·1·11··11·····11··1···1··11·11···1·1···11·11····11····11·11····· |
| check 74 (126) | ·····11···111·1······1··1·····1··1·1··1···1···11··1·11·1···1·1·1····1·······1···1·1111··1·········1·1111·1··1·11111·····1·····1·1·1·11111111·1···11·11111···1·····1·1···1111······1··1·····1···11···1··1·111111·····1·1·1···1······1······1·1111··1······1·1111·1·····1··1·1·111····1····111·11111111·11··111111····1·· |
| check 75 (158) | ···········11···1·1·11·11····1·1····1·11···111111···1··1·1····1··111·1·1·1·1·111111·····11···111·111·111·1··11··1·1·1···1···11·111·1···111··111·111·11·11··11·1··111··11··111111111·1···11····1·1··11·1·11·111·1···11····1·1·1··1···11··11··1·11·11·111·1·1··1·11·11·11111··111····1111·1··1··1·111·1··111··11·11··11·1 |
| check 76 (160) | ·11··11·1·111···1111···11·11··1·1··1·1··1·11··11·111·····1······1···11·11·111·1··1111··1·1·111···11···1·11···1··1·11··1·1·1··1··11·11·111·1·111·1·1·1··1····1···11·······1·11···1·1·111··11··111··111·1111·1·11·1111·1·1··111·111·1···1·1·11·1··1····1··111·1111··1·1·111·1·1111·1111111··1···111·1111·1·····1111·1···1 |
| check 77 (168) | ··11···11··1111···11··11···11·1·1·11·11·111·111·111··1··1111·1·111···1···1111·111··1111·11··111111····11···1··1·1111·1·1·1111···11··1··11·1·1··1···1·11······1·····11111111··11······11····1111······111·1·11··1·1·11··1111·111···111··11111111········11··111111··111·111·1111··11··1··11111··1·1·11·1··1·11111·11··1· |
| check 78 (168) | ·1·111·11··1111··1·1······11111·11·11·1····11111···111·11·11111111·1··11··11111·11·1··11·1·1·11111·1·11·1·1·111·1111·1·111·11·1111····1···11··1·····1·11··1·11·1·1·1111········11··1111·111·111111·1···1·111··1·11111111··11·11··1·······1··11··111·1·1···1·1·1·1··1·1··11·······1·1··1·1·1·1····1111·1111·11··11··1·1· |
| check 79 (152) | ·····1··1·1·111·1·111·11·······11111··1······1··1111·1··11·111·111·······11·1·11·111·1·111···111···1·······111·····1····111·11·111···1·111··1111·····111111·11····1··1·1·1····1·1111111······1···111····111·1···11·····1··1····11·1·1····1·11·1·11····1111·111111····111·1111111····111··11·1··1·111111··1··1111·111·1· |
| check 80 (158) | ··11·11····11··1·1··1·111··11·11·1···1·111·111··11·1·1·····111··1·1··111·1·11·1·11·11·····1·11·111·111111···111·111·11·1·1··1111·1··11··11·1·1···1·1·1111111·1··111·1····11·111111111·1··111·1·1···1··11·1111·······111··1·1111111··1·····11·11·····1··1·1······1·····11·1···111··1·1·11···11·11··11··11···1······1111· |
| check 81 (144) | ··11·11··1····1···11·1··1···11·1··111··11111111111111···1··1·11·····1·····1·11··11····1·1···11·····111···111·1···11111·111··11·111··1···111····11···1··11··111··111·1··1···1····111··1·111·11·11·1·11·1······1··1···1·11····1····1·11·····11····1·1··11···111···111·1·1·111111····1···11·11·1·1···111···11·1··11·1··1·1 |
| check 82 (144) | ··11··1···111···1·11····1···1··111··11····1··1·1··1···11111·1111·111·111·1·1··1··1·11·1·····1·····11··111·1··1··1·1···111·1·1···1·111·1··1111·11·111·111111111··11··1···111···1·11···1····1··111··11···11·11···1··111····11·111111·11······1·11·1····1···11··111···1···1·····1·1··111·1·1··1···1·11··1·1·1·1······11·1· |
The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.
Figures of merit
inputs n311Noisy T states per run.
outputs k71
distance d3Exact, proved and witnessed here.
error coefficient A_{3}1,056Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.
wires N83
checks r12
V_{\mathrm{ex}}71T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.3445Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.3445Overhead per output qubit.
\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.
T-countnot computedMinimal T-count of the output gate. Not computable at this width.
phase-polynomial degreenot computedMinimised over changes of output basis.
effective width71Rank of the output rows modulo the check rows.
Output gate
71 T0 CS0 CCZon 71 output wires
As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}
As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70 (output wires per term, separated by +)
This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.
