The circuit
The 98\times399 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 |
|---|---|
| out 0 (151) | 111111111111111111111111111························································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 1 (151) | 11111111111111·············1111111111111··················1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111······························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111····························································· |
| out 2 (181) | 111111········111111·······1111111······1111111····································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 3 (7) | ······11············11············11···········1······························································································································································································································································································································································· |
| out 4 (213) | 11111·11111···111·····111··1111···11····111·····11········1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 5 (153) | 1111··1·1111··1··11·1······111·11·1·1···11111··1111·······1·1··1·111·11·11·111·11··111···111·1·1····11··111111·······················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 6 (115) | 11····111·····1111·1111··········1··111·11·1·11······················································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 7 (63) | ····1111·1··1·111111111111·11·1111··111···1111··1·········1·1··1·111·11·11·111·11··111···111·1·1····11··111111································································································································································································································································································· |
| out 8 (179) | 111·1·111·1···1···1·111···1···111···11··111·1···1··································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 9 (149) | 1····1··11·111····1···11··1111·1·1······1111111·1·1·······1·1··1·111·11·11·111·11··111···111·1·1····11··111111·······················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| out 10 (93) | 1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111···················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111····························································· |
| out 11 (151) | ·························································111111111111111111111111111·······························111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 12 (121) | ·························································1·1·11·1···1···11·111·11··1··111···1·1·1···11··111111·····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···························································· |
| out 13 (181) | ·························································111111········111111·······1111111······1111111···········111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 14 (7) | ·······························································11············11············11···········1······································································································································································································································································································ |
| out 15 (183) | ·························································1·1·1··1····111···111···1·1··11·11·11·1·11111··1··111·····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 16 (115) | ·························································1·1········1111111·1··11··1··1·1·1····1·111········11·······················································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 17 (115) | ·························································11····111·····1111·1111··········1··111·11·1·11·····························································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 18 (25) | ··························································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111································································································································································································································································································· |
| out 19 (179) | ·························································111·1·111·1···1···1·111···1···111···11··111·1···1·········111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 20 (119) | ·························································11·1·11···11···11··11········1·11·1·1·1·111··111·1·11·······················································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| out 21 (93) | ·························································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111··························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···························································· |
| out 22 (121) | ··················································································································1···1·1·1····11··11·1·11··1··111··1·1·1·11··1111·111·1······························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 23 (91) | ··················································································································11·11····11·1·····1·1111111·······11111111·1·11·1···11·····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·····························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··························································· |
| out 24 (151) | ··················································································································1···1··1·1111·1··11··1··11·11···111·1·1···11···1·111·1·····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 25 (7) | ························································································································11············11············11···········1············································································································································································································································· |
| out 26 (153) | ··················································································································11·111···111·1111·1·11···11····11111······11·11··1··11·····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 27 (115) | ··················································································································1·1········1111111·1··11··1··1·1·1····1·111········11·······························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 28 (115) | ··················································································································11····111·····1111·1111··········1··111·11·1·11·····································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 29 (25) | ···················································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111········································································································································································································································ |
| out 30 (157) | ··················································································································1··1111·11·11·111·111·1·111··1··1·1··11···1··1111111·1·····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 31 (119) | ··················································································································11·1·11···11···11··11········1·11·1·1·1·111··111·1·11·······························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| out 32 (93) | ··················································································································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111··111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·····························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··························································· |
| out 33 (121) | ···········································································································································································1···1·1·1····11··11·1·11··1··111··1·1·1·11··1111·111·1···1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 34 (61) | ···········································································································································································111····11·1··111·1·1·1·1·111··111·1···11·111··111·1···1···························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·························································· |
| out 35 (121) | ···········································································································································································1·11····1·11·1·1···1111··1··1·11·111·11·1··1·1···1·11·1··1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 36 (7) | ·················································································································································································11············11············11···········1···················································································································································································· |
| out 37 (123) | ···········································································································································································111··1·11·111···11·1·11·1111··1··11·11··1··1··11·11···1··1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 38 (115) | ···········································································································································································1·1········1111111·1··11··1··1·1·1····1·111········11····1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 39 (115) | ···········································································································································································11····111·····1111·1111··········1··111·11·1·11··········1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 40 (25) | ············································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111··············································································································································································· |
| out 41 (119) | ···········································································································································································1·1··111···1·1··11·······111·111··111·1·1·····1·11·11·1··1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 42 (119) | ···········································································································································································11·1·11···11···11··11········1·11·1·1·1·111··111·1·11····1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| out 43 (55) | ···········································································································································································1··1··111··1·111·1·····111··1·1·1·111····1·······1·1···11·························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·························································· |
| out 44 (91) | ···········································································································································································································································1··1111111·1··1111······1111··1·11···1·1111··1111·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 45 (61) | ····································································································································································································································111····11·1··111·1·1·1·1·111··111·1···11·111··111·1···1··1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11························································· |
| out 46 (91) | ······································································································································································································································111·11····11··11·1··1·111·11·11·111··111·1····111····1·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 47 (7) | ··········································································································································································································································11············11············11···········1··························································································································· |
