The circuit
The 130\times512 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 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 |
|---|---|
| out 0 (64) | 1111111111111111111111111111111111111111111111111111111111111111································································································································································································································································································································································································································································ |
| out 1 (64) | 11111111111111111111111111111111································11111111111111111111111111111111································································································································································································································································································································································································································ |
| out 2 (64) | 1111111111111111················1111111111111111················1111111111111111················1111111111111111················································································································································································································································································································································································································ |
| out 3 (64) | 11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········································································································································································································································································································································································································ |
| out 4 (64) | 1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111···································································································································································································································································································································································································· |
| out 5 (64) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·································································································································································································································································································································································································· |
| out 6 (64) | 1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1································································································································································································································································································································································································· |
| out 7 (64) | 11111111111111111111111111111111·······························································································11111111111111111111111111111111································································································································································································································································································································································· |
| out 8 (64) | 1111111111111111················1111111111111111···············································································1111111111111111················1111111111111111················································································································································································································································································································································· |
| out 9 (64) | 11111111········11111111········11111111········11111111·······································································11111111········11111111········11111111········11111111········································································································································································································································································································································· |
| out 10 (64) | 1111····1111····1111····1111····1111····1111····1111····1111···································································1111····1111····1111····1111····1111····1111····1111····1111····································································································································································································································································································································· |
| out 11 (64) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·································································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··································································································································································································································································································································· |
| out 12 (64) | 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································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·································································································································································································································································································································· |
| out 13 (64) | 1111111111111111················································1111111111111111···············································1111111111111111···············································1111111111111111·················································································································································································································································································································· |
| out 14 (64) | 11111111········11111111········································11111111········11111111·······································11111111········11111111·······································11111111········11111111·········································································································································································································································································································· |
| out 15 (64) | 1111····1111····1111····1111····································1111····1111····1111····1111···································1111····1111····1111····1111···································1111····1111····1111····1111······································································································································································································································································································ |
| out 16 (64) | 11··11··11··11··11··11··11··11··································11··11··11··11··11··11··11··11·································11··11··11··11··11··11··11··11·································11··11··11··11··11··11··11··11···································································································································································································································································································· |
| out 17 (64) | 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································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1··································································································································································································································································································· |
| out 18 (64) | 11111111························11111111························11111111························11111111·······················11111111························11111111·······················11111111·······················11111111··························································································································································································································································································· |
| out 19 (64) | 1111····1111····················1111····1111····················1111····1111····················1111····1111···················1111····1111····················1111····1111···················1111····1111···················1111····1111······················································································································································································································································································· |
| out 20 (64) | 11··11··11··11··················11··11··11··11··················11··11··11··11··················11··11··11··11·················11··11··11··11··················11··11··11··11·················11··11··11··11·················11··11··11··11····················································································································································································································································································· |
| out 21 (64) | 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·················1·1·1·1·1·1·1·1················1·1·1·1·1·1·1·1················1·1·1·1·1·1·1·1···················································································································································································································································································· |
| out 22 (64) | 1111············1111············1111············1111············1111············1111············1111············1111···········1111············1111············1111············1111···········1111············1111···········1111···········1111················································································································································································································································································ |
