The circuit
The 85\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) | 11111111························································11111111111111111111111111111111111111111111111111111111········································································································································································································································································································································································································ |
| out 2 (64) | 1·······1111111·················································1111111·················································1111111111111111111111111111111111111111111111111······················································································································································································································································································································································· |
| out 3 (64) | 1111····111····111111111········································111····111111111········································111111111········································111111111111111111111111111···························································································································································································································································································································· |
| out 4 (64) | 11··11··1··11··1········11111111································1··11··1········11111111································1········11111111································1··························11111111111111111111111111·································································································································································································································································································· |
| out 5 (64) | 1·1·1·1··1·1·1··1·······1·······1111111··························1·1·1··1·······1·······1111111··························1·······1·······1111111··························1·························1·························1111111111111111111111111········································································································································································································································································· |
| out 6 (64) | 11111111·1·1·1··111·····111·····111111111111111·················1······1·11······11············11·························1·······1·············1··························111·······················111···············································111111111111111·························································································································································································································································· |
| out 7 (64) | 1·1·1·1·1··········1·······1···················1················1111111·11·1····11·1····11111111·1111111················1··11······11············11···························111·······················111···························································111111111111111··········································································································································································································································· |
| out 8 (64) | 11······11111111·1··1····1··1··········1········1················1·1·1······1·······1···················1················1·1·1···1·1·1···1111111·1·1111111·······················111·······················111·······································································111111111111111···························································································································································································································· |
| out 9 (64) | 1111····1··11··1···1·1···1··1···1·······1········11·············111····111111111········································1··11·····1···1··1·········1······11·············1····1111··1111·············1········1···············1························11····························11·············11111111111················································································································································································································· |
| out 10 (64) | 11··11···1·1·1···1······111······11····1·11·····················1··11··1········11111111··································1······11····1··11····1···········11·············1························1111···1···1111············11························11111·························11······················11111111········································································································································································································· |
| out 11 (64) | 1·1·1·1·111·····1··1··1····1·····1·1···········1···11············1·1·1··1·······1·······1111111··························1·1·1·····1······1·1····1··11····················1···1·········1···············1······················1·1111111······························1111111··········································11111111································································································································································································· |
| out 12 (64) | 11··11··111····1·1··1······1·1···1·······1·········1·1··········111····1····11···11·····1········1·······11·············111111111········································1·1·····1111····111·············1·········1·············1·······················11···········1······1·········································1·······1111111111······················································································································································································· |