Clifford correction
With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 75 single-wire gates and 741 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{Z} on output 6, \mathrm{Z} on output 7, \mathrm{Z} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{Z} on output 14, \mathrm{S} on output 15, \mathrm{Z} on output 16, \mathrm{Z} on output 17, \mathrm{S} on output 18, \mathrm{S} on output 19, \mathrm{Z} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23 and 792 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 816 correction gates
\mathrm{Z} on output 0, \mathrm{Z} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{Z} on output 6, \mathrm{Z} on output 7, \mathrm{Z} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{Z} on output 14, \mathrm{S} on output 15, \mathrm{Z} on output 16, \mathrm{Z} on output 17, \mathrm{S} on output 18, \mathrm{S} on output 19, \mathrm{Z} on output 20, \mathrm{S} on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23, \mathrm{S} on output 24, \mathrm{Z} on output 25, \mathrm{Z} on output 26, \mathrm{Z} on output 27, \mathrm{S} on output 28, \mathrm{S} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{Z} on output 32, \mathrm{Z} on output 33, \mathrm{S} on output 34, \mathrm{S} on output 35, \mathrm{Z} on output 36, \mathrm{Z} on output 37, \mathrm{S} on output 38, \mathrm{Z} on output 39, \mathrm{Z} on output 40, \mathrm{Z} on output 41, \mathrm{Z} on output 42, \mathrm{S} on output 43, \mathrm{S} on output 44, \mathrm{Z} on output 45, \mathrm{S} on output 46, \mathrm{Z} on output 47, \mathrm{S} on output 48, \mathrm{Z} on output 49, \mathrm{S} on output 50, \mathrm{S} on output 51, \mathrm{Z} on output 52, \mathrm{S} on output 53, \mathrm{Z} on output 54, \mathrm{Z} on output 55, \mathrm{Z} on output 56, \mathrm{Z} on output 57, \mathrm{S} on output 58, \mathrm{S} on output 59, \mathrm{S} on output 60, \mathrm{Z} on output 61, \mathrm{S} on output 62, \mathrm{S} on output 63, \mathrm{Z} on output 64, \mathrm{S} on output 65, \mathrm{S} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{Z} on output 69, \mathrm{S} on output 70, \mathrm{S} on check 71, \mathrm{S} on check 74, \mathrm{S} on check 75, \mathrm{S} on check 80, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 4, \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 11, \mathrm{CZ} on output 0, output 12, \mathrm{CZ} on output 0, output 14, \mathrm{CZ} on output 0, output 16, \mathrm{CZ} on output 0, output 17, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 23, \mathrm{CZ} on output 0, output 25, \mathrm{CZ} on output 0, output 26, \mathrm{CZ} on output 0, output 27, \mathrm{CZ} on output 0, output 32, \mathrm{CZ} on output 0, output 33, \mathrm{CZ} on output 0, output 36, \mathrm{CZ} on output 0, output 37, \mathrm{CZ} on output 0, output 39, \mathrm{CZ} on output 0, output 40, \mathrm{CZ} on output 0, output 41, \mathrm{CZ} on output 0, output 42, \mathrm{CZ} on output 0, output 45, \mathrm{CZ} on output 0, output 47, \mathrm{CZ} on output 0, output 49, \mathrm{CZ} on output 0, output 52, \mathrm{CZ} on output 0, output 54, \mathrm{CZ} on output 0, output 55, \mathrm{CZ} on output 0, output 56, \mathrm{CZ} on output 0, output 57, \mathrm{CZ} on output 0, output 61, \mathrm{CZ} on output 0, output 64, \mathrm{CZ} on output 0, output 69, \mathrm{CZ} on output 0, check 71, \mathrm{CZ} on output 0, check 74, \mathrm{CZ} on output 0, check 75, \mathrm{CZ} on output 0, check 80, \mathrm{CZ} on output 1, output 4, \mathrm{CZ} on output 1, output 6, \mathrm{CZ} on output 1, output 7, \mathrm{CZ} on output 1, output 8, \mathrm{CZ} on output 1, output 11, \mathrm{CZ} on output 1, output 12, \mathrm{CZ} on output 1, output 14, \mathrm{CZ} on output 1, output 16, \mathrm{CZ} on output 1, output 17, \mathrm{CZ} on output 1, output 20, \mathrm{CZ} on output 1, output 23, \mathrm{CZ} on output 1, output 25, \mathrm{CZ} on output 1, output 26, \mathrm{CZ} on output 1, output 27, \mathrm{CZ} on output 1, output 32, \mathrm{CZ} on output 1, output 33, \mathrm{CZ} on output 1, output 36, \mathrm{CZ} on output 1, output 37, \mathrm{CZ} on output 1, output 39, \mathrm{CZ} on output 1, output 40, \mathrm{CZ} on output 1, output 41, \mathrm{CZ} on output 1, output 42, \mathrm{CZ} on output 1, output 45, \mathrm{CZ} on output 1, output 47, \mathrm{CZ} on output 1, output 49, \mathrm{CZ} on output 1, output 52, \mathrm{CZ} on output 1, output 54, \mathrm{CZ} on output 1, output 55, \mathrm{CZ} on output 1, output 56, \mathrm{CZ} on output 1, output 57, \mathrm{CZ} on output 1, output 61, \mathrm{CZ} on output 1, output 64, \mathrm{CZ} on output 1, output 