| out 23 (64) | 11··11··········11··11··········11··11··········11··11··········11··11··········11··11··········11··11··········11··11·········11··11··········11··11··········11··11··········11··11·········11··11··········11··11·········11··11·········11··11·············································································································································································································································································· |
| out 24 (64) | 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·········1·1·1·1········1·1·1·1·········1·1·1·1········1·1·1·1········1·1·1·1············································································································································································································································································· |
| out 25 (64) | 11······11······11······11······11······11······11······11······11······11······11······11······11······11······11······11·····11······11······11······11······11······11······11······11·····11······11······11······11·····11······11·····11·····11··········································································································································································································································································· |
| out 26 (64) | 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·····1·1····1·1·····1·1·····1·1·····1·1····1·1·····1·1····1·1····1·1·········································································································································································································································································· |
| out 27 (64) | 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···1··1···1···1···1···1···1···1···1··1···1···1···1··1···1··1··1········································································································································································································································································· |
| out 28 (64) | 11111111111111111111111111111111·······················································································································································································································11111111111111111111111111111111········································································································································································································································· |
| out 29 (64) | 1111111111111111················1111111111111111·······································································································································································································1111111111111111················1111111111111111························································································································································································································· |
| out 30 (64) | 11111111········11111111········11111111········11111111·······························································································································································································11111111········11111111········11111111········11111111················································································································································································································· |
| out 31 (64) | 1111····1111····1111····1111····1111····1111····1111····1111···························································································································································································1111····1111····1111····1111····1111····1111····1111····1111············································································································································································································· |
| out 32 (64) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·························································································································································································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··········································································································································································································· |
| out 33 (64) | 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························································································································································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·········································································································································································································· |
| out 34 (64) | 1111111111111111················································1111111111111111·······································································································································································1111111111111111···············································1111111111111111·························································································································································································· |
| out 35 (64) | 11111111········11111111········································11111111········11111111·······························································································································································11111111········11111111·······································11111111········11111111·················································································································································································· |
| out 36 (64) | 1111····1111····1111····1111····································1111····1111····1111····1111···························································································································································1111····1111····1111····1111···································1111····1111····1111····1111·············································································································································································· |
| out 37 (64) | 11··11··11··11··11··11··11··11··································11··11··11··11··11··11··11··11·························································································································································11··11··11··11··11··11··11··11·································11··11··11··11··11··11··11··11············································································································································································ |
| out 38 (64) | 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························································································································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1··········································································································································································· |
| out 39 (64) | 11111111························11111111························11111111························11111111···············································································································································11111111························11111111·······················11111111·······················11111111··································································································································································· |
| out 40 (64) | 1111····1111····················1111····1111····················1111····1111····················1111····1111···········································································································································1111····1111····················1111····1111···················1111····1111···················1111····1111······························································································································································· |
| out 41 (64) | 11··11··11··11··················11··11··11··11··················11··11··11··11··················11··11··11··11·········································································································································11··11··11··11··················11··11··11··11·················11··11··11··11·················11··11··11··11····························································································································································· |
| out 42 (64) | 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·················1·1·1·1·1·1·1·1················1·1·1·1·1·1·1·1················1·1·1·1·1·1·1·1···························································································································································· |
| out 43 (64) | 1111············1111············1111············1111············1111············1111············1111············1111···································································································································1111············1111············1111············1111···········1111············1111···········1111···········1111························································································································································ |
| out 44 (64) | 11··11··········11··11··········11··11··········11··11··········11··11··········11··11··········11··11··········11··11·································································································································11··11··········11··11··········11··11··········11··11·········11··11··········11··11·········11··11·········11··11······················································································································································ |
| out 45 (64) | 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·········1·1·1·1········1·1·1·1·········1·1·1·1········1·1·1·1········1·1·1·1····················································································································································· |
| out 46 (64) | 11······11······11······11······11······11······11······11······11······11······11······11······11······11······11······11·····························································································································11······11······11······11······11······11······11······11·····11······11······11······11·····11······11·····11·····11··················································································································································· |
| out 47 (64) | 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·····1·1····1·1·····1·1·····1·1·····1·1····1·1·····1·1····1·1····1·1·················································································································································· |
| out 48 (64) | 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···1··1···1···1···1···1···1···1···1··1···1···1···1··1···1··1··1················································································································································· |