| out 48 (89) | ·····································································································································································································································11·111········1···11·1··1·1·1··1·1···1111·1·11111·11··1·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 49 (89) | ······································································································································································································································1·1·111·1··11····111111·····111···11·11·1··1··1·1···11·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 50 (85) | ·····································································································································································································································1··1·····111·1····1··1·1·1··11·1······11··1··1·1·111·11·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 51 (25) | ·····································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111······················································································································ |
| out 52 (89) | ······································································································································································································································1·11··1·1·11·1····11··11·1···11111·1·111···11··11····1·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 53 (89) | ·····································································································································································································································1·111·11···1····1·1·1··1·1···11·11··1·11·1···11111···11·1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| out 54 (55) | ····································································································································································································································1··1··111··1·111·1·····111··1·1·1·111····1·······1·1···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11························································· |
| out 55 (61) | ·····························································································································································································································································································1111·1·······1·1111·11··1·111··1··11···1·1··11··1·11111·1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 56 (31) | ································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111························································· |
| out 57 (61) | ·····························································································································································································································································································11··111···11·11·1··11··111·1·1·1·11·11·1···1·1111··1····1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 58 (7) | ···································································································································································································································································································11············11············11···········1·································································· |
| out 59 (59) | ·····························································································································································································································································································1··11·11··111·11·1·1···1·11·11···111·111···1····1·1·1···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 60 (63) | ·····························································································································································································································································································11·1111·1··111···1·1·1··1·111·11·1·11··1·11···1111·1··1·1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 61 (59) | ·····························································································································································································································································································1·1111·1·········1·11··11··1111··1·1·1·1·1·1·1·111··1·1·1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 62 (25) | ······························································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111····························································· |
| out 63 (55) | ·····························································································································································································································································································11·11··11··1·111·1···111111·1··1··1····1·······1···1····1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 64 (59) | ·····························································································································································································································································································1·1·1···1·11··1····111111··11·111·11···1·11··1··1··1··1·1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1 |
| out 65 (25) | ······························································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1······························································· |
| out 66 (31) | ·························································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11·· |
| out 67 (31) | ·························································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111 |
| out 68 (7) | ························································································································································································································································································································································1··1····1·1·····························1·····1···1···· |
| out 69 (7) | ····························································································································································································································································································································································11············11············11···········1········· |
| out 70 (25) | ·······················································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11····· |
| out 71 (25) | ························································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1·· |
| out 72 (25) | ·······················································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1·· |
| out 73 (25) | ·······················································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111···· |
| out 74 (25) | ························································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1···· |
| out 75 (25) | ·······················································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1·· |
| out 76 (25) | ·······················································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1······ |
| check 77 (62) | ·1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111································································································································································································································································································· |
| check 78 (62) | ·111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111········································································································································································································································ |
| check 79 (62) | ··111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·····················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111··············································································································································································· |
| check 80 (62) | 1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·············································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······················································································································ |
| check 81 (62) | 1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·····································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111····························································· |
| check 82 (62) | 111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1······························································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111···· |
| check 83 (62) | ··························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1······································································································································································································································· |
| check 84 (62) | ···························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·············································································································································································· |
| check 85 (62) | ·························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11····················································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····················································································································· |
| check 86 (62) | ·························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11············································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···························································· |
| check 87 (62) | ·························································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·····································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··· |
| check 88 (62) | ····················································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111············································································································································································· |
| check 89 (62) | ··················································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11····························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111···················································································································· |
| check 90 (62) | ··················································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11····················································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··························································· |
| check 91 (62) | ··················································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·············································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·· |
| check 92 (62) | ···········································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··················································································································· |
| check 93 (62) | ···········································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·························································· |
| check 94 (62) | ···········································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1··················································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11· |
| check 95 (62) | ····································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11························································· |
| check 96 (62) | ····································································································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11 |
| check 97 (62) | ·····························································································································································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···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 n399Noisy T states per run.
outputs k77
distance d3Exact, proved and witnessed here.
error coefficient A_{3}3,395Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.
wires N98
checks r21
V_{\mathrm{ex}}77T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.4975Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.4975Overhead 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 width77Rank of the output rows modulo the check rows.
Output gate
77 T0 CS0 CCZon 77 output wires
As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}
As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76 (output wires per term, separated by +)
This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.