| out 13 (64) | 1·1·1·1·1··11······1····1··1··1·1···1··········1·1····1·········1··11····1······11·1·····11····1··11····················1········11111111······································1····················1·1·111····1····111·················11·············1······1········11·····111···················1····································1111111················································································································································································ |
| out 14 (64) | 1111·····1·1·1··111······1······1····1·11··1·····················1·1·1··1···1·1·····1····1·1············1··11············1·······1·······1111111··························1·······1·········1··············1··················1···11····1·1111·······································1·111111········1··········································1111111········································································································································································· |
| out 15 (64) | 1·1·1·1··1·1·1··1·······1·······1111111·························111·····11·1·····1······1···1··1·1··1····················11···1···1······1···1··1·········1···1···········1·1················1········1·······················1··1··1·····1···1111·····1·1·1··1111····································1························1·······················111111··································································································································································· |
| out 16 (64) | 1111····111····111111111········································1··11··1·11·········11···1········1········1·1··········1·1····1···11·····1·········1·······1··1·········1·111·1·····1···1····11············1··········1··········1····································1······1········1·····1·················1········1·······················1············11111111··························································································································································· |
| out 17 (64) | 11··11··1··11··1········11111111·································1·1·1······1···1···1·1·1····1··········11····1············1·····1·1·1···1····1··1·1··1··························1··················1···1··111··1···1···11····················1···1···················1··1···········11··1····11································1····································1111111···················································································································································· |
| out 18 (64) | 111111111··11··1···1·1··111111111···1···1···1··1·11···111········1······1···1·1·········1···1············1·····1···········1·············1·········1··························1··1····1·······································1···············11······················1···1··········11··············1·11·······················1····································111····1111················································································································································ |
| out 19 (64) | 11······11111111·1··1····1··1··········1········1···············1··11··1············11··································1·1····1·11111111·11····1···1··1····11·111·······1·1·············1···········1·····1111··1·····1··1·································1··························11····1··1··············11············································1··················11·············································································································································· |
| out 20 (64) | 1·1·1·1··1······1················1·1····························1111111·11·1····11·1····11111111·1111111·················11···1···········1·1···············1·····1·······1·1················1·································1·1111111·················1·····1·················································1·············1·······················1······1···················1111·········································································································································· |
| out 21 (64) | 1···1···1111111·········1··1··1··11················1·····1······111··············1······1········1······················111111111·1···1··1···1··1··1····1·11··1·1··1··································1··1···········1···········1············1·1········1·1··········1······1·········································1·······1·11·····················11···········1················1111······································································································································ |
| out 22 (64) | 11111111·1·1·1··111·····111·····111111111111111····················1············1···1·1··11················1····1················1········11························································1······1····1··············11·1··1··11·1·······1···································11·························11····························111·······································111··································································································································· |
| out 23 (64) | 1111····1······1···1·1··········································1111111111111111····11···1·1······1··1··1··111···11·····1··11······11············11······················1····1111··1111····················1··········1···············································1···1··1··1············1································································11····························111································································································································ |
| out 24 (64) | 11111111111····111111111···1·1···1·1·····1···1·1···111·1··1······1······1···1·1·········1···1············1·····1·········1·1·1············································1···1··111··1·1···1···1································1··1·································1···1············································1·1······1··11·······································1···················11······························································································································ |
| out 25 (64) | 1···1···1111111·········1··1··1··11················1·····1······1··11···········11·1····································1·1····1·11111111·11····1···1··1····11·111··································1·1·111····1····111········11························1·1·····················································1··1·····1······1····················································1···········111··························································································································· |