| out 49 (64) | 1111111111111111···············································································································1111111111111111········································································································1111111111111111········································································································1111111111111111································································································································· |
| out 50 (64) | 11111111········11111111·······································································································11111111········11111111································································································11111111········11111111································································································11111111········11111111························································································································· |
| out 51 (64) | 1111····1111····1111····1111···································································································1111····1111····1111····1111····························································································1111····1111····1111····1111····························································································1111····1111····1111····1111····················································································································· |
| out 52 (64) | 11··11··11··11··11··11··11··11·································································································11··11··11··11··11··11··11··11··························································································11··11··11··11··11··11··11··11··························································································11··11··11··11··11··11··11··11··················································································································· |
| out 53 (64) | 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·························································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·························································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·················································································································· |
| out 54 (64) | 11111111························11111111·······················································································11111111························11111111················································································11111111························11111111················································································11111111·······················11111111·········································································································· |
| out 55 (64) | 1111····1111····················1111····1111···················································································1111····1111····················1111····1111············································································1111····1111····················1111····1111············································································1111····1111···················1111····1111······································································································ |
| out 56 (64) | 11··11··11··11··················11··11··11··11·················································································11··11··11··11··················11··11··11··11··········································································11··11··11··11··················11··11··11··11··········································································11··11··11··11·················11··11··11··11···································································································· |
| out 57 (64) | 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·················1·1·1·1·1·1·1·1·········································································1·1·1·1·1·1·1·1················1·1·1·1·1·1·1·1··································································································· |
| out 58 (64) | 1111············1111············1111············1111···········································································1111············1111············1111············1111····································································1111············1111············1111············1111····································································1111············1111···········1111···········1111······························································································· |
| out 59 (64) | 11··11··········11··11··········11··11··········11··11·········································································11··11··········11··11··········11··11··········11··11··································································11··11··········11··11··········11··11··········11··11··································································11··11··········11··11·········11··11·········11··11····························································································· |
| out 60 (64) | 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·········1·1·1·1·································································1·1·1·1·········1·1·1·1········1·1·1·1········1·1·1·1···························································································· |
| out 61 (64) | 11······11······11······11······11······11······11······11·····································································11······11······11······11······11······11······11······11······························································11······11······11······11······11······11······11······11······························································11······11······11······11·····11······11·····11·····11·························································································· |
| out 62 (64) | 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·····1·1·····························································1·1·····1·1·····1·1·····1·1····1·1·····1·1····1·1····1·1························································································· |
| out 63 (64) | 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···1···························································1···1···1···1···1···1···1···1··1···1···1···1··1···1··1··1························································································ |
| out 64 (64) | 11111111························································11111111·······················································11111111·······················································11111111·················································11111111·······················································11111111·················································11111111·················································11111111················································································ |
| out 65 (64) | 1111····1111····················································1111····1111···················································1111····1111···················································1111····1111·············································1111····1111···················································1111····1111·············································1111····1111·············································1111····1111············································································ |
| out 66 (64) | 11··11··11··11··················································11··11··11··11·················································11··11··11··11·················································11··11··11··11···········································11··11··11··11·················································11··11··11··11···········································11··11··11··11···········································11··11··11··11·········································································· |
| out 67 (64) | 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················································1·1·1·1·1·1·1·1··········································1·1·1·1·1·1·1·1··········································1·1·1·1·1·1·1·1········································································· |
| out 68 (64) | 1111············1111············································1111············1111···········································1111············1111···········································1111············1111·····································1111············1111···········································1111············1111·····································1111············1111·····································1111···········1111····································································· |
| out 69 (64) | 11··11··········11··11··········································11··11··········11··11·········································11··11··········11··11·········································11··11··········11··11···································11··11··········11··11·········································11··11··········11··11···································11··11··········11··11···································11··11·········11··11··································································· |
| out 70 (64) | 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·········1·1·1·1··································1·1·1·1·········1·1·1·1··································1·1·1·1········1·1·1·1·································································· |
| out 71 (64) | 11······11······11······11······································11······11······11······11·····································11······11······11······11·····································11······11······11······11·······························11······11······11······11·····································11······11······11······11·······························11······11······11······11·······························11······11·····11·····11································································ |
| out 72 (64) | 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·····1·1······························1·1·····1·1·····1·1·····1·1······························1·1·····1·1····1·1····1·1······························································· |
| out 73 (64) | 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···1····························1···1···1···1···1···1···1···1····························1···1···1···1··1···1··1··1······························································ |
| out 74 (64) | 1111····························1111····························1111····························1111···························1111····························1111···························1111···························1111······················1111····························1111···························1111···························1111······················1111···························1111······················1111······················1111·························································· |
| out 75 (64) | 11··11··························11··11··························11··11··························11··11·························11··11··························11··11·························11··11·························11··11····················11··11··························11··11·························11··11·························11··11····················11··11·························11··11····················11··11····················11··11························································ |