Clifford correction
With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 75 single-wire gates and 493 \mathrm{CZ} gates: \mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{S}^\dagger on output 6, \mathrm{S} on output 7, \mathrm{S}^\dagger on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{S} on output 11, \mathrm{Z} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{S}^\dagger on output 16, \mathrm{S}^\dagger on output 17, \mathrm{S}^\dagger on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{S}^\dagger on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{S}^\dagger on output 27, \mathrm{S}^\dagger on output 28 and 544 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 568 correction gates
\mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{S}^\dagger on output 6, \mathrm{S} on output 7, \mathrm{S}^\dagger on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{S} on output 11, \mathrm{Z} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15, \mathrm{S}^\dagger on output 16, \mathrm{S}^\dagger on output 17, \mathrm{S}^\dagger on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{S}^\dagger on output 23, \mathrm{S} on output 24, \mathrm{S} on output 25, \mathrm{S}^\dagger on output 27, \mathrm{S}^\dagger on output 28, \mathrm{Z} on output 30, \mathrm{S} on output 31, \mathrm{Z} on output 32, \mathrm{Z} on output 34, \mathrm{S} on output 36, \mathrm{S}^\dagger on output 37, \mathrm{S}^\dagger on output 38, \mathrm{S}^\dagger on output 39, \mathrm{S} on output 41, \mathrm{S} on output 42, \mathrm{S} on output 43, \mathrm{S}^\dagger on output 44, \mathrm{Z} on output 45, \mathrm{S}^\dagger on output 46, \mathrm{S} on output 47, \mathrm{Z} on output 50, \mathrm{S} on output 54, \mathrm{Z} on output 55, \mathrm{S} on output 56, \mathrm{Z} on output 57, \mathrm{S} on output 58, \mathrm{S}^\dagger on output 59, \mathrm{S} on output 60, \mathrm{S}^\dagger on output 61, \mathrm{S} on output 63, \mathrm{S}^\dagger on output 64, \mathrm{S} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{S} on output 69, \mathrm{S} on check 77, \mathrm{S} on check 78, \mathrm{S} on check 79, \mathrm{S} on check 80, \mathrm{S} on check 81, \mathrm{S} on check 82, \mathrm{S} on check 83, \mathrm{S} on check 84, \mathrm{S} on check 85, \mathrm{S} on check 86, \mathrm{S} on check 87, \mathrm{S} on check 88, \mathrm{S} on check 89, \mathrm{S} on check 90, \mathrm{S} on check 91, \mathrm{S} on check 92, \mathrm{S} on check 93, \mathrm{S} on check 94, \mathrm{S} on check 95, \mathrm{S} on check 96, \mathrm{S} on check 97, \mathrm{CZ} on output 0, output 5, \mathrm{CZ} on output 0, output 6, \mathrm{CZ} on output 0, output 7, \mathrm{CZ} on output 0, output 8, \mathrm{CZ} on output 0, check 78, \mathrm{CZ} on output 0, check 80, \mathrm{CZ} on output 0, check 81, \mathrm{CZ} on output 0, check 82, \mathrm{CZ} on output 1, output 2, \mathrm{CZ} on output 1, output 5, \mathrm{CZ} on output 1, output 7, \mathrm{CZ} on output 1, output 8, \mathrm{CZ} on output 1, output 9, \mathrm{CZ} on output 1, output 10, \mathrm{CZ} on output 1, check 77, \mathrm{CZ} on output 1, check 78, \mathrm{CZ} on output 1, check 79, \mathrm{CZ} on output 1, check 81, \mathrm{CZ} on output 2, output 4, \mathrm{CZ} on output 2, output 5, \mathrm{CZ} on output 2, output 6, \mathrm{CZ} on output 2, output 7, \mathrm{CZ} on output 2, output 10, \mathrm{CZ} on output 2, check 78, \mathrm{CZ} on output 2, check 79, \mathrm{CZ} on output 2, check 80, \mathrm{CZ} on output 2, check 81, \mathrm{CZ} on output 2, check 82, \mathrm{CZ} on output 4, output 5, \mathrm{CZ} on output 4, output 7, \mathrm{CZ} on output 4, output 8, \mathrm{CZ} on output 4, check 77, \mathrm{CZ} on output 4, check 78, \mathrm{CZ} on output 4, check 79, \mathrm{CZ} on output 4, check 81, \mathrm{CZ} on output 5, output 7, \mathrm{CZ} on output 5, output 8, \mathrm{CZ} on output 5, check 77, \mathrm{CZ} on output 5, check 82, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 9, \mathrm{CZ} on output 6, check 80, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, check 77, \mathrm{CZ} on output 7, check 80, \mathrm{CZ} on output 7, check 81, \mathrm{CZ} on output 7, check 82, \mathrm{CZ} on output 8, output 10, \mathrm{CZ} on output 8, check 78, \mathrm{CZ} on output 8, check 79, \mathrm{CZ} on output 8, check 80, \mathrm{CZ} on output 8, check 82, \mathrm{CZ} on output 9, output 10, \mathrm{CZ} on output 9, check 77, \mathrm{CZ} on output 9, check 80, \mathrm{CZ} on output 9, check 81, \mathrm{CZ} on output 10, check 79, \mathrm{CZ} on output 10, check 80, \mathrm{CZ} on output 10, check 81, \mathrm{CZ} on output 11, output 16, \mathrm{CZ} on output 11, output 17, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 19, \mathrm{CZ} on output 11, check 83, \mathrm{CZ} on output 11, check 85, \mathrm{CZ} on output 11, check 86, \mathrm{CZ} on output 11, check 87, \mathrm{CZ} on output 12, output 13, \mathrm{CZ} on output 12, output 15, \mathrm{CZ} on output 12, output 19, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, check 83, \mathrm{CZ} on output 12, check 84, \mathrm{CZ} on output 12, check 86, \mathrm{CZ} on output 13, output 15, \mathrm{CZ} on output 13, output 16, \mathrm{CZ} on output 13, output 17, \mathrm{CZ} on output 13, output 18, \mathrm{CZ} on output 13, output 21, \mathrm{CZ} on output 13, check 83, \mathrm{CZ} on output 13, check 84, \mathrm{CZ} on output 13, check 85, \mathrm{CZ} on output 13, check 86, \mathrm{CZ} on output 13, check 87, \mathrm{CZ} on output 15, output 19, \mathrm{CZ} on output 15, output 20, \mathrm{CZ} on output 15, check 83, \mathrm{CZ} on output 15, check 84, \mathrm{CZ} on output 15, check 86, \mathrm{CZ} on output 16, output 19, \mathrm{CZ} on output 16, output 20, \mathrm{CZ} on output 16, check 87, \mathrm{CZ} on output 17, output 19, \mathrm{CZ} on output 17, output 20, \mathrm{CZ} on output 17, check 85, \mathrm{CZ} on output 18, check 85, \mathrm{CZ} on output 18, check 86, \mathrm{CZ} on output 18, check 87, \mathrm{CZ} on output 19, output 21, \mathrm{CZ} on output 19, check 83, \mathrm{CZ} on output 19, check 84, \mathrm{CZ} on output 19, check 85, \mathrm{CZ} on output 19, check 87, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, check 85, \mathrm{CZ} on output 20, check 86, \mathrm{CZ} on output 21, check 84, \mathrm{CZ} on output 21, check 85, \mathrm{CZ} on output 21, check 86, \mathrm{CZ} on output 22, output 23, \mathrm{CZ} on output 22, output 24, \mathrm{CZ} on output 22, output 26, \mathrm{CZ} on output 22, output 27, \mathrm{CZ} on output 22, output 28, \mathrm{CZ} on output 22, output 29, \mathrm{CZ} on output 22, check 89, \mathrm{CZ} on output 22, check 90, \mathrm{CZ} on output 22, check 91, \mathrm{CZ} on output 23, output 32, \mathrm{CZ} on output 23, check 88, \mathrm{CZ} on output 23, check 90, \mathrm{CZ} on output 24, output 27, \mathrm{CZ} on output 24, output 28, \mathrm{CZ} on output 24, output 29, \mathrm{CZ} on output 24, output 30, \mathrm{CZ} on output 24, output 32, \mathrm{CZ} on output 24, check 88, \mathrm{CZ} on output 24, check 89, \mathrm{CZ} on output 24, check 90, \mathrm{CZ} on output 24, check 91, \mathrm{CZ} on output 26, output 31, \mathrm{CZ} on output 26, check 88, \mathrm{CZ} on output 26, check 90, \mathrm{CZ} on output 27, output 30, \mathrm{CZ} on output 27, output 31, \mathrm{CZ} on output 27, check 91, \mathrm{CZ} on output 28, output 30, \mathrm{CZ} on output 28, output 31, \mathrm{CZ} on output 28, check 89, \mathrm{CZ} on output 29, check 89, \mathrm{CZ} on output 29, check 90, \mathrm{CZ} on output 29, check 91, \mathrm{CZ} on output 30, output 32, \mathrm{CZ} on output 30, check 88, \mathrm{CZ} on output 30, check 89, \mathrm{CZ} on output 30, check 91, \mathrm{CZ} on output 31, output 32, \mathrm{CZ} on output 31, check 89, \mathrm{CZ} on output 31, check 90, \mathrm{CZ} on