69, \mathrm{CZ} on output 1, check 71, \mathrm{CZ} on output 1, check 74, \mathrm{CZ} on output 1, check 75, \mathrm{CZ} on output 1, check 80, \mathrm{CZ} on output 4, output 6, \mathrm{CZ} on output 4, output 7, \mathrm{CZ} on output 4, output 8, \mathrm{CZ} on output 4, output 11, \mathrm{CZ} on output 4, output 12, \mathrm{CZ} on output 4, output 14, \mathrm{CZ} on output 4, output 16, \mathrm{CZ} on output 4, output 17, \mathrm{CZ} on output 4, output 20, \mathrm{CZ} on output 4, output 23, \mathrm{CZ} on output 4, output 25, \mathrm{CZ} on output 4, output 26, \mathrm{CZ} on output 4, output 27, \mathrm{CZ} on output 4, output 32, \mathrm{CZ} on output 4, output 33, \mathrm{CZ} on output 4, output 36, \mathrm{CZ} on output 4, output 37, \mathrm{CZ} on output 4, output 39, \mathrm{CZ} on output 4, output 40, \mathrm{CZ} on output 4, output 41, \mathrm{CZ} on output 4, output 42, \mathrm{CZ} on output 4, output 45, \mathrm{CZ} on output 4, output 47, \mathrm{CZ} on output 4, output 49, \mathrm{CZ} on output 4, output 52, \mathrm{CZ} on output 4, output 54, \mathrm{CZ} on output 4, output 55, \mathrm{CZ} on output 4, output 56, \mathrm{CZ} on output 4, output 57, \mathrm{CZ} on output 4, output 61, \mathrm{CZ} on output 4, output 64, \mathrm{CZ} on output 4, output 69, \mathrm{CZ} on output 4, check 71, \mathrm{CZ} on output 4, check 74, \mathrm{CZ} on output 4, check 75, \mathrm{CZ} on output 4, check 80, \mathrm{CZ} on output 6, output 7, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 11, \mathrm{CZ} on output 6, output 12, \mathrm{CZ} on output 6, output 14, \mathrm{CZ} on output 6, output 16, \mathrm{CZ} on output 6, output 17, \mathrm{CZ} on output 6, output 20, \mathrm{CZ} on output 6, output 23, \mathrm{CZ} on output 6, output 25, \mathrm{CZ} on output 6, output 26, \mathrm{CZ} on output 6, output 27, \mathrm{CZ} on output 6, output 32, \mathrm{CZ} on output 6, output 33, \mathrm{CZ} on output 6, output 36, \mathrm{CZ} on output 6, output 37, \mathrm{CZ} on output 6, output 39, \mathrm{CZ} on output 6, output 40, \mathrm{CZ} on output 6, output 41, \mathrm{CZ} on output 6, output 42, \mathrm{CZ} on output 6, output 45, \mathrm{CZ} on output 6, output 47, \mathrm{CZ} on output 6, output 49, \mathrm{CZ} on output 6, output 52, \mathrm{CZ} on output 6, output 54, \mathrm{CZ} on output 6, output 55, \mathrm{CZ} on output 6, output 56, \mathrm{CZ} on output 6, output 57, \mathrm{CZ} on output 6, output 61, \mathrm{CZ} on output 6, output 64, \mathrm{CZ} on output 6, output 69, \mathrm{CZ} on output 6, check 71, \mathrm{CZ} on output 6, check 74, \mathrm{CZ} on output 6, check 75, \mathrm{CZ} on output 6, check 80, \mathrm{CZ} on output 7, output 8, \mathrm{CZ} on output 7, output 11, \mathrm{CZ} on output 7, output 12, \mathrm{CZ} on output 7, output 14, \mathrm{CZ} on output 7, output 16, \mathrm{CZ} on output 7, output 17, \mathrm{CZ} on output 7, output 20, \mathrm{CZ} on output 7, output 23, \mathrm{CZ} on output 7, output 25, \mathrm{CZ} on output 7, output 26, \mathrm{CZ} on output 7, output 27, \mathrm{CZ} on output 7, output 32, \mathrm{CZ} on output 7, output 33, \mathrm{CZ} on output 7, output 36, \mathrm{CZ} on output 7, output 37, \mathrm{CZ} on output 7, output 39, \mathrm{CZ} on output 7, output 40, \mathrm{CZ} on output 7, output 41, \mathrm{CZ} on output 7, output 42, \mathrm{CZ} on output 7, output 45, \mathrm{CZ} on output 7, output 47, \mathrm{CZ} on output 7, output 49, \mathrm{CZ} on output 7, output 52, \mathrm{CZ} on output 7, output 54, \mathrm{CZ} on output 7, output 55, \mathrm{CZ} on output 7, output 56, \mathrm{CZ} on output 7, output 57, \mathrm{CZ} on output 7, output 61, \mathrm{CZ} on output 7, output 64, \mathrm{CZ} on output 7, output 69, \mathrm{CZ} on output 7, check 71, \mathrm{CZ} on output 7, check 74, \mathrm{CZ} on output 7, check 75, \mathrm{CZ} on output 7, check 80, \mathrm{CZ} on output 8, output 11, \mathrm{CZ} on output 8, output 12, \mathrm{CZ} on output 8, output 14, \mathrm{CZ} on output 8, output 16, \mathrm{CZ} on output 8, output 17, \mathrm{CZ} on output 8, output 20, \mathrm{CZ} on output 8, output 23, \mathrm{CZ} on output 8, output 25, \mathrm{CZ} on output 8, output 26, \mathrm{CZ} on output 8, output 27, \mathrm{CZ} on output 8, output 32, \mathrm{CZ} on output 8, output 33, \mathrm{CZ} on output 8, output 36, \mathrm{CZ} on output 8, output 37, \mathrm{CZ} on output 8, output 39, \mathrm{CZ} on output 8, output 40, \mathrm{CZ} on output 8, output 41, \mathrm{CZ} on output 8, output 42, \mathrm{CZ} on output 8, output 45, \mathrm{CZ} on output 8, output 47, \mathrm{CZ} on output 8, output 49, \mathrm{CZ} on