| out 76 (64) | 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························1·1·1·1···················1·1·1·1························1·1·1·1···················1·1·1·1···················1·1·1·1······················································· |
| out 77 (64) | 11······11······················11······11······················11······11······················11······11·····················11······11······················11······11·····················11······11·····················11······11················11······11······················11······11·····················11······11·····················11······11················11······11·····················11······11················11······11················11·····11····················································· |
| out 78 (64) | 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·····1·1···············1·1·····1·1····················1·1·····1·1···············1·1·····1·1···············1·1····1·1···················································· |
| out 79 (64) | 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···1·············1···1···1···1··················1···1···1···1·············1···1···1···1·············1···1··1··1··················································· |
| out 80 (64) | 11··············11··············11··············11··············11··············11··············11··············11·············11··············11··············11··············11·············11··············11·············11·············11·········11··············11··············11··············11·············11··············11·············11·············11·········11··············11·············11·············11·········11·············11·········11·········11················································· |
| out 81 (64) | 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············1·1········1·1·············1·1············1·1············1·1········1·1············1·1········1·1········1·1················································ |
| out 82 (64) | 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···1······1···1···········1···1··········1···1··········1···1······1···1··········1···1······1···1······1··1··············································· |
| out 83 (64) | 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······1···1·······1·······1·······1······1·······1······1······1···1·······1······1······1···1······1···1···1·············································· |
| check 84 (512) | 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 |
| check 85 (256) | 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111····························································································································································································································111111111···································· |
| check 86 (256) | 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·····································································································1·······11111111···························· |
| check 87 (256) | 1111111111111111111111111111111111111111111111111111111111111111·······························································111111111111111111111111111111111111111111111111111111111111111·························································111111111111111111111111111111111111111111111111111111111111111·························································111111111111111111111111111111111111111111111111111111111·············································1·······1······1111111····················· |
| check 88 (256) | 11111111111111111111111111111111································11111111111111111111111111111111·······························11111111111111111111111111111111·······························1111111111111111111111111111111··························11111111111111111111111111111111·······························1111111111111111111111111111111··························1111111111111111111111111111111··························11111111111111111111111111····················1·······1······1·····111111··············· |
| check 89 (256) | 1111111111111111················1111111111111111················1111111111111111················1111111111111111···············1111111111111111················1111111111111111···············1111111111111111···············111111111111111···········1111111111111111················1111111111111111···············1111111111111111···············111111111111111···········1111111111111111···············111111111111111···········111111111111111···········11111111111··········1·······1······1·····1····11111·········· |
| check 90 (256) | 11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111·······11111111········11111111········11111111········11111111·······11111111········11111111·······11111111·······1111111····11111111········11111111········11111111········11111111·······11111111········11111111·······11111111·······1111111····11111111········11111111·······11111111·······1111111····11111111·······1111111····1111111····1111·······1·······1······1·····1····1···1111······ |
| check 91 (256) | 1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111···1111····1111····1111····1111····1111····1111····1111····1111···1111····1111····1111····1111···1111····1111···1111···111·1111····1111····1111····1111····1111····1111····1111····1111···1111····1111····1111····1111···1111····1111···1111···111·1111····1111····1111····1111···1111····1111···1111···111·1111····1111···1111···111·1111···111·111·1·······1·······1······1·····1····1···1··111··· |
| check 92 (256) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·11··11··11··11··11··11··11··11·11··11··11··11·11··11·11·111··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·11··11··11··11··11··11··11··11·11··11··11··11·11··11·11·111··11··11··11··11··11··11··11·11··11··11··11·11··11·11·111··11··11··11·11··11·11·111··11·11·111·11········1·······1······1·····1····1···1··1·11· |
| check 93 (256) | 1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·11·1·1·11·111·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·11·1·1·11·111·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·11·1·1·11·111·1·1·1·1·1·1·11·1·1·11·111·1·1·11·111·111·········1·······1······1·····1····1···1··1·11 |
| check 94 (128) | 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·····················································································································································································································································································································································1··········································· |
| check 95 (128) | 1111111111111111111111111111111111111111111111111111111111111111·······························································111111111111111111111111111111111111111111111111111111111111111·······················································································································································································································································································1·········································· |
| check 96 (128) | 11111111111111111111111111111111································11111111111111111111111111111111·······························11111111111111111111111111111111·······························1111111111111111111111111111111·························································································································································································································································1········································· |
| check 97 (128) | 1111111111111111················1111111111111111················1111111111111111················1111111111111111···············1111111111111111················1111111111111111···············1111111111111111···············111111111111111···········································································································································································································································1········································ |
| check 98 (128) | 11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111·······11111111········11111111········11111111········11111111·······11111111········11111111·······11111111·······1111111·····································································································································································································································1······································· |
| check 99 (128) | 1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111···1111····1111····1111····1111····1111····1111····1111····1111···1111····1111····1111····1111···1111····1111···1111···111···································································································································································································································1······································ |
| check 100 (128) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·11··11··11··11··11··11··11··11·11··11··11··11·11··11·11·1···································································································································································································································1····································· |
| check 101 (128) | 1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·11·1·1·11·11····································································································································································································································1···································· |
| check 102 (128) | 1111111111111111111111111111111111111111111111111111111111111111·······················································································································································································111111111111111111111111111111111111111111111111111111111111111·······································································································································································1·································· |
| check 103 (128) | 11111111111111111111111111111111································11111111111111111111111111111111·······················································································································································11111111111111111111111111111111·······························1111111111111111111111111111111·········································································································································1································· |
| check 104 (128) | 1111111111111111················1111111111111111················1111111111111111················1111111111111111·······································································································································1111111111111111················1111111111111111···············1111111111111111···············111111111111111···························································································································1································ |