| out 26 (64) | 1111·······1·············1······1·······1·······················1111111111111111····11···1·1······1··1··1··111···11··············11····1·1····1···········1·········1································1·····1·····1············1·········1···1··········11····························1···1···········11··11······························1·······1·1·················································1111······················································································································· |
| out 27 (64) | 11111111111····111111111···1·1···1·1·····1···1·1···111·1··1·····1······1·11······11············11·······················1·1····1·········································1·111·1·····1···1····11·········1·········1·····································11····1··1············1·················································1···1···································································111···················································································································· |
| out 28 (64) | 11··11·····1············111·····································11111111····11··111111111····1···1····1·111···1··1·1·············11····1·1····1···········1·········1·······························1111···1···1111···························1···1··································1···1···············1··············································1·············1·1····························1······111················································································································· |
| out 29 (64) | 1·1·····1111111·1··1··1·········1····1···········1·········1·····1·1·1··1················1·1·····························1·1·1···1·1·1···1111111·1·1111111················1···1·········1·····································1···11····1·1111·························1···1···························1················1··1··············1····································································1111············································································································· |
| out 30 (64) | 11··11···1·1·1···1······111······11····1·11·····················111····1····11···11·····1········1·······11··············11···1···1······1···1··1·········1···1············1······1·······1··········111·························1············1·1········11111·······················1····1··············1·····················1···1··1·················11············1·····································1······111·········································································································· |
| out 31 (64) | 1·1·1·1·111·····1··1··1····1·····1·1···········1···11···········1··11····1······11·1·····11····1··11····················1·1····1···11·····1·········1·······1··1············1··1··············1·········111····················1··1··1···················1·····1·······11·····111································1······1·1·1····1····························1··1················1···············1······1············1········································································································· |
| out 32 (64) | 1111····1··11··1···1·1···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··1····1····················111················1·········1···1··························1···1·········11··1····11·····1·11·································1······1·1···········1·····························1·················1·······11······································································································· |
| out 33 (64) | 1·1·1·1·1··11······1····1··1··1·1···1··········1·1····1·········111·····11·1·····1······1···1··1·1··1···················1··11·····1···1··1·········1······11··················111·····················1··1···········1········1···············11·······1······1·······1···1··1·1··1·················1·11···1·······························1············1·1··········1·······1·········1·································1······································································································ |
| out 34 (64) | 1111·····1·1·1··111······1······1····1·11··1····················1··11··1·11·········11···1········1········1·1············1······11····1··11····1···········11·············111·······················1·····1·····1················1·····1··1···········11···1···1··1···················11······················11························1······111···········1···1···································1···················11···································································································· |
| out 35 (64) | 11··11··111····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··11···························111····················1···1···········1······1·1····1·······························1··1·············1···1·11··1················1····1··1··1··1··11····································1··················································111································································································· |
| out 36 (64) | 1·1·····1111111·1··1··1·········1····1···········1·········1····111·····11·1············································111111111·1···1··1···1··1··1····1·11··1·1··1······1·1·111·······1····11··1····························1···········1············1········1···································1·11···1···············································1····················································1··············11······························································································· |
| out 37 (64) | 111111111··11··1···1·1··111111111···1···1···1··1·11···111··········1············1···1·1··11················1····1················1·1·1······························································1···1··111··1···1···11··············11·····························11·································································1·1····1·············1··························1····························1·········11····························································································· |
