The circuit
The 52\times206 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 |
|---|---|
| out 0 (77) | 1·11·1·1········1·1··111·1·1···1···1·1···1··1··1··1······11····111·1·····11··1··1···1111·11···1···1·1·1·1···11·1·······1·1·1111·1··1··1···1··1···1···1··1·····11·····1·1·11····11······1···1··1111111···1·1··1 |
| out 1 (75) | 1····11·····11·············11······111·····11·1111···1·1····1·1····11···111·1·1··1·1·11··1111·········1·1····11·····11··········1·1···1·111·····11··1111····11···1··1·····11··1111····1·1···11·11·111111······ |
| out 2 (79) | 1·1····111·1·····11··11··11·····11··1111··1··1··1···1··1···1·1·11··11········11····1111····1··1···1·1···1···1··111·1····11·11·11····11···1111·1···1···1···1··1··1··1·111··11···········11····1111····1··1·1··1 |
| out 3 (85) | 1·1··1·1·11·11··11·1·11··1··1··11··11····1·111·11····1···1···11··1·1····11·1·······1·111··1········11···1···11·1·11·11·11·111·1··1111·1··1···1··111··11·····1·1····11····11···11·11··········1·111··1·1·····11 |
| out 4 (87) | 1·····111·1111··1··1·111··11···11···1·11·11··11···1·11···11·11··11·1···1··1·11···1··1··1····1·····1·····1·····111·1111·1··1111·11··11····1·1111···1·1···1·1·1·11·1·1···1·11·1···1····111····1·1··1·····1··1··· |
| out 5 (85) | 1·······1·111····111·1··111·1···11···111··11·1······1··1··11·111·1·11···1··1··1····11·1····1··1··11·1···1·······1·111···1111··11··1·11····111·1·1·1·······1··1·11··111···111··1··11·····1····11·1····11·111··1 |
| out 6 (87) | ··1·······1·11··111····1·11····1·····1···11·1·1·1·1··1·1·11111·1·1··1··11·1·1·1·11·1·111··11··1·····1·······1·····1·11·111···111···1······1··11··1··1·1·1···111111·1·1···1·11·1·1···1·1·1··111·111··11··1····1 |
| out 7 (79) | ··1···1···1·11··1·1····1·1·····1·1···11··1··1·1·111··1···1111··1·1··1···1·1·1·1··1·1·11····1··1···1·1····1··1·1···1·11·1·1···11····1·1····11·1···1··1·111···1·1111···1···1·1··1·1·····1·1···11·11····1··1·1··1 |
| out 8 (77) | ·11··1··1··11···11·1···1··11···11··1·1·1·1··11·1··1·1··111···1······1···111···1····1·11··1·1·····1····1···1·11··1··11··11·1··1·11··11·1···1·11···11··1··1·1··11····1·······1··111·······1····1·11·11·1···1···· |
| out 9 (83) | 1····11·1···1···1·11···1·1·1···1·1·1·11··111···11·1········1·11·1··1····11···1······111··1··1·1··11·1·1·1··1·11·1···1··1·11··11·1··1·11···11·11·1····11·1·······1··11··1··1···11·1·····1······111·11··11111··1 |
| out 10 (31) | ········1·1········1·1··············1·1·······1·1··············11·······1·1··········1·1·······1·1··············1·1·······11·············1·1········1·1··············1·1······1·1··············1·1·······1···· |
| out 11 (85) | ·····111··11·1···111·····111····11·1··11··1·1111·1··11····11111··1·······1··1····1·······11·1·1···111·1······111··11·1··111···111···111····11·1··11·11·1·11·1··111·11····1·····1······1·····1·····111··11·1·11 |
| out 12 (93) | ··1··1·111·111···1·····1·11·1······1··11··111·11·11·1·····1·11··111····11111·1···1·1111···1·1····1·11·······11·111·111··1····111··1···1····11·1·11··11·11·1····1·1·1···1·1··1·11111····1····11111···1·11·1··11 |
| out 13 (77) | ··1··1·····1····11·····1··11···1···1·111·11·11·11·1·1··1·1···1·1·1··1····11···1····1·111·111··········1·····11·····1···11····1·11··1··1···11111··11··11·1·1··11····1·1···1·1···11·······1·1··1·1111111········ |
| out 14 (83) | 1·1··11···1···1·1·1··1·1·1·1···1·1·11·1··111···1·11······111·111·1·11····11··1······1····1··1·1·····1·1·1···111···1····1·1·1·11·1··1·11··1·1·11·1····1·11·····111··111···111···111·····1······1···11··111····1 |