| check 105 (128) | 11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111·······························································································································11111111········11111111········11111111········11111111·······11111111········11111111·······11111111·······1111111·····················································································································1······························· |
| check 106 (128) | 1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111···························································································································1111····1111····1111····1111····1111····1111····1111····1111···1111····1111····1111····1111···1111····1111···1111···111···················································································································1······························ |
| check 107 (128) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·························································································································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·11··11··11··11··11··11··11··11·11··11··11··11·11··11·11·1···················································································································1····························· |
| check 108 (128) | 1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1························································································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·11·1·1·11·11····················································································································1···························· |
| check 109 (128) | 11111111111111111111111111111111·······························································································11111111111111111111111111111111························································································11111111111111111111111111111111························································································1111111111111111111111111111111·······················································································1·························· |
| check 110 (128) | 1111111111111111················1111111111111111···············································································1111111111111111················1111111111111111········································································1111111111111111················1111111111111111········································································1111111111111111···············111111111111111·········································································1························· |
| check 111 (128) | 11111111········11111111········11111111········11111111·······································································11111111········11111111········11111111········11111111································································11111111········11111111········11111111········11111111································································11111111········11111111·······11111111·······1111111···································································1························ |
| check 112 (128) | 1111····1111····1111····1111····1111····1111····1111····1111···································································1111····1111····1111····1111····1111····1111····1111····1111····························································1111····1111····1111····1111····1111····1111····1111····1111····························································1111····1111····1111····1111···1111····1111···1111···111·································································1······················· |
| check 113 (128) | 11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11·································································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··························································11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··11··························································11··11··11··11··11··11··11··11·11··11··11··11·11··11·11·1·································································1······················ |
| check 114 (128) | 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································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·························································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·························································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·11·1·1·1·1·1·1·11·1·1·11·11··································································1····················· |
| check 115 (128) | 1111111111111111················································1111111111111111···············································1111111111111111···············································1111111111111111·········································1111111111111111···············································1111111111111111·········································1111111111111111·········································111111111111111·····················································1··················· |
| check 116 (128) | 11111111········11111111········································11111111········11111111·······································11111111········11111111·······································11111111········11111111·································11111111········11111111·······································11111111········11111111·································11111111········11111111·································11111111·······1111111···············································1·················· |
| check 117 (128) | 1111····1111····1111····1111····································1111····1111····1111····1111···································1111····1111····1111····1111···································1111····1111····1111····1111·····························1111····1111····1111····1111···································1111····1111····1111····1111·····························1111····1111····1111····1111·····························1111····1111···1111···111·············································1················· |
| check 118 (128) | 11··11··11··11··11··11··11··11··································11··11··11··11··11··11··11··11·································11··11··11··11··11··11··11··11·································11··11··11··11··11··11··11··11···························11··11··11··11··11··11··11··11·································11··11··11··11··11··11··11··11···························11··11··11··11··11··11··11··11···························11··11··11··11·11··11·11·1·············································1················ |
| check 119 (128) | 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································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1································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································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1··························1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1··························1·1·1·1·1·1·1·11·1·1·11·11··············································1··············· |
| check 120 (128) | 11111111························11111111························11111111························11111111·······················11111111························11111111·······················11111111·······················11111111··················11111111························11111111·······················11111111·······················11111111··················11111111·······················11111111··················11111111··················1111111·········································1············· |
| check 121 (128) | 1111····1111····················1111····1111····················1111····1111····················1111····1111···················1111····1111····················1111····1111···················1111····1111···················1111····1111··············1111····1111····················1111····1111···················1111····1111···················1111····1111··············1111····1111···················1111····1111··············1111····1111··············1111···111·······································1············ |
| check 122 (128) | 11··11··11··11··················11··11··11··11··················11··11··11··11··················11··11··11··11·················11··11··11··11··················11··11··11··11·················11··11··11··11·················11··11··11··11············11··11··11··11··················11··11··11··11·················11··11··11··11·················11··11··11··11············11··11··11··11·················11··11··11··11············11··11··11··11············11··11·11·1·······································1··········· |
| check 123 (128) | 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·················1·1·1·1·1·1·1·1················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················1·1·1·1·1·1·1·1···········1·1·1·1·1·1·1·1················1·1·1·1·1·1·1·1···········1·1·1·1·1·1·1·1···········1·1·1·11·11········································1·········· |
| check 124 (128) | 1111············1111············1111············1111············1111············1111············1111············1111···········1111············1111············1111············1111···········1111············1111···········1111···········1111·······1111············1111············1111············1111···········1111············1111···········1111···········1111·······1111············1111···········1111···········1111·······1111···········1111·······1111·······111·······································1········ |
| check 125 (128) | 11··11··········11··11··········11··11··········11··11··········11··11··········11··11··········11··11··········11··11·········11··11··········11··11··········11··11··········11··11·········11··11··········11··11·········11··11·········11··11·····11··11··········11··11··········11··11··········11··11·········11··11··········11··11·········11··11·········11··11·····11··11··········11··11·········11··11·········11··11·····11··11·········11··11·····11··11·····11·1·······································1······· |
| check 126 (128) | 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·········1·1·1·1········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········1·1·1·1····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····1·11········································1······ |
| check 127 (128) | 11······11······11······11······11······11······11······11······11······11······11······11······11······11······11······11·····11······11······11······11······11······11······11······11·····11······11······11······11·····11······11·····11·····11··11······11······11······11······11······11······11······11·····11······11······11······11·····11······11·····11·····11··11······11······11······11·····11······11·····11·····11··11······11·····11·····11··11·····11··11··1·········································1···· |
| check 128 (128) | 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·····1·1····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····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··· |
| check 129 (128) | 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···1··1···1···1···1···1···1···1···1··1···1···1···1··1···1··1··11···1···1···1···1···1···1···1···1···1···1···1···1···1···1···1··1···1···1···1···1···1···1···1··1···1···1···1··1···1··1··11···1···1···1···1···1···1···1··1···1···1···1··1···1··1··11···1···1···1··1···1··1··11···1··1··11··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 n512Noisy T states per run.