output 8, output 52, \mathrm{CZ} on output 8, output 54, \mathrm{CZ} on output 8, output 55, \mathrm{CZ} on output 8, output 56, \mathrm{CZ} on output 8, output 57, \mathrm{CZ} on output 8, output 61, \mathrm{CZ} on output 8, output 64, \mathrm{CZ} on output 8, output 69, \mathrm{CZ} on output 8, check 71, \mathrm{CZ} on output 8, check 74, \mathrm{CZ} on output 8, check 75, \mathrm{CZ} on output 8, check 80, \mathrm{CZ} on output 11, output 12, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 16, \mathrm{CZ} on output 11, output 17, \mathrm{CZ} on output 11, output 20, \mathrm{CZ} on output 11, output 23, \mathrm{CZ} on output 11, output 25, \mathrm{CZ} on output 11, output 26, \mathrm{CZ} on output 11, output 27, \mathrm{CZ} on output 11, output 32, \mathrm{CZ} on output 11, output 33, \mathrm{CZ} on output 11, output 36, \mathrm{CZ} on output 11, output 37, \mathrm{CZ} on output 11, output 39, \mathrm{CZ} on output 11, output 40, \mathrm{CZ} on output 11, output 41, \mathrm{CZ} on output 11, output 42, \mathrm{CZ} on output 11, output 45, \mathrm{CZ} on output 11, output 47, \mathrm{CZ} on output 11, output 49, \mathrm{CZ} on output 11, output 52, \mathrm{CZ} on output 11, output 54, \mathrm{CZ} on output 11, output 55, \mathrm{CZ} on output 11, output 56, \mathrm{CZ} on output 11, output 57, \mathrm{CZ} on output 11, output 61, \mathrm{CZ} on output 11, output 64, \mathrm{CZ} on output 11, output 69, \mathrm{CZ} on output 11, check 71, \mathrm{CZ} on output 11, check 74, \mathrm{CZ} on output 11, check 75, \mathrm{CZ} on output 11, check 80, \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 20, \mathrm{CZ} on output 12, output 23, \mathrm{CZ} on output 12, output 25, \mathrm{CZ} on output 12, output 26, \mathrm{CZ} on output 12, output 27, \mathrm{CZ} on output 12, output 32, \mathrm{CZ} on output 12, output 33, \mathrm{CZ} on output 12, output 36, \mathrm{CZ} on output 12, output 37, \mathrm{CZ} on output 12, output 39, \mathrm{CZ} on output 12, output 40, \mathrm{CZ} on output 12, output 41, \mathrm{CZ} on output 12, output 42, \mathrm{CZ} on output 12, output 45, \mathrm{CZ} on output 12, output 47, \mathrm{CZ} on output 12, output 49, \mathrm{CZ} on output 12, output 52, \mathrm{CZ} on output 12, output 54, \mathrm{CZ} on output 12, output 55, \mathrm{CZ} on output 12, output 56, \mathrm{CZ} on output 12, output 57, \mathrm{CZ} on output 12, output 61, \mathrm{CZ} on output 12, output 64, \mathrm{CZ} on output 12, output 69, \mathrm{CZ} on output 12, check 71, \mathrm{CZ} on output 12, check 74, \mathrm{CZ} on output 12, check 75, \mathrm{CZ} on output 12, check 80, \mathrm{CZ} on output 14, output 16, \mathrm{CZ} on output 14, output 17, \mathrm{CZ} on output 14, output 20, \mathrm{CZ} on output 14, output 23, \mathrm{CZ} on output 14, output 25, \mathrm{CZ} on output 14, output 26, \mathrm{CZ} on output 14, output 27, \mathrm{CZ} on output 14, output 32, \mathrm{CZ} on output 14, output 33, \mathrm{CZ} on output 14, output 36, \mathrm{CZ} on output 14, output 37, \mathrm{CZ} on output 14, output 39, \mathrm{CZ} on output 14, output 40, \mathrm{CZ} on output 14, output 41, \mathrm{CZ} on output 14, output 42, \mathrm{CZ} on output 14, output 45, \mathrm{CZ} on output 14, output 47, \mathrm{CZ} on output 14, output 49, \mathrm{CZ} on output 14, output 52, \mathrm{CZ} on output 14, output 54, \mathrm{CZ} on output 14, output 55, \mathrm{CZ} on output 14, output 56, \mathrm{CZ} on output 14, output 57, \mathrm{CZ} on output 14, output 61, \mathrm{CZ} on output 14, output 64, \mathrm{CZ} on output 14, output 69, \mathrm{CZ} on output 14, check 71, \mathrm{CZ} on output 14, check 74, \mathrm{CZ} on output 14, check 75, \mathrm{CZ} on output 14, check 80, \mathrm{CZ} on output 16, output 17, \mathrm{CZ} on output 16, output 20, \mathrm{CZ} on output 16, output 23, \mathrm{CZ} on output 16, output 25, \mathrm{CZ} on output 16, output 26, \mathrm{CZ} on output 16, output 27, \mathrm{CZ} on output 16, output 32, \mathrm{CZ} on output 16, output 33, \mathrm{CZ} on output 16, output 36, \mathrm{CZ} on output 16, output 37, \mathrm{CZ} on output 16, output 39, \mathrm{CZ} on output 16, output 40, \mathrm{CZ} on output 16, output 41, \mathrm{CZ} on output 16, output 42, \mathrm{CZ} on output 16, output 45, \mathrm{CZ} on output 16, output 47, \mathrm{CZ} on output 16, output 49, \mathrm{CZ} on output 16, output 52, \mathrm{CZ} on output 16, output 54, \mathrm{CZ} on output 16, output 55, \mathrm{CZ} on output 16, output 56, \mathrm{CZ} on output 16, output 57, \mathrm{CZ} on output 16, output 61, \mathrm{CZ} on output 16, output 64, \mathrm{CZ} on output 