output 32, check 88, \mathrm{CZ} on output 32, check 89, \mathrm{CZ} on output 32, check 90, \mathrm{CZ} on output 33, output 34, \mathrm{CZ} on output 33, output 35, \mathrm{CZ} on output 33, output 37, \mathrm{CZ} on output 33, output 38, \mathrm{CZ} on output 33, output 39, \mathrm{CZ} on output 33, output 40, \mathrm{CZ} on output 33, output 48, \mathrm{CZ} on output 33, output 49, \mathrm{CZ} on output 33, output 51, \mathrm{CZ} on output 33, output 54, \mathrm{CZ} on output 33, output 59, \mathrm{CZ} on output 33, output 60, \mathrm{CZ} on output 33, output 62, \mathrm{CZ} on output 33, output 65, \mathrm{CZ} on output 33, output 70, \mathrm{CZ} on output 33, output 71, \mathrm{CZ} on output 33, output 73, \mathrm{CZ} on output 33, output 76, \mathrm{CZ} on output 33, check 92, \mathrm{CZ} on output 33, check 93, \mathrm{CZ} on output 33, check 94, \mathrm{CZ} on output 34, output 35, \mathrm{CZ} on output 34, output 37, \mathrm{CZ} on output 34, output 41, \mathrm{CZ} on output 34, output 59, \mathrm{CZ} on output 34, output 60, \mathrm{CZ} on output 34, output 62, \mathrm{CZ} on output 34, output 65, \mathrm{CZ} on output 34, check 93, \mathrm{CZ} on output 35, output 37, \mathrm{CZ} on output 35, output 38, \mathrm{CZ} on output 35, output 39, \mathrm{CZ} on output 35, output 40, \mathrm{CZ} on output 35, output 48, \mathrm{CZ} on output 35, output 49, \mathrm{CZ} on output 35, output 51, \mathrm{CZ} on output 35, output 54, \mathrm{CZ} on output 35, output 59, \mathrm{CZ} on output 35, output 60, \mathrm{CZ} on output 35, output 62, \mathrm{CZ} on output 35, output 65, \mathrm{CZ} on output 35, output 70, \mathrm{CZ} on output 35, output 71, \mathrm{CZ} on output 35, output 73, \mathrm{CZ} on output 35, output 76, \mathrm{CZ} on output 35, check 92, \mathrm{CZ} on output 35, check 93, \mathrm{CZ} on output 35, check 94, \mathrm{CZ} on output 37, output 41, \mathrm{CZ} on output 37, output 42, \mathrm{CZ} on output 37, output 43, \mathrm{CZ} on output 37, output 48, \mathrm{CZ} on output 37, output 49, \mathrm{CZ} on output 37, output 51, \mathrm{CZ} on output 37, output 54, \mathrm{CZ} on output 37, output 59, \mathrm{CZ} on output 37, output 60, \mathrm{CZ} on output 37, output 62, \mathrm{CZ} on output 37, output 65, \mathrm{CZ} on output 37, output 70, \mathrm{CZ} on output 37, output 71, \mathrm{CZ} on output 37, output 73, \mathrm{CZ} on output 37, output 76, \mathrm{CZ} on output 37, check 93, \mathrm{CZ} on output 38, output 41, \mathrm{CZ} on output 38, output 42, \mathrm{CZ} on output 38, output 48, \mathrm{CZ} on output 38, output 49, \mathrm{CZ} on output 38, output 51, \mathrm{CZ} on output 38, output 54, \mathrm{CZ} on output 38, output 59, \mathrm{CZ} on output 38, output 60, \mathrm{CZ} on output 38, output 62, \mathrm{CZ} on output 38, output 65, \mathrm{CZ} on output 38, output 70, \mathrm{CZ} on output 38, output 71, \mathrm{CZ} on output 38, output 73, \mathrm{CZ} on output 38, output 76, \mathrm{CZ} on output 38, check 94, \mathrm{CZ} on output 39, output 41, \mathrm{CZ} on output 39, output 42, \mathrm{CZ} on output 39, output 48, \mathrm{CZ} on output 39, output 49, \mathrm{CZ} on output 39, output 51, \mathrm{CZ} on output 39, output 54, \mathrm{CZ} on output 39, output 59, \mathrm{CZ} on output 39, output 60, \mathrm{CZ} on output 39, output 62, \mathrm{CZ} on output 39, output 65, \mathrm{CZ} on output 39, output 70, \mathrm{CZ} on output 39, output 71, \mathrm{CZ} on output 39, output 73, \mathrm{CZ} on output 39, output 76, \mathrm{CZ} on output 39, check 92, \mathrm{CZ} on output 40, check 92, \mathrm{CZ} on output 40, check 93, \mathrm{CZ} on output 40, check 94, \mathrm{CZ} on output 41, output 48, \mathrm{CZ} on output 41, output 49, \mathrm{CZ} on output 41, output 51, \mathrm{CZ} on output 41, output 54, \mathrm{CZ} on output 41, output 59, \mathrm{CZ} on output 41, output 60, \mathrm{CZ} on output 41, output 62, \mathrm{CZ} on