| out 15 (85) | ·1····1·11111··11111··11·11·1·1111···111·····1···11·1····111·1···1······1··1·1·······1······1·1···111·····1···1·11111·11111·1111··1111····111·····1····11·1···111··1·····1····1··11····1·······1······111·1·11 |
| out 16 (77) | ·····1··1··11···11···1·1··11···11··11111111·11·1··1·1··1·11··1······1····1····1····1··11··11·····1····1······1··1··11··11··1·1·11··11·1··111111··11··1··1·1··111···1·······1···1········1····1··11·111···1···· |
| out 17 (77) | ·····1·1111··1···11··111···1····11··1·····1·11····1··1····11·1··11·········11······11·1··11·1·1··111··1······1·1111··1··11·111··1···11···1····1··11·····1···1··11·11···1·1········1···1······11·1·111··1111·1· |
| out 18 (85) | 1·1··1·1··1··1·····1·11····1·······111······1·11··1··1·1··1·11··11·11····1··111··1·1111··1111····11···1·1···11·1··1··1····111···1·····1··11······1··11··1···11·1·1·1···1·111···1······111···11111·1111·1·111·· |
| out 19 (79) | ··1··11·1111·······1·111·11········11·11··1·1·11111·11····1·1·1··········1·1·····1·11·1···1·1······11··1····111·1111······111111······1··1·11·1··1··11111·1·1··1·1··1··········1··1·········111·1···1··1····11 |
| out 20 (99) | ··1··1·····111···11··11··1111···11·11111··111111·1··11·····11···1·······111·11···1·1·11··11·1·1···1·1·1·····11·····111··11·11·111·1·1111·1111·1·111·11·1··1·1···11·····1······1111····11····11·11·111·111·1··1 |
| out 21 (83) | ············11··111···11·······1·1··1·1··1·1··1·111··1·1·1·111·111·11··11·1·1·1··1·1·······11·1···1·1···············11·111··11·····1·1···1·1·1··1···1·111···111·11·1·1·1·1111·1·11·1··1·1···11·······1111·1··1 |
| out 22 (79) | 1·····111·1111·111····11··1·1··11······1·11··11···1·11···11·11··11·1·1··1···1····1··11······1·····1·····1·····111·1111111···11·1··111·······111···1·1···1·1·1·11·1·1···1·11···1·······1·····1·11·······1··1··· |
| out 23 (77) | 1·1····1···1·····11······11·11··11··1111··1111··1···1··1···1·1··1··11·····1········1111····11·1···1·1···1···1··1···1····11····11··1·11···1111·1·111···1···1··1··1··1···1··11····11···········1111····1111·1··1 |
| out 24 (91) | 1·1··1······11···1···1·····11····1·111·····11·111····1·1··1·111····11··111··1·1·11·1111··1111·1···1···1·1···11······11··1··1····1·1··11··11·····11·1111·····11·1·1·11·····111·11·1····1·1··111111·1111111·1··· |
| out 25 (53) | ··1···11··1·1······1·11········1····1·····111···1·········1··11·11······1·1····1·····1····1·1····1··········1·11··1·1·····111······1·····1····1·11····1········1···11··1·1····1·11·············1····1·11·1···· |
| out 26 (79) | ··1··11·11·1·····1·11111·11·1······11111··1···11·11·1·····1·1·1·1······1···1·1···1·11·····1······1·11·······111·11·1····1·111111··1···1··1111·1·····11·11·1····1·1··1··1····1·····1····1····111·····1····1··11 |
| out 27 (85) | 1·1···1···1·11··1·1··111·1·····1·1··1·1··1·1··1·111··111·1111··1·1··1···1···1·1··1·1·······11·1···1·1···1···1·1···1·11·1·1·1111····1·1···1·1·1··1···1·111···111111···1···1·1··1··1····1·1···11·······1111·1··1 |
| out 28 (83) | ··1··111···1····11···111··11···111·11····111·1·11·1·1··1·1····11·1··1····1····1·1··1····11111·········1·····1111···1···11··111·11··1111··1···11·1·1··11·1·1··11·····11···1·1···1·1······1··1·1····111111······ |
| out 29 (77) | 111····1·11·1··11··1·11········1·····1·····1······1····1·11··1·111·11···1··1·11····111····111····111····1·1·1··1·11·1·11··111······1······1·····1·······1····111···1·1·1·111··1···1····111···111····11·1·11·1· |