16, output 69, \mathrm{CZ} on output 16, check 71, \mathrm{CZ} on output 16, check 74, \mathrm{CZ} on output 16, check 75, \mathrm{CZ} on output 16, check 80, \mathrm{CZ} on output 17, output 20, \mathrm{CZ} on output 17, output 23, \mathrm{CZ} on output 17, output 25, \mathrm{CZ} on output 17, output 26, \mathrm{CZ} on output 17, output 27, \mathrm{CZ} on output 17, output 32, \mathrm{CZ} on output 17, output 33, \mathrm{CZ} on output 17, output 36, \mathrm{CZ} on output 17, output 37, \mathrm{CZ} on output 17, output 39, \mathrm{CZ} on output 17, output 40, \mathrm{CZ} on output 17, output 41, \mathrm{CZ} on output 17, output 42, \mathrm{CZ} on output 17, output 45, \mathrm{CZ} on output 17, output 47, \mathrm{CZ} on output 17, output 49, \mathrm{CZ} on output 17, output 52, \mathrm{CZ} on output 17, output 54, \mathrm{CZ} on output 17, output 55, \mathrm{CZ} on output 17, output 56, \mathrm{CZ} on output 17, output 57, \mathrm{CZ} on output 17, output 61, \mathrm{CZ} on output 17, output 64, \mathrm{CZ} on output 17, output 69, \mathrm{CZ} on output 17, check 71, \mathrm{CZ} on output 17, check 74, \mathrm{CZ} on output 17, check 75, \mathrm{CZ} on output 17, check 80, \mathrm{CZ} on output 20, output 23, \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 32, \mathrm{CZ} on output 20, output 33, \mathrm{CZ} on output 20, output 36, \mathrm{CZ} on output 20, output 37, \mathrm{CZ} on output 20, output 39, \mathrm{CZ} on output 20, output 40, \mathrm{CZ} on output 20, output 41, \mathrm{CZ} on output 20, output 42, \mathrm{CZ} on output 20, output 45, \mathrm{CZ} on output 20, output 47, \mathrm{CZ} on output 20, output 49, \mathrm{CZ} on output 20, output 52, \mathrm{CZ} on output 20, output 54, \mathrm{CZ} on output 20, output 55, \mathrm{CZ} on output 20, output 56, \mathrm{CZ} on output 20, output 57, \mathrm{CZ} on output 20, output 61, \mathrm{CZ} on output 20, output 64, \mathrm{CZ} on output 20, output 69, \mathrm{CZ} on output 20, check 71, \mathrm{CZ} on output 20, check 74, \mathrm{CZ} on output 20, check 75, \mathrm{CZ} on output 20, check 80, \mathrm{CZ} on output 23, output 25, \mathrm{CZ} on output 23, output 26, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 32, \mathrm{CZ} on output 23, output 33, \mathrm{CZ} on output 23, output 36, \mathrm{CZ} on output 23, output 37, \mathrm{CZ} on output 23, output 39, \mathrm{CZ} on output 23, output 40, \mathrm{CZ} on output 23, output 41, \mathrm{CZ} on output 23, output 42, \mathrm{CZ} on output 23, output 45, \mathrm{CZ} on output 23, output 47, \mathrm{CZ} on output 23, output 49, \mathrm{CZ} on output 23, output 52, \mathrm{CZ} on output 23, output 54, \mathrm{CZ} on output 23, output 55, \mathrm{CZ} on output 23, output 56, \mathrm{CZ} on output 23, output 57, \mathrm{CZ} on output 23, output 61, \mathrm{CZ} on output 23, output 64, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, check 71, \mathrm{CZ} on output 23, check 74, \mathrm{CZ} on output 23, check 75, \mathrm{CZ} on output 23, check 80, \mathrm{CZ} on output 25, output 26, \mathrm{CZ} on output 25, output 27, \mathrm{CZ} on output 25, output 32, \mathrm{CZ} on output 25, output 33, \mathrm{CZ} on output 25, output 36, \mathrm{CZ} on output 25, output 37, \mathrm{CZ} on output 25, output 39, \mathrm{CZ} on output 25, output 40, \mathrm{CZ} on output 25, output 41, \mathrm{CZ} on output 25, output 42, \mathrm{CZ} on output 25, output 45, \mathrm{CZ} on output 25, output 47, \mathrm{CZ} on output 25, output 49, \mathrm{CZ} on output 25, output 52, \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 57, \mathrm{CZ} on output 25, output 61, \mathrm{CZ} on output 25, output 64, \mathrm{CZ} on output 25, output 69, \mathrm{CZ} on output 25, check 71, \mathrm{CZ} on output 25, check 74, \mathrm{CZ} on output 25, check 75, \mathrm{CZ} on output 25, check 80, \mathrm{CZ} on output 26, output 27, \mathrm{CZ} on output 26, output 32, \mathrm{CZ} on output 26, output 33, \mathrm{CZ} on output 26, output 36, \mathrm{CZ} on output 26, output 37, \mathrm{CZ} on output 26, output 39, \mathrm{CZ} on output 26, output 40, \mathrm{CZ} on output 26, output 41, \mathrm{CZ} on output 26, output 42, \mathrm{CZ} on output 26, output 45, \mathrm{CZ} on output 26, output 47, \mathrm{CZ} on output 26, output 49, \mathrm{CZ} on output 26, output 52, \mathrm{CZ} on output 26, output 54, \mathrm{CZ} on output 26, output 55, \mathrm{CZ} on output 26, output 56, \mathrm{CZ} on output 26, output 57, \mathrm{CZ} on output 26, output 61, \mathrm{CZ} on output 26, output 64, \mathrm{CZ} on output 26, output 69, \mathrm{CZ} on output 26, check 71, \mathrm{CZ} on