output 41, output 65, \mathrm{CZ} on output 41, output 70, \mathrm{CZ} on output 41, output 71, \mathrm{CZ} on output 41, output 73, \mathrm{CZ} on output 41, output 76, \mathrm{CZ} on output 41, check 92, \mathrm{CZ} on output 41, check 94, \mathrm{CZ} on output 42, output 43, \mathrm{CZ} on output 42, output 48, \mathrm{CZ} on output 42, output 49, \mathrm{CZ} on output 42, output 51, \mathrm{CZ} on output 42, output 54, \mathrm{CZ} on output 42, output 59, \mathrm{CZ} on output 42, output 60, \mathrm{CZ} on output 42, output 62, \mathrm{CZ} on output 42, output 65, \mathrm{CZ} on output 42, output 70, \mathrm{CZ} on output 42, output 71, \mathrm{CZ} on output 42, output 73, \mathrm{CZ} on output 42, output 76, \mathrm{CZ} on output 42, check 92, \mathrm{CZ} on output 42, check 93, \mathrm{CZ} on output 43, output 59, \mathrm{CZ} on output 43, output 60, \mathrm{CZ} on output 43, output 62, \mathrm{CZ} on output 43, output 65, \mathrm{CZ} on output 43, check 92, \mathrm{CZ} on output 43, check 93, \mathrm{CZ} on output 44, output 45, \mathrm{CZ} on output 44, output 48, \mathrm{CZ} on output 44, output 49, \mathrm{CZ} on output 44, output 52, \mathrm{CZ} on output 44, output 53, \mathrm{CZ} on output 44, output 54, \mathrm{CZ} on output 44, output 60, \mathrm{CZ} on output 44, output 61, \mathrm{CZ} on output 44, output 62, \mathrm{CZ} on output 44, output 63, \mathrm{CZ} on output 44, output 71, \mathrm{CZ} on output 44, output 72, \mathrm{CZ} on output 44, output 73, \mathrm{CZ} on output 44, output 74, \mathrm{CZ} on output 44, check 95, \mathrm{CZ} on output 44, check 96, \mathrm{CZ} on output 45, output 46, \mathrm{CZ} on output 45, output 48, \mathrm{CZ} on output 45, output 52, \mathrm{CZ} on output 45, output 60, \mathrm{CZ} on output 45, output 61, \mathrm{CZ} on output 45, output 62, \mathrm{CZ} on output 45, output 63, \mathrm{CZ} on output 45, check 95, \mathrm{CZ} on output 46, output 48, \mathrm{CZ} on output 46, output 49, \mathrm{CZ} on output 46, output 52, \mathrm{CZ} on output 46, output 53, \mathrm{CZ} on output 46, output 54, \mathrm{CZ} on output 46, output 60, \mathrm{CZ} on output 46, output 61, \mathrm{CZ} on output 46, output 62, \mathrm{CZ} on output 46, output 63, \mathrm{CZ} on output 46, output 71, \mathrm{CZ} on output 46, output 72, \mathrm{CZ} on output 46, output 73, \mathrm{CZ} on output 46, output 74, \mathrm{CZ} on output 46, check 95, \mathrm{CZ} on output 46, check 96, \mathrm{CZ} on output 48, output 49, \mathrm{CZ} on output 48, output 51, \mathrm{CZ} on output 48, output 52, \mathrm{CZ} on output 48, output 53, \mathrm{CZ} on output 48, output 60, \mathrm{CZ} on output 48, output 61, \mathrm{CZ} on output 48, output 62, \mathrm{CZ} on output 48, output 63, \mathrm{CZ} on output 48, output 71, \mathrm{CZ} on output 48, output 72, \mathrm{CZ} on output 48, output 73, \mathrm{CZ} on output 48, output 74, \mathrm{CZ} on output 48, check 92, \mathrm{CZ} on output 48, check 95, \mathrm{CZ} on output 49, output 51, \mathrm{CZ} on output 49, output 52, \mathrm{CZ} on output 49, output 53, \mathrm{CZ} on output 49, output 54, \mathrm{CZ} on output 49, output 60, \mathrm{CZ} on output 49, output 61, \mathrm{CZ} on output 49, output 62, \mathrm{CZ} on output 49, output 63, \mathrm{CZ} on output 49, output 71, \mathrm{CZ} on output 49, output 72, \mathrm{CZ} on output 49, output 73, \mathrm{CZ} on output 49, output 74, \mathrm{CZ} on output 49, check 92, \mathrm{CZ} on output 49, check 96, \mathrm{CZ} on output 50, output 51, \mathrm{CZ} on output 50, output 54, \mathrm{CZ} on output 50, output 60, \mathrm{CZ} on output 50, output 61, \mathrm{CZ} on output 50, output 62, \mathrm{CZ} on output 50, output 63, \mathrm{CZ} on output 50, output 71, \mathrm{CZ} on output 50, output 72, \mathrm{CZ} on output 50, output 73, \mathrm{CZ} on output 50, output 74, \mathrm{CZ} on output 51, output 52, \mathrm{CZ} on output 51, output 