| out 38 (64) | 11··11···1·······1···············1·······1······················11111111····11··111111111····1···1····1·111···1··1·1·····11···1···········1·1···············1·····1········1······1·······1····································1·1····1··················11····························1···1···················1·11··1·········1···1··1············································1········································1······11··························································································· |
| check 39 (512) | 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 |
| check 40 (256) | 1111111111111111111111111111111111111111111111111111111111111111111····111111111·11·····1···1··111··1····11····1····1···111111111·1···1··1···1··1··1····1·11··1·1··1·····111111111111111111111111111·111·1····1····1·1·····1··1··1··1·····1···1111·····1111111111111111···1··1·1··1··11···1·······1·11111111111········1·1·····1111111111··1········1··111111········111····11111·····1111······11·······1111···1··111···1·····11·····111111111111111111111111·································································· |
| check 41 (256) | 11111111111111111111111111111111111111111111111111111111111111111··11··1·11·····11111111·11····11·11·······1·1··1····1··1·1····1·11111111·11····1···1··1····11·111·······1·111·1·····1···1····11····11111111111111111111111111·11·1··1··11·1·······1···111111111111111·11·····111······11····1··1···1·······1··11111111·1·1·1····1···1···1111111111··········11111111···········111···1···111·····111·1··111·····1····11··11·1·1·11····11111··················1111111111111111111··············································· |
| check 42 (256) | 111111111··11··1···1·1··111111111···1···1···1··1·11···111·······111111111111111111111111111111111111111111111111111111111··11····111111111····1··111··1···11········11···1····1111··1111············111111111111111111111111111·········11··1·11··1·1··11·····1·····1·11111111111111111··1····11····11111111111·················1······1·1111111·1·1····1·1····11····11111111111·······1··1··111·····1111·1·1111·······111·······11····1····1111···············1111··············111111111111111································ |
| check 43 (256) | 1·1·1·1·1111111·1··1··1·1··1··1·1111111········1·1·11·1··1·11···1111111·11·1····11·1····11111111·1111111················1111111111111111111111111111111111111111111111111·1·1·111·······1····11··1··1·1·111····1····111·······11111111111111111111111111·1·1··1111····111111111111111···············1·11···1·····1··1··111111111·11······1111111·······111111·1··1···1····1··1····11111111········111··1·1···1·1111···1··11····11·······1·······111················1111···········11111·········11111111111····················· |
| check 44 (256) | 11··11··11111111·1··1···11111111·11····1·11·····1··1·1···1···1··11111111····11··111111111····1···1····1·111···1··1·1····11111111111111111111111111111111111111111111111111·1·····1111····111········11111111111111111111111111·111····1·······1·1·1··1···11111········1··1···1·····1·111111111111111·····1···1·111111111··1··1·1111111111···············11···1·······1111111····11·1··1111····1···1111······111····111······111····11····1··1······111·················111········1····111·······1111······11111111············· |
| check 45 (256) | 1111····1111111111111111·1··1···1····1·11··1····111········1··1·1111111111111111····11···1·1······1··1··1··111···11·····1111111111111111111111111111111111111111111111111111111111111111111111111111·1·····1111··1·····1··1···1···11····1·1111·········11···1···1··1···1···1··1··1···1111111111111111111111111111·······1··1·············11··1··1111111····1·11111111···········11··1········111·····1111······11111···11·11···11··1······1········1··111······1···1······11·······1···1··1··········111····111····111111······· |
| check 46 (256) | 11111111·1·1·1··111·····111·····111111111111111·················11111111111111111111111111111111111111111111111111111111·11···1··11····1·11111111·········1·111···1·1·1···1111····1·······1·11····1·1111···1···1111···········1111111111111111111111111111111111111111···············1·111111········11··11····11111111········1···1··1··1····1·1111111111111·1···1···1·1·····1···1111····111···1····1111···111····111····111······11········1········1··111····1···1·······11······1······11····1···1··1···1··11···11···1111··· |
| check 47 (256) | 11111111111····111111111···1·1···1·1·····1···1·1···111·1··1·····11111111111111111111111111111111111111111111111111111111111111111··11·····1·1····11·11······1··1··1····1·111111111111111111111111111····111·1······1···11···1··1·1111111·················11····1··1···111111111111111··1···1·11··1·············1·11··1·111111111111111111·······1····1·1·····11111111····1··1·····1111·····1·111111······111··········1·····111··1·11·········1·1········1··1····1·····1····1·11········1····11···1···1··1···1···1··1·11··11·11· |
| check 48 (256) | 1111111111111111111111111111111111111111111111111111111111111111·1·1·1··1···1·1·1···1·1·1111111·········11·11·111·····1··1·1·1···1·1·1···1111111·1·1111111················1···1··111··1·1···1···1···1···1··111··1···1···11····1111111111111111111111111···············1111111········111111111111111·1·11·········11···11111111·1··11·····1·1···1111111········1···1·11111111111········1·1111··11·1···········1111·1··11···111··11··············1··1··1··1··1·······1··1·1···1·1····1·····1·1·1···1······1····1··1···1·1·1·1·11 |
| check 49 (128) | 11111111111111111111111111111111111111111111111111111111111111111······1·11······11············11·······················1·1····1··1···1·········1···············1········1·111·1·····1···1····11·····111·1····1····1·1·····1···························111111111111111·········1····················1·······1····················1···1·····1····································1·····1··················111···················1·······11111···················································································· |
| check 50 (128) | 111111111··11··1···1·1··111111111···1···1···1··1·11···111·······111····111111111·11·····1···1··111··1····11····1····1···1··11·····1···1··1·········1······11·············1····1111··1111·············111·1····1····1·1·····1··1···············11·······11·····1·····1·1···1··1·1··1··11·············11111111111·················1······1···1············1·1··········111····1111·······1··················1·1············1·············1····1111················································································ |