output 26, check 74, \mathrm{CZ} on output 26, check 75, \mathrm{CZ} on output 26, check 80, \mathrm{CZ} on output 27, output 32, \mathrm{CZ} on output 27, output 33, \mathrm{CZ} on output 27, output 36, \mathrm{CZ} on output 27, output 37, \mathrm{CZ} on output 27, output 39, \mathrm{CZ} on output 27, output 40, \mathrm{CZ} on output 27, output 41, \mathrm{CZ} on output 27, output 42, \mathrm{CZ} on output 27, output 45, \mathrm{CZ} on output 27, output 47, \mathrm{CZ} on output 27, output 49, \mathrm{CZ} on output 27, output 52, \mathrm{CZ} on output 27, output 54, \mathrm{CZ} on output 27, output 55, \mathrm{CZ} on output 27, output 56, \mathrm{CZ} on output 27, output 57, \mathrm{CZ} on output 27, output 61, \mathrm{CZ} on output 27, output 64, \mathrm{CZ} on output 27, output 69, \mathrm{CZ} on output 27, check 71, \mathrm{CZ} on output 27, check 74, \mathrm{CZ} on output 27, check 75, \mathrm{CZ} on output 27, check 80, \mathrm{CZ} on output 32, output 33, \mathrm{CZ} on output 32, output 36, \mathrm{CZ} on output 32, output 37, \mathrm{CZ} on output 32, output 39, \mathrm{CZ} on output 32, output 40, \mathrm{CZ} on output 32, output 41, \mathrm{CZ} on output 32, output 42, \mathrm{CZ} on output 32, output 45, \mathrm{CZ} on output 32, output 47, \mathrm{CZ} on output 32, output 49, \mathrm{CZ} on output 32, output 52, \mathrm{CZ} on output 32, output 54, \mathrm{CZ} on output 32, output 55, \mathrm{CZ} on output 32, output 56, \mathrm{CZ} on output 32, output 57, \mathrm{CZ} on output 32, output 61, \mathrm{CZ} on output 32, output 64, \mathrm{CZ} on output 32, output 69, \mathrm{CZ} on output 32, check 71, \mathrm{CZ} on output 32, check 74, \mathrm{CZ} on output 32, check 75, \mathrm{CZ} on output 32, check 80, \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 61, \mathrm{CZ} on output 33, output 64, \mathrm{CZ} on output 33, output 69, \mathrm{CZ} on output 33, check 71, \mathrm{CZ} on output 33, check 74, \mathrm{CZ} on output 33, check 75, \mathrm{CZ} on output 33, check 80, \mathrm{CZ} on output 36, output 37, \mathrm{CZ} on output 36, output 39, \mathrm{CZ} on output 36, output 40, \mathrm{CZ} on output 36, output 41, \mathrm{CZ} on output 36, output 42, \mathrm{CZ} on output 36, output 45, \mathrm{CZ} on output 36, output 47, \mathrm{CZ} on output 36, output 49, \mathrm{CZ} on output 36, output 52, \mathrm{CZ} on output 36, output 54, \mathrm{CZ} on output 36, output 55, \mathrm{CZ} on output 36, output 56, \mathrm{CZ} on output 36, output 57, \mathrm{CZ} on output 36, output 61, \mathrm{CZ} on output 36, output 64, \mathrm{CZ} on output 36, output 69, \mathrm{CZ} on output 36, check 71, \mathrm{CZ} on output 36, check 74, \mathrm{CZ} on output 36, check 75, \mathrm{CZ} on output 36, check 80, \mathrm{CZ} on output 37, output 39, \mathrm{CZ} on output 37, output 40, \mathrm{CZ} on output 37, output 41, \mathrm{CZ} on output 37, output 42, \mathrm{CZ} on output 37, output 45, \mathrm{CZ} on output 37, output 47, \mathrm{CZ} on output 37, output 49, \mathrm{CZ} on output 37, output 52, \mathrm{CZ} on output 37, output 54, \mathrm{CZ} on output 37, output 55, \mathrm{CZ} on output 37, output 56, \mathrm{CZ} on output 37, output 57, \mathrm{CZ} on output 37, output 61, \mathrm{CZ} on output 37, output 64, \mathrm{CZ} on output 37, output 69, \mathrm{CZ} on output 37, check 71, \mathrm{CZ} on output 37, check 74, \mathrm{CZ} on output 37, check 75, \mathrm{CZ} on output 37, check 80, \mathrm{CZ} on output 39, output 40, \mathrm{CZ} on output 39, output 41, \mathrm{CZ} on output 39, output 42, \mathrm{CZ} on output 39, output 45, \mathrm{CZ} on output 39, output 47, \mathrm{CZ} on output 39, output 49, \mathrm{CZ} on output 39, output 52, \mathrm{CZ} on output 39, output 54, \mathrm{CZ} on output 39, output 55, \mathrm{CZ} on output 39, output 56, \mathrm{CZ} on output 39, output 57, \mathrm{CZ} on output 39, output 61, \mathrm{CZ} on output 39, output 64, \mathrm{CZ} on output 39, output 69, \mathrm{CZ} on output 39, check 71, \mathrm{CZ} on output 39, check 74, \mathrm{CZ} on output 39, check 75, \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 45, \mathrm{CZ} on output 40, output 47, \mathrm{CZ} on output 40, output 49, \mathrm{CZ} on output 40, output 52, \mathrm{CZ} on output 40, output 54, \mathrm{CZ} on output 40, output 55, \mathrm{CZ} on output 40, output 56, \mathrm{CZ} on output 40, output 57, \mathrm{CZ} on output 40, output 61, \mathrm{CZ} on output 40, output 64, \mathrm{CZ} on output 40, output 69, \mathrm{CZ} on output 40, check 71, \mathrm{CZ} on output 40, check 74, \mathrm{CZ} on output 40, check 75, \mathrm{CZ} on output 40, check 