outputs k84
distance d≥ 6A lower bound proved here.
error coefficient A_{6}not definedUndefined while the distance is only a lower bound.
wires N130
checks r46
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 d1.0088Overhead 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 width84Rank of the output rows modulo the check rows.
Output gate
0 T0 CS280 CCZon 84 output wires
As gates: CCZ0,64,83·CCZ0,65,82·CCZ0,66,81·CCZ0,67,80·CCZ0,68,79·CCZ0,69,78·CCZ0,70,77·CCZ0,71,76·CCZ0,72,75·CCZ0,73,74·CCZ1,54,83·CCZ1,55,82·CCZ1,56,81·CCZ1,57,80·CCZ1,58,79·CCZ1,59,78·CCZ1,60,77·CCZ1,61,76·CCZ1,62,75·CCZ1,63,74·CCZ2,50,83·CCZ2,51,82·CCZ2,52,81·CCZ2,53,80·CCZ2,58,73·CCZ2,59,72·CCZ2,60,71·CCZ2,61,70·CCZ2,62,69·CCZ2,63,68·CCZ3,49,83·CCZ3,51,79·CCZ3,52,78·CCZ3,53,77·CCZ3,55,73·CCZ3,56,72·CCZ3,57,71·CCZ3,61,67·CCZ3,62,66·CCZ3,63,65·CCZ4,49,82·CCZ4,50,79·CCZ4,52,76·CCZ4,53,75·CCZ4,54,73·CCZ4,56,70·CCZ4,57,69·CCZ4,59,67·CCZ4,60,66·CCZ4,63,64·CCZ5,49,81·CCZ5,50,78·CCZ5,51,76·CCZ5,53,74·CCZ5,54,72·CCZ5,55,70·CCZ5,57,68·CCZ5,58,67·CCZ5,60,65·CCZ5,62,64·CCZ6,49,80·CCZ6,50,77·CCZ6,51,75·CCZ6,52,74·CCZ6,54,71·CCZ6,55,69·CCZ6,56,68·CCZ6,58,66·CCZ6,59,65·CCZ6,61,64·CCZ7,39,83·CCZ7,40,82·CCZ7,41,81·CCZ7,42,80·CCZ7,43,79·CCZ7,44,78·CCZ7,45,77·CCZ7,46,76·CCZ7,47,75·CCZ7,48,74·CCZ8,35,83·CCZ8,36,82·CCZ8,37,81·CCZ8,38,80·CCZ8,43,73·CCZ8,44,72·CCZ8,45,71·CCZ8,46,70·CCZ8,47,69·CCZ8,48,68·CCZ9,34,83·CCZ9,36,79·CCZ9,37,78·CCZ9,38,77·CCZ9,40,73·CCZ9,41,72·CCZ9,42,71·CCZ9,46,67·CCZ9,47,66·CCZ9,48,65·CCZ10,34,82·CCZ10,35,79·CCZ10,37,76·CCZ10,38,75·CCZ10,39,73·CCZ10,41,70·CCZ10,42,69·CCZ10,44,67·CCZ10,45,66·CCZ10,48,64·CCZ11,34,81·CCZ11,35,78·CCZ11,36,76·CCZ11,38,74·CCZ11,39,72·CCZ11,40,70·CCZ11,42,68·CCZ11,43,67·CCZ11,45,65·CCZ11,47,64·CCZ12,34,80·CCZ12,35,77·CCZ12,36,75·CCZ12,37,74·CCZ12,39,71·CCZ12,40,69·CCZ12,41,68·CCZ12,43,66·CCZ12,44,65·CCZ12,46,64·CCZ13,30,83·CCZ13,31,82·CCZ13,32,81·CCZ13,33,80·CCZ13,43,63·CCZ13,44,62·CCZ13,45,61·CCZ13,46,60·CCZ13,47,59·CCZ13,48,58·CCZ14,29,83·CCZ14,31,79·CCZ14,32,78·CCZ14,33,77·CCZ14,40,63·CCZ14,41,62·CCZ14,42,61·CCZ14,46,57·CCZ14,47,56·CCZ14,48,55·CCZ15,29,82·CCZ15,30,79·CCZ15,32,76·CCZ15,33,75·CCZ15,39,63·CCZ15,41,60·CCZ15,42,59·CCZ15,44,57·CCZ15,45,56·CCZ15,48,54·CCZ16,29,81·CCZ16,30,78·CCZ16,31,76·CCZ16,33,74·CCZ16,39,62·CCZ16,40,60·CCZ16,42,58·CCZ16,43,57·CCZ16,45,55·CCZ16,47,54·CCZ17,29,80·CCZ17,30,77·CCZ17,31,75·CCZ17,32,74·CCZ17,39,61·CCZ17,40,59·CCZ17,41,58·CCZ17,43,56·CCZ17,44,55·CCZ17,46,54·CCZ18,28,83·CCZ18,31,73·CCZ18,32,72·CCZ18,33,71·CCZ18,36,63·CCZ18,37,62·CCZ18,38,61·CCZ18,46,53·CCZ18,47,52·CCZ18,48,51·CCZ19,28,82·CCZ19,30,73·CCZ19,32,70·CCZ19,33,69·CCZ19,35,63·CCZ19,37,60·CCZ19,38,59·CCZ19,44,53·CCZ19,45,52·CCZ19,48,50·CCZ20,28,81·CCZ20,30,72·CCZ20,31,70·CCZ20,33,68·CCZ20,35,62·CCZ20,36,60·CCZ20,38,58·CCZ20,43,53·CCZ20,45,51·CCZ20,47,50·CCZ21,28,80·CCZ21,30,71·CCZ21,31,69·CCZ21,32,68·CCZ21,35,61·CCZ21,36,59·CCZ21,37,58·CCZ21,43,52·CCZ21,44,51·CCZ21,46,50·CCZ22,28,79·CCZ22,29,73·CCZ22,32,67·CCZ22,33,66·CCZ22,34,63·CCZ22,37,57·CCZ22,38,56·CCZ22,41,53·CCZ22,42,52·CCZ22,48,49·CCZ23,28,78·CCZ23,29,72·CCZ23,31,67·CCZ23,33,65·CCZ23,34,62·CCZ23,36,57·CCZ23,38,55·CCZ23,40,53·CCZ23,42,51·CCZ23,47,49·CCZ24,28,77·CCZ24,29,71·CCZ24,31,66·CCZ24,32,65·CCZ24,34,61·CCZ24,36,56·CCZ24,37,55·CCZ24,40,52·CCZ24,41,51·CCZ24,46,49·CCZ25,28,76·CCZ25,29,70·CCZ25,30,67·CCZ25,33,64·CCZ25,34,60·CCZ25,35,57·CCZ25,38,54·CCZ25,39,53·CCZ25,42,50·CCZ25,45,49·CCZ26,28,75·CCZ26,29,69·CCZ26,30,66·CCZ26,32,64·CCZ26,34,59·CCZ26,35,56·CCZ26,37,54·CCZ26,39,52·CCZ26,41,50·CCZ26,44,49·CCZ27,28,74·CCZ27,29,68·CCZ27,30,65·CCZ27,31,64·CCZ27,34,58·CCZ27,35,55·CCZ27,36,54·CCZ27,39,51·CCZ27,40,50·CCZ27,43,49
As monomials: 0,64,83+0,65,82+0,66,81+0,67,80+0,68,79+0,69,78+0,70,77+0,71,76+0,72,75+0,73,74+1,54,83+1,55,82+1,56,81+1,57,80+1,58,79+1,59,78+1,60,77+1,61,76+1,62,75+1,63,74+2,50,83+2,51,82+2,52,81+2,53,80+2,58,73+2,59,72+2,60,71+2,61,70+2,62,69+2,63,68+3,49,83+3,51,79+3,52,78+3,53,77+3,55,73+3,56,72+3,57,71+3,61,67+3,62,66+3,63,65+4,49,82+4,50,79+4,52,76+4,53,75+4,54,73+4,56,70+4,57,69+4,59,67+4,60,66+4,63,64+5,49,81+5,50,78+5,51,76+5,53,74+5,54,72+5,55,70+5,57,68+5,58,67+5,60,65+5,62,64+6,49,80+6,50,77+6,51,75+6,52,74+6,54,71+6,55,69+6,56,68+6,58,66+6,59,65+6,61,64+7,39,83+7,40,82+7,41,81+7,42,80+7,43,79+7,44,78+7,45,77+7,46,76+7,47,75+7,48,74+8,35,83+8,36,82+8,37,81+8,38,80+8,43,73+8,44,72+8,45,71+8,46,70+8,47,69+8,48,68+9,34,83+9,36,79+9,37,78+9,38,77+9,40,73+9,41,72+9,42,71+9,46,67+9,47,66+9,48,65+10,34,82+10,35,79+10,37,76+10,38,75+10,39,73+10,41,70+10,42,69+10,44,67+10,45,66+10,48,64+11,34,81+11,35,78+11,36,76+11,38,74+11,39,72+11,40,70+11,42,68+11,43,67+11,45,65+11,47,64+12,34,80+12,35,77+12,36,75+12,37,74+12,39,71+12,40,69+12,41,68+12,43,66+12,44,65+12,46,64+13,30,83+13,31,82+13,32,81+13,33,80+13,43,63+13,44,62+13,45,61+13,46,60+13,47,59+13,48,58+14,29,83+14,31,79+14,32,78+14,33,77+14,40,63+14,41,62+14,42,61+14,46,57+14,47,56+14,48,55+15,29,82+15,30,79+15,32,76+15,33,75+15,39,63+15,41,60+15,42,59+15,44,57+15,45,56+15,48,54+16,29,81+16,30,78+16,31,76+16,33,74+16,39,62+16,40,60+16,42,58+16,43,57+16,45,55+16,47,54+17,29,80+17,30,77+17,31,75+17