| check 51 (128) | 1·1·1·1·1111111·1··1··1·1··1··1·1111111········1·1·11·1··1·11···111·····11·1·····1······1···1··1·1··1···················111111111·1···1··1···1··1··1····1·11··1·1··1······1·1·111·······1····11··1····1··1···········1········1··1··1·····1···1111·····1·1·1··1111····1···1··1·1··1·················1·11···1···········1·1·····1·11········1···········111111········1·······1········1111···············1······1········1·····11·······1·······111············································································· |
| check 52 (128) | 11··11··11111111·1··1···11111111·11····1·11·····1··1·1···1···1··111····1····11···11·····1········1·······11·············111111111·1···1··1···1··1··1····1·11··1·1··1·····1·1·····1111····111·········111·1····1····1·1·····1·····1············1·1········11111········1······1·······11···1·······1······1···1·········1·······1111111111···············11···········111········1·····1111··················1······111···················1··1······111·········································································· |
| check 53 (128) | 1111····1111111111111111·1··1···1····1·11··1····111········1··1·111····111111111········································111111111·1···1··1···1··1··1····1·11··1·1··1·····111111111111111111111111111·1········1···············1···········1············11···1···1··1·················11···1·······1·11111111111·····································1······1····················1·······························1··1···········11·········1········1··111······································································· |
| check 54 (128) | 11111111·1·1·1··111·····111·····111111111111111·················111····111111111·11·····1···1··111··1····11····1····1····11···1···1······1···1··1·········1···1···········1111····1·······1·11····1··111······················1··1··1·····1···1111·····111111111111111···············1····1··········11··11····················1···1··1·············1··111111·········1·······1·················1···········1······111·······················1········1··111···································································· |
| check 55 (128) | 11111111111····111111111···1·1···1·1·····1···1·1···111·1··1·····111····111111111·11·····1···1··111··1····11····1····1···111111111········································111111111111111111111111111·····1·········1·············1··1····················11····1··1···1···1··1·1··1····································1·1·····1111111111··············1····················1···················11·······111··································1·1········1··1··································································· |
| check 56 (128) | 1111111111111111111111111111111111111111111111111111111111111111·1······1···1·1·········1···1············1·····1·········1·1·1···········1···1·····1····1·················1···1··111··1·1···1···1·····························1··1··1·····1···1111····················1···1··········11···1·······1··1·11··············1·1······1··11···············1················111····1111········1·······11··············1···1····························1··1··1··1··1·································································· |
| check 57 (128) | 111111111··11··1···1·1··111111111···1···1···1··1·11···111·······1··11··1·11·····11111111·11····11·11·······1·1··1····1··1········11111111································1·····1·····1··············11111111111111111111111111··········11·············11·····1·····1··11·····111···················1·······1····························1111111·1·············11·························1···········1···1············1·········11····1·······················1111····························································· |
| check 58 (128) | 1·1·1·1·1111111·1··1··1·1··1··1·1111111········1·1·11·1··1·11···1··11····1······11·1·····11····1··11····················1·1····1·11111111·11····1···1··1····11·111··········1··1··············1·····1·1·111····1····111········11·1··1··11·1·······1···1·1·1··1111·····11·····111···················1············1··1···1·1·1····1·······1111111··············1··1················1···1···········111····1·······1····1···1····1········1··························1111························································· |
| check 59 (128) | 11··11··11111111·1··1···11111111·11····1·11·····1··1·1···1···1··1··11··1········11111111································1·1····1·11111111·11····1···1··1····11·111·······1·1·············1··········11111111111111111111111111·11························11111·························11····1··1··············11111111···1······1···1·······················1··················11····1···········111························1···········1·····························111······················································ |
| check 60 (128) | 1111····1111111111111111·1··1···1····1·11··1····111········1··1·1··11··1·11·········11···1········1········1·1··········1·1····1·11111111·11····1···1··1····11·111·······1·111·1·····1···1····11·····1·····1111··1·····1··1·······1·····1··1···········11···1···1··1···1······1········11····1··1···1·······1··11·······1················11··1··111··········11111111···········11····················1··········1·····1··11···1··········1····················1···1······11···················································· |
| check 61 (128) | 11111111·1·1·1··111·····111·····111111111111111·················1··11··1·11·····11111111·11····11·11·······1·1··1····1····1······11····1··11····1···········11·············111······················1111···1···1111············11·1··1··11·1·······1···111111111111111·················11······················11111111··················1····1·111···········1···1···············1·······111·········1···················11····································1···1·······11·················································· |
| check 62 (128) | 11111111111····111111111···1·1···1·1·····1···1·1···111·1··1·····1··11··1·11·····11111111·11····11·11·······1·1··1····1··1·1····1···11·····1·········1·······1··1·········1·111·1·····1···1····11········111·1······1···11···1··1··1··1···················11····1··1····11·····111······1·····1·················1·11··1··1·1·1····1···1··········1············11111111·············1········1······1······111··········1······1···1·······························1·····1····1·11················································ |
| check 63 (128) | 1111111111111111111111111111111111111111111111111111111111111111···1············1···1·1··11················1····1················1·1·1····11········1··1············································1···1··111··1···1···11·····11·1··1··11·1·······1···················11··············11····1··1·················11····1·1·1·············1·1···111············1···1······················111······1·············1·····1·····1···11··································1··1·1···1·1··············································· |