53, \mathrm{CZ} on output 51, check 92, \mathrm{CZ} on output 51, check 95, \mathrm{CZ} on output 51, check 96, \mathrm{CZ} on output 52, output 53, \mathrm{CZ} on output 52, output 54, \mathrm{CZ} on output 52, output 60, \mathrm{CZ} on output 52, output 61, \mathrm{CZ} on output 52, output 62, \mathrm{CZ} on output 52, output 63, \mathrm{CZ} on output 52, output 71, \mathrm{CZ} on output 52, output 72, \mathrm{CZ} on output 52, output 73, \mathrm{CZ} on output 52, output 74, \mathrm{CZ} on output 52, check 96, \mathrm{CZ} on output 53, output 60, \mathrm{CZ} on output 53, output 61, \mathrm{CZ} on output 53, output 62, \mathrm{CZ} on output 53, output 63, \mathrm{CZ} on output 53, output 71, \mathrm{CZ} on output 53, output 72, \mathrm{CZ} on output 53, output 73, \mathrm{CZ} on output 53, output 74, \mathrm{CZ} on output 53, check 95, \mathrm{CZ} on output 54, output 60, \mathrm{CZ} on output 54, output 61, \mathrm{CZ} on output 54, output 62, \mathrm{CZ} on output 54, output 63, \mathrm{CZ} on output 54, check 92, \mathrm{CZ} on output 54, check 95, \mathrm{CZ} on output 55, output 57, \mathrm{CZ} on output 55, output 60, \mathrm{CZ} on output 55, output 62, \mathrm{CZ} on output 55, output 63, \mathrm{CZ} on output 55, output 70, \mathrm{CZ} on output 55, output 72, \mathrm{CZ} on output 55, output 73, \mathrm{CZ} on output 55, output 75, \mathrm{CZ} on output 55, check 97, \mathrm{CZ} on output 56, output 62, \mathrm{CZ} on output 56, output 63, \mathrm{CZ} on output 56, output 64, \mathrm{CZ} on output 56, output 65, \mathrm{CZ} on output 57, output 60, \mathrm{CZ} on output 57, output 62, \mathrm{CZ} on output 57, output 63, \mathrm{CZ} on output 57, output 70, \mathrm{CZ} on output 57, output 72, \mathrm{CZ} on output 57, output 73, \mathrm{CZ} on output 57, output 75, \mathrm{CZ} on output 57, check 97, \mathrm{CZ} on output 59, output 60, \mathrm{CZ} on output 59, output 63, \mathrm{CZ} on output 59, output 65, \mathrm{CZ} on output 59, output 70, \mathrm{CZ} on output 59, output 72, \mathrm{CZ} on output 59, output 73, \mathrm{CZ} on output 59, output 75, \mathrm{CZ} on output 59, check 93, \mathrm{CZ} on output 60, output 61, \mathrm{CZ} on output 60, output 64, \mathrm{CZ} on output 60, output 65, \mathrm{CZ} on output 60, output 70, \mathrm{CZ} on output 60, output 72, \mathrm{CZ} on output 60, output 73, \mathrm{CZ} on output 60, output 75, \mathrm{CZ} on output 60, check 93, \mathrm{CZ} on output 60, check 95, \mathrm{CZ} on output 60, check 97, \mathrm{CZ} on output 61, output 63, \mathrm{CZ} on output 61, output 65, \mathrm{CZ} on output 61, output 70, \mathrm{CZ} on output 61, output 72, \mathrm{CZ} on output 61, output 73, \mathrm{CZ} on output 61, output 75, \mathrm{CZ} on output 61, check 95, \mathrm{CZ} on output 62, output 65, \mathrm{CZ} on output 62, check 93, \mathrm{CZ} on output 62, check 95, \mathrm{CZ} on output 62, check 97, \mathrm{CZ} on output 63, output 64, \mathrm{CZ} on output 63, output 65, \mathrm{CZ} on output 63, output 70, \mathrm{CZ} on output 63, output 72, \mathrm{CZ} on output 63, output 73, \mathrm{CZ} on output 63, output 75, \mathrm{CZ} on output 63, check 95, \mathrm{CZ} on output 63, check 97, \mathrm{CZ} on output 64, output 65, \mathrm{CZ} on output 64, output 70, \mathrm{CZ} on output 64, output 72, \mathrm{CZ} on output 64, output 73, \mathrm{CZ} on output 64, output 75, \mathrm{CZ} on output 65, check 93, \mathrm{CZ} on output 67, output 73, \mathrm{CZ} on output 67, output 74, \mathrm{CZ} on output 67, output 75, \mathrm{CZ} on output 67, output 76, \mathrm{CZ} on output 70, output 71, \mathrm{CZ} on output 70, output 72, \mathrm{CZ} on output 70, output 73, \mathrm{CZ} on output 70, output 74, \mathrm{CZ} on output 70, output 75, \mathrm{CZ} on output 70, output 76, \mathrm{CZ} on output 70, check 94, \mathrm{CZ} on output 70, check 97, \mathrm{CZ} on output 71, output 72, \mathrm{CZ} on output 71, output 73, \mathrm{CZ} on