,32,74+17,39,61+17,40,59+17,41,58+17,43,56+17,44,55+17,46,54+18,28,83+18,31,73+18,32,72+18,33,71+18,36,63+18,37,62+18,38,61+18,46,53+18,47,52+18,48,51+19,28,82+19,30,73+19,32,70+19,33,69+19,35,63+19,37,60+19,38,59+19,44,53+19,45,52+19,48,50+20,28,81+20,30,72+20,31,70+20,33,68+20,35,62+20,36,60+20,38,58+20,43,53+20,45,51+20,47,50+21,28,80+21,30,71+21,31,69+21,32,68+21,35,61+21,36,59+21,37,58+21,43,52+21,44,51+21,46,50+22,28,79+22,29,73+22,32,67+22,33,66+22,34,63+22,37,57+22,38,56+22,41,53+22,42,52+22,48,49+23,28,78+23,29,72+23,31,67+23,33,65+23,34,62+23,36,57+23,38,55+23,40,53+23,42,51+23,47,49+24,28,77+24,29,71+24,31,66+24,32,65+24,34,61+24,36,56+24,37,55+24,40,52+24,41,51+24,46,49+25,28,76+25,29,70+25,30,67+25,33,64+25,34,60+25,35,57+25,38,54+25,39,53+25,42,50+25,45,49+26,28,75+26,29,69+26,30,66+26,32,64+26,34,59+26,35,56+26,37,54+26,39,52+26,41,50+26,44,49+27,28,74+27,29,68+27,30,65+27,31,64+27,34,58+27,35,55+27,36,54+27,39,51+27,40,50+27,43,49 (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
None. With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the circuit's action is exactly the gate above, and an error-free run passes every check with certainty.
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/512.84.6.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-512.84.6.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
6\le d\le 8. No fault of weight below 6 is both undetectable and damaging. None of weight 6 has been found, and one of weight 8 is, so the distance lies between the two.
A damaging fault of weight 8 sits on columns [127,147,200,220,411,421,498,503].
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
- N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, "On Optimality of CSS Codes for Transversal T," IEEE J. Sel. Areas Inf. Theory 1, 499 (2020). doi.org/10.1109/JSAIT.2020.3012914
- C. Vuillot and N. P. Breuckmann, "Quantum Pin Codes," IEEE Trans. Inf. Theory 68, 5955 (2022). doi.org/10.1109/TIT.2022.3170846
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": "/private/tmp/claude-501/-Users-shubhamjain-Documents-Claude-remote-magic-states-AI/25937cc1-0367-40c1-acc9-031067b831d4/scratchpad/msai_for_merge.jsonl",
"label": "msAI:90ead2abdc2b7d71",
"N": 130,
"d": 6,
"d_is_exact": false,
"origin": "magic-states-AI/master_catalogue/master_catalogue.jsonl",
"provenance": "magic-states-AI/master_catalogue/master_catalogue.jsonl",
"notes": "gamma_campaign"
}
]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/512.84.6.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[1112].