| check 64 (128) | 1·1·1·1·1··11······1····1··1··1·1···1··········1·1····1·········1111111·11·1····11·1····11111111·1111111················1··11····111111111····1··111··1···11········11········111···················1·1·111····1····111·······1·········11··1·11··1·1··1······1·······111111111111111···············1·11···1·····························1111111········1·1··········1····1··1·········1···············1·····1·1·········1························································11111········································· |
| check 65 (128) | 11··11··1··11··1········11111111································11111111····11··111111111····1···1····1·111···1··1·1····1··11····111111111····1··111··1···11········11···1·······1··1···············11111111111111111111111111················1···1···················1··1···1·····1·11··1····11·········1···1··················1······1················1············1111111···········1······1······1······111·····························1·····································1····111······································ |
| check 66 (128) | 1111····1··11··1···1·1···1··1···1·······1········11·············1111111111111111····11···1·1······1··1··1··111···11·····1··11····111111111····1··111··1···11········11···1····1111··1111·············1·····1111··1·····1··1···1·········1···1··········11··············1···1··1··1···11··1····11····11111111111··························11··1···1·1···········11····························111·····1111······1·······11······································1···················1···1··1····································· |
| check 67 (128) | 11111111···1············111·····1···1···1···1···················11111111111111111111111111111111111111111111111111111111·········11····1·1····1···········1·········1·······························1111···1···1111···········1·········11··1·11··1·1··11·····1·····1················1···1···········11··11······························1····1··1·1····1·1···········1·1·····1···········1··········1111···111······························1··················1···················1······11··································· |
| check 68 (128) | 111111111······1···1·1·····1·1·················1·······1········111111111111111111111111111111111111111111111111111111111··11······11············11······················1····1111··1111················111·1······1···11···1·········································111111111111111·········1·································1······1·······················11········1··1················111··········1······················1············1··················1······················1····11································· |
| check 69 (128) | 111111111··11··1···1·1··111111111···1···1···1··1·11···111········1·1·1··1···1·1·1···1·1·1111111·········11·11·111·····1····1·····1·1·1···1····1··1·1··1·······················1··1····1·············1···1··111··1···1···11····1·········11··1·11··1·1·················1111111········11··1····11·····1·11·······················1·········1·1····1·1···········1·····11111111111··········1··1·················1·······11········11··················································1·····1·1·1································ |
| check 70 (128) | 1···1···1111111·········1··1··1··11················1·····1······1111111·········11·1····1····1···1····1·················1111111111111111111111111111111111111111111111111···························1·1·111····1····111········111····1·······1·1·1··1···1·1··········1··1···1·····1·····························1··1··1··1··1·1·11·····················11···········1····1········1··1111········111········1····································································1··············1111··························· |
| check 71 (128) | 1·1·····1111111·1··1··1·········1····1···········1·········1····1111111·11·1·············1·1······1··1··················1111111111111111111111111111111111111111111111111·1·1·111·······1····11··1····························1···11····1·1111·········1········1······1···1··1··1··················1·11···1············1··1·············11··1·············1··1··1··················1··················1·······1111·······1····11··································1···············1·················111························ |
| check 72 (128) | 1·1·1·1··1·1·1··1·······1·······1111111·························1111111·11·1····11·1····11111111·1111111·················11···1··11····1·11111111·········1·111···1·1·1···1·1················1······1·1········1··············11111111111111111111111111·1·1··1111····································1··········1··1··········1·········1····1········111111·1···················1111·················1·····1············1·········································1···············1············1···1··1······················· |
| check 73 (128) | 1·1·1·1·111·····1··1··1····1·····1·1···········1···11···········1111111·11·1····11·1····11111111·1111111················111111111··11·····1·1····11·11······1··1··1····1··1·1·111·······1····11··1······111····················1·1111111·················1·····1······111111111111111····························1·····111111111·11····················1······1··1················1111············1······1············1·························1·················································1···1··1······················ |
| check 74 (128) | 1·1·1·1·1111111·1··1··1·1··1··1·1111111········1·1·11·1··1·11····1·1·1··1·······1·······1111111··························1·1·1···1·1·1···1111111·1·1111111················1···1·········1···········1···1···········1·········1111111111111111111111111···············1111111··························1···············11111111···········1·1························1····1··1··········1··········1···········1111······························1···················1···············1·············1······1····················· |
| check 75 (128) | 11······11111111·1··1····1··1··········1········1···············11111111····11······11··················1········1······11111111111111111111111111111111111111111111111111·1·····1111····111·········1·····1111··1·····1··1·································1························111111111111111·····1···1·11············································1··················11············1······1·············1···············1···············1···································1····················111················· |