80, \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 61, \mathrm{CZ} on output 41, output 64, \mathrm{CZ} on output 41, output 69, \mathrm{CZ} on output 41, check 71, \mathrm{CZ} on output 41, check 74, \mathrm{CZ} on output 41, check 75, \mathrm{CZ} on output 41, check 80, \mathrm{CZ} on output 42, output 45, \mathrm{CZ} on output 42, output 47, \mathrm{CZ} on output 42, output 49, \mathrm{CZ} on output 42, output 52, \mathrm{CZ} on output 42, output 54, \mathrm{CZ} on output 42, output 55, \mathrm{CZ} on output 42, output 56, \mathrm{CZ} on output 42, output 57, \mathrm{CZ} on output 42, output 61, \mathrm{CZ} on output 42, output 64, \mathrm{CZ} on output 42, output 69, \mathrm{CZ} on output 42, check 71, \mathrm{CZ} on output 42, check 74, \mathrm{CZ} on output 42, check 75, \mathrm{CZ} on output 42, check 80, \mathrm{CZ} on output 45, output 47, \mathrm{CZ} on output 45, output 49, \mathrm{CZ} on output 45, output 52, \mathrm{CZ} on output 45, output 54, \mathrm{CZ} on output 45, output 55, \mathrm{CZ} on output 45, output 56, \mathrm{CZ} on output 45, output 57, \mathrm{CZ} on output 45, output 61, \mathrm{CZ} on output 45, output 64, \mathrm{CZ} on output 45, output 69, \mathrm{CZ} on output 45, check 71, \mathrm{CZ} on output 45, check 74, \mathrm{CZ} on output 45, check 75, \mathrm{CZ} on output 45, check 80, \mathrm{CZ} on output 47, output 49, \mathrm{CZ} on output 47, output 52, \mathrm{CZ} on output 47, output 54, \mathrm{CZ} on output 47, output 55, \mathrm{CZ} on output 47, output 56, \mathrm{CZ} on output 47, output 57, \mathrm{CZ} on output 47, output 61, \mathrm{CZ} on output 47, output 64, \mathrm{CZ} on output 47, output 69, \mathrm{CZ} on output 47, check 71, \mathrm{CZ} on output 47, check 74, \mathrm{CZ} on output 47, check 75, \mathrm{CZ} on output 47, check 80, \mathrm{CZ} on output 49, output 52, \mathrm{CZ} on output 49, output 54, \mathrm{CZ} on output 49, output 55, \mathrm{CZ} on output 49, output 56, \mathrm{CZ} on output 49, output 57, \mathrm{CZ} on output 49, output 61, \mathrm{CZ} on output 49, output 64, \mathrm{CZ} on output 49, output 69, \mathrm{CZ} on output 49, check 71, \mathrm{CZ} on output 49, check 74, \mathrm{CZ} on output 49, check 75, \mathrm{CZ} on output 49, check 80, \mathrm{CZ} on output 52, output 54, \mathrm{CZ} on output 52, output 55, \mathrm{CZ} on output 52, output 56, \mathrm{CZ} on output 52, output 57, \mathrm{CZ} on output 52, output 61, \mathrm{CZ} on output 52, output 64, \mathrm{CZ} on output 52, output 69, \mathrm{CZ} on output 52, check 71, \mathrm{CZ} on output 52, check 74, \mathrm{CZ} on output 52, check 75, \mathrm{CZ} on output 52, check 80, \mathrm{CZ} on output 54, output 55, \mathrm{CZ} on output 54, output 56, \mathrm{CZ} on output 54, output 57, \mathrm{CZ} on output 54, output 61, \mathrm{CZ} on output 54, output 64, \mathrm{CZ} on output 54, output 69, \mathrm{CZ} on output 54, check 71, \mathrm{CZ} on output 54, check 74, \mathrm{CZ} on output 54, check 75, \mathrm{CZ} on output 54, check 80, \mathrm{CZ} on output 55, output 56, \mathrm{CZ} on output 55, output 57, \mathrm{CZ} on output 55, output 61, \mathrm{CZ} on output 55, output 64, \mathrm{CZ} on output 55, output 69, \mathrm{CZ} on output 55, check 71, \mathrm{CZ} on output 55, check 74, \mathrm{CZ} on output 55, check 75, \mathrm{CZ} on output 55, check 80, \mathrm{CZ} on output 56, output 57, \mathrm{CZ} on output 56, output 61, \mathrm{CZ} on output 56, output 64, \mathrm{CZ} on output 56, output 69, \mathrm{CZ} on output 56, check 71, \mathrm{CZ} on output 56, check 74, \mathrm{CZ} on output 56, check 75, \mathrm{CZ} on output 56, check 80, \mathrm{CZ} on output 57, output 61, \mathrm{CZ} on output 57, output 64, \mathrm{CZ} on output 57, output 69, \mathrm{CZ} on output 57, check 71, \mathrm{CZ} on output 57, check 74, \mathrm{CZ} on output 57, check 75, \mathrm{CZ} on output 57, check 80, \mathrm{CZ} on output 61, output 64, \mathrm{CZ} on output 61, output 69, \mathrm{CZ} on output 61, check 71, \mathrm{CZ} on output 61, check 74, \mathrm{CZ} on output 61, check 75, \mathrm{CZ} on output 61, check 80, \mathrm{CZ} on output 64, output 69, \mathrm{CZ} on output 64, check 71, \mathrm{CZ} on output 64, check 74, \mathrm{CZ} on output 64, check 75, \mathrm{CZ} on output 64, check 80, \mathrm{CZ} on output 69, check 71, \mathrm{CZ} on output 69, check 74, \mathrm{CZ} on output 69, check 75, \mathrm{CZ} on output 69, check 80, \mathrm{CZ} on check 71, check 74, \mathrm{CZ} on check 71, check 75, \mathrm{CZ} on check 71, check 80, \mathrm{CZ} on check 74, check 75, \mathrm{CZ} on check 74, check 80, \mathrm{CZ} on check 75, check 80