output 71, output 74, \mathrm{CZ} on output 71, output 75, \mathrm{CZ} on output 71, output 76, \mathrm{CZ} on output 71, check 94, \mathrm{CZ} on output 71, check 96, \mathrm{CZ} on output 72, output 73, \mathrm{CZ} on output 72, output 74, \mathrm{CZ} on output 72, output 75, \mathrm{CZ} on output 72, output 76, \mathrm{CZ} on output 72, check 96, \mathrm{CZ} on output 72, check 97, \mathrm{CZ} on output 73, output 74, \mathrm{CZ} on output 73, output 75, \mathrm{CZ} on output 73, output 76, \mathrm{CZ} on output 73, check 94, \mathrm{CZ} on output 73, check 96, \mathrm{CZ} on output 73, check 97, \mathrm{CZ} on output 74, output 75, \mathrm{CZ} on output 74, output 76, \mathrm{CZ} on output 74, check 96, \mathrm{CZ} on output 75, output 76, \mathrm{CZ} on output 75, check 97, \mathrm{CZ} on output 76, check 94
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 1, 2, 4, 5, 6, 13, 15, 16, 23, 25, 30, 36, 38, 39, 40, 42, 44, 45, 47, 51, 57, 63, 72, 73 and 133 more (listed below); \mathrm{T}^5 on rotations 8, 9, 10, 58, 66, 67, 71, 121, 122, 124, 128, 175, 176, 178, 186, 231, 238, 239, 286, 295, 299, 343, 345, 346 and 1 more (listed below); \mathrm{T}^\dagger on rotations 0, 7, 14, 60, 61, 64, 171, 182, 185, 229, 232, 234, 241, 242, 285, 288, 289, 292, 349, 352, and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.
All 157 rotations at T³
1, 2, 4, 5, 6, 13, 15, 16, 23, 25, 30, 36, 38, 39, 40, 42, 44, 45, 47, 51, 57, 63, 72, 73, 76, 79, 86, 89, 90, 94, 97, 98, 99, 104, 105, 107, 109, 110, 111, 112, 114, 116, 117, 119, 120, 125, 132, 134, 137, 140, 144, 145, 146, 147, 149, 154, 155, 156, 157, 158, 163, 165, 167, 168, 170, 172, 177, 184, 189, 190, 191, 193, 196, 197, 200, 202, 206, 207, 208, 209, 210, 211, 213, 214, 216, 219, 220, 221, 223, 226, 227, 228, 230, 233, 235, 243, 244, 251, 253, 258, 264, 266, 267, 268, 270, 272, 273, 275, 279, 291, 300, 301, 304, 307, 314, 317, 318, 322, 325, 326, 327, 332, 333, 335, 337, 338, 339, 340, 342, 344, 348, 350, 353, 357, 359, 360, 362, 363, 364, 365, 369, 371, 372, 374, 376, 377, 378, 379, 381, 382, 383, 387, 388, 389, 391, 394, 396
All 25 rotations at T⁵
8, 9, 10, 58, 66, 67, 71, 121, 122, 124, 128, 175, 176, 178, 186, 231, 238, 239, 286, 295, 299, 343, 345, 346, 356
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/399.77.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-399.77.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 3,395 faults of weight 3 are undetectable and damaging, so A_{3}=3{,}395. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).
A damaging fault of weight 3 sits on columns [0,1,38].
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 that glues catalogued small factories along a graph of paired-column contractions; exact distance verified from columns; a verified witness, not a maximum
Found by: AI search: graph gluing
Discovery: AI search
1 recorded source
[
{
"regime": "AI search: graph gluing",
"file": "master_catalog/imports/2026-09-18_graph_gluing_d3/factories.json",
"label": "graph gluing [[399,77,3]]",
"N": 98,
"d": 3,
"d_is_exact": true,
"origin": null,
"provenance": "AI search: graph gluing -- seven [[63,11,3]] glued along K7 by 21 paired-column contraction(s) (independent ports); construction and witness in master_catalog/imports/2026-09-18_graph_gluing_d3/witnesses/graph_complete_n399_k77_d3.json",
"notes": "Exact A3=3395 independently counted; details in master_catalog/imports/2026-09-18_graph_gluing_d3/README.md. General gluing has prior art; publication novelty is not asserted."
}
]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/399.77.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]
facts, problems = VC.derive(columns, k, N) # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N) # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
problems or "verified")
Raw record
Show the JSON this page is built from
Source: master_catalog.json, factories[1017].