| check 76 (128) | 11··11···1·1·1···1······111······11····1·11·····················11111111····11··111111111····1···1····1·111···1··1·1·····11···1··11····1·11111111·········1·111···1·1·1····1······1·······1·········1111···1···1111············111····1·······1·1·1··1···11111·······················1·111111············1·····11111111········1···1··1·················11············1·1··········1·················1······111····111······1······11····························································1··········1··11··············· |
| check 77 (128) | 11··11··111····1·1··1······1·1···1·······1·········1·1··········11111111····11··111111111····1···1····1·111···1··1·1····111111111··11·····1·1····11·11······1··1··1····1·1·1·····1111····111············111·1······1···11···1··1·1····1··················11···········1··1···1·····1···1···1·11··1·············1·11··1·1··1··1·1111111111····················1···········1·········1··········1···1·························111····11··································1················1·········1··········1···1·············· |
| check 78 (128) | 11··11··11111111·1··1···11111111·11····1·11·····1··1·1···1···1···1·1·1······1···1···1·1·1····1··········11····1··········1·1·1···1·1·1···1111111·1·1111111·······················111················1···1··111··1···1···11·····111····1·······1·1·1··1················1··1···········111111111111111··············11···1··1··1··1··11································1111111············1··········1················1·······111·····················1···················1··························1···········1··1············· |
| check 79 (128) | 1111·····1·1·1··111······1······1····1·11··1····················1111111111111111····11···1·1······1··1··1··111···11······11···1··11····1·11111111·········1·111···1·1·1···1111····1·······1·11····1··1·····1·····1············1···11····1·1111·········11···1···1··1·················1·111111········11··11····11························1······1111111····1··1···1·················1················1111··········1······11·······1··················1··············································1······1·······11·········· |
| check 80 (128) | 1111····111····111111111········································1111111111111111····11···1·1······1··1··1··111···11·····111111111··11·····1·1····11·11······1··1··1····1·111111111111111111111111111········1··········1··········11···································1···1··1··1·····1···1·11··1·············1········1··1····················1····1·······11111111···············1········111···································1··································································1······1······1·11········ |
| check 81 (128) | 1111····1111111111111111·1··1···1····1·11··1····111········1··1··1·1·1··1···1·1·····1····1·1············1··11············1·1·1···1·1·1···1111111·1·1111111················1···1··111··1·1···1···1··········111················1···11····1·1111·························1···1·········111111111111111·1·11···············1··1··············1·····1111111········1···1·························1·················1111····11······························1··················1···········································1·1······· |
| check 82 (128) | 11111111·1······111··············1·1·····1···1··················11111111111111111111111111111111111111111111111111111111·11···1···········1·1···············1·····1·······1111····1·······1·11····1····························1·1111111·················11····1··1····················1···1···················1·11··1·········1···1··1·········1····1·1······1···1···············1111·····1····1···························1······11····················1··················1·······································1·····11···· |
| check 83 (128) | 11111111·1·1·1··111·····111·····111111111111111··················1·1·1··1···1·1·1···1·1·1111111·········11·11·111·····1··1·······1·······1111111··························1·······1·········1·······1······1····1·············1111111111111111111111111······························1·111111········1············11···············1············1111111···············1·1·····1···········111···1···················1·······1·····························1································1···················1··········1·1··· |
| check 84 (128) | 11111111111····111111111···1·1···1·1·····1···1·1···111·1··1······1·1·1··1···1·1·1···1·1·1111111·········11·11·111·····1··1·1·1·····1······1·1····1··11····················1···1··111··1·1···1···1·······1···1···········1······1·1111111······························1111111··········1···1·11··1················1····11111111·1··11···········1····1·········1···1·····1··1··············1·1··11··························111··1············································1··············1························1···1···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 k39
distance d≥ 6A lower bound proved here.
error coefficient A_{6}not definedUndefined while the distance is only a lower bound.
wires N85
checks r46
V_{\mathrm{ex}}26T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.6633Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.4370Overhead 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 width39Rank of the output rows modulo the check rows.
Output gate
0 T0 CS13 CCZon 39 output wires
As gates: \mathrm{CCZ}_{0,1,2}\cdot \mathrm{CCZ}_{3,4,5}\cdot \mathrm{CCZ}_{6,7,8}\cdot \mathrm{CCZ}_{9,10,11}\cdot \mathrm{CCZ}_{12,13,14}\cdot \mathrm{CCZ}_{15,16,17}\cdot \mathrm{CCZ}_{18,19,20}\cdot \mathrm{CCZ}_{21,22,23}\cdot \mathrm{CCZ}_{24,25,26}\cdot \mathrm{CCZ}_{27,28,29}\cdot \mathrm{CCZ}_{30,31,32}\cdot \mathrm{CCZ}_{33,34,35}\cdot \mathrm{CCZ}_{36,37,38}
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 (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
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/512.39.6.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-512.39.6.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 [5,142,188,213,243,382,416,463].
A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.
Original source
S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535
Provenance
found by an AI search campaign; a verified witness, not a maximum
Found by: AI search
Discovery: AI search
1 recorded source
[
{
"regime": "AI search",
"file": "/private/tmp/claude-501/-Users-shubhamjain-Documents-Claude-remote-magic-states-AI/25937cc1-0367-40c1-acc9-031067b831d4/scratchpad/msai_for_merge.jsonl",
"label": "msAI:c0b8a4247f38f1d9",
"N": 85,
"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/512.39.6.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[1111].