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 8, 16, 27, 36, 47, 59, 62, 68, 80, 81, 82, 86, 88, 90, 91, 93, 94, 95, 99, 101, 103, 104, 105, 108 and 85 more (listed below); \mathrm{T}^5 on rotations 0, 4, 5, 10, 13, 15, 20, 22, 25, 32, 33, 38, 39, 44, 49, 54, 55, 56, 64, 70, 72, 79, 172; \mathrm{T}^\dagger on rotations 1, 3, 19, 26, 28, 40, 50, 61, 63, 130, 183, 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 109 rotations at T³
8, 16, 27, 36, 47, 59, 62, 68, 80, 81, 82, 86, 88, 90, 91, 93, 94, 95, 99, 101, 103, 104, 105, 108, 109, 113, 114, 116, 117, 118, 119, 121, 123, 126, 138, 139, 143, 144, 145, 150, 151, 158, 160, 162, 164, 165, 167, 168, 169, 170, 171, 176, 178, 181, 187, 189, 190, 191, 192, 195, 196, 199, 200, 201, 204, 205, 206, 208, 209, 213, 217, 219, 223, 225, 226, 227, 228, 233, 237, 238, 239, 245, 249, 251, 253, 259, 261, 265, 267, 269, 276, 278, 280, 281, 283, 286, 287, 288, 289, 290, 291, 295, 299, 300, 303, 304, 305, 308, 310
Rotations are numbered by matrix column, from 0. The correction comes from the columns by the weight expansion of Bravyi and Haah (2012). verify_catalog.py re-derives it, checks the corrected circuit's phase input by input against the gate, and on small circuits simulates it gate by gate.
Convert the output with CNOT and S
A CNOT circuit on the outputs, followed by S, Z and CZ gates, turns this factory's gate into other gates that prepare the same magic state. Type a target gate to check whether it is reachable. If it is, you get the circuit, checked on every basis state.
Or list every gate it reaches. The list is built in your browser and saved as a text file, one gate per line.
Python code that writes the same list
import json, urllib.request
NAMES = {1: "T", 2: "CS", 3: "CCZ"}
def equivalent_gates(k, terms, limit=1_000_000):
"""Every gate a CNOT circuit and S, Z, CZ gates reach from this one.
A gate is its set of terms mod Clifford: {a} is T, {a,b} is CS and
{a,b,c} is CCZ on those outputs. CNOT c->t sends x_t to
x_c + x_t - 2 x_c x_t, so a term on t but not c adds the term with t
replaced by c, and, below CCZ, the term with c added.
"""
start = frozenset(frozenset(m) for m in terms)
seen, queue = {start}, [start]
for gate in queue:
for c in range(k):
for t in range(k):
if c == t:
continue
new = set(gate)
for m in gate:
if t in m and c not in m:
new ^= {(m - {t}) | {c}}
if len(m) < 3:
new ^= {m | {c}}
new = frozenset(new)
if new not in seen:
seen.add(new)
queue.append(new)
if len(seen) > limit:
raise RuntimeError(f"more than {limit} equivalent gates")
return seen
def name(gate, k):
sep = "," if k > 10 else ""
terms = sorted((sorted(m) for m in gate), key=lambda m: (len(m), m))
return "·".join(NAMES[len(m)] + sep.join(map(str, m)) for m in terms) or "I"
url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/311.71.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-311.71.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 1,056 faults of weight 3 are undetectable and damaging, so A_{3}=1{,}056. 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 [0,16,200].
A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.
Original source
S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535
Provenance
a paired-column contraction of an existing triorthogonal code, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows
Found by: AI search (gamma frontier): contraction of an existing code
Discovery: AI search
1 recorded source
[
{
"regime": "AI search (gamma frontier): contraction of an existing code",
"file": "gamma_frontier_release/protocols/paired_column_contraction_311_71_3_229dd70f662d.json",
"label": "paired_column_contraction_311_71_3_229dd70f662d",
"N": 83,
"d": 3,
"d_is_exact": true,
"origin": "Existing triorthogonal code with physical paired-column contraction",
"provenance": "gamma frontier release record paired_column_contraction_311_71_3_229dd70f662d (source catalogue id paired_column_contraction_311_71_3_229dd70f662d); construction: Existing triorthogonal code with physical paired-column contraction; matrix 229dd70f662d2e66...; the release states d=3 (exact), gamma=1.3445262267443594 (exact)",
"notes": "matrix gamma_frontier_release/matrices/229dd70f662d2e66d406e08dcb3ce01ce1f10e899b7b6704702ad42d8360e123.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/311.71.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]
facts, problems = VC.derive(columns, k, N) # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N) # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
problems or "verified")
Raw record
Show the JSON this page is built from
Source: master_catalog.json, factories[965].