| out 30 (93) | ··1··111···1····1·1····1··11···111·1·111·11·11·1·11·1··1·1····11·1··1··1·11···1·1··1·111·111·····11···1·····1111···1···1·1···1·11··1111···11111··11··1·11·1··11·····11···1·111·11·······1··1·1·1111111···11··· |
| out 31 (85) | 1·····111·1111···1···1·1··1·1··11······1·111111·111·11···11·11··11·1··1·1·1·1····1··11···········1······1·····111·1111··1··1·1·1··111·······111·111·1·111·1·1·11·1·1···1·11···1·11····1·····1·11······1··1···· |
| out 32 (31) | ··1···1··········1···1······1·········1···1········1······1··1·········1··1··1·········1··1·········1·······1·1·········1··1······1········1··1················1···1········1···1······1·········1··1········1 |
| out 33 (63) | ··1····1·11·1···11·1··1··1·1···11····1·······11········1·1··1·······1······1··1··1··1··1·1·11·····111·······1··1·11·1··11·1·1·1·1··11·····1·······1·1······1·11··1·········1······1·····1···1·1··11··1·1··1·11 |
| out 34 (77) | 1·1···111··11·····1······11·····111····1···1·1···1··1··1···1···111·11··1··1··11··1·11··1··11··1··1··1···1···1·111··11····1····11····11······1···1·1····1··1··1··1····1·1·1111···11·····11···111··1··111·11···1 |
| out 35 (87) | 1····111·11·······11·1·1····1···11·1·11······11··11····1··1111111··11··1·111··1··1···1·1··11··1·1·11····1····111·11······111·1····1·111···11······1·1··11····1·111·111·1··111··11·1·····1···1··1·1··11··1·1·1· |
| out 36 (45) | ······11·············11·············11····111···11···········11···········1··········11···111····11···········11···········11············11···1111····11···········11···········11·············11···1111·11··· |
| out 37 (77) | 1···11·1··1··1···1···11····11······1·1····1·1·11·····1·1·····1··11·11··111··1·1··1·11·1··1·11····11···1·1····1·1··1··1··1··11···1·1···1···1···1··1··11······11·····1···1·1111·11······1·1···111·1·11·1·1·11··· |
| out 38 (93) | ··1···1·····11··111···11·1··1··1·1··1····1·1·11··11··1·1·1111··111··1··11·1·111··1·1···1···1111··11·1·······1·1·····11·111··111···11·1···1···1··1·1·1··11···111111···1·1·1·11·1·11····111···11···1···111111··1 |
| out 39 (93) | 1····11··1··1····11··111····1···11··111···11·111111····1··1111·1·1·11···1111··1··11····1···1··1··111····1····11··1··1···11·111····1·11···111··1·1·1·11111····1·111·1·1···111··11111·····1···1····1···11·111·1· |
| out 40 (75) | 1····11···11····1·1····1·1·1···1···11····1·1···1··1······1·1·111·1·1·····1···1··1···1··1·11·1·1···1·1·1·1····11···11···1·1···11·1··1··1··1···1··1····1··1·····1·1··111··111····1·1·····1···1··1··1111·111·1··1 |
| out 41 (91) | 1·1··111········111··1·1·1·11··1···11·1··111···1111·1····111·1·111·1···1·11·····1···1····1··1·1··1··111·1···1111·······111·1·11·1·11··1··1·1·11·1····1111·1···111··1·1·1·11·1··111·········1··1···11··1111···1 |
| check 42 (92) | 1·1·····11·1····111··11···111··1····1·11·111··1·1···1····11111·1·1·1···11··1····11·1·111·1··1·1····1··1·1···1···11·1···111·11··11·11·····1·1111·1···1·1···1···1111·1·1···11·1·1··11········111·11111··111···1· |
| check 43 (78) | 1·····1·11·1·1·1·····111·1·1···1····1··1···1·1·1111······1·11··1····1··1·11··1··11·1·11····1·····1··1·1·1·····1·11·1·11····1111·1··1·····1··1···1·1··1111·····1·11···1·····11··11······1···111·11··1·1···1···1 |
| check 44 (94) | 11·····11·1·11·11·11·············1·1··11·11·1·11·11·11·1·111··111··11··11·······11·1111···1·1····1·11·1·1·1····11·1·1111·11··········11····1111··1··11·11·1·11111···11·1··111·1············111111··11··1·1··11 |
| check 45 (124) | 11·11········11111··11·111··1111·111···11···11111··11·1·1··11·····1·1111·111·111111·····11··11·111··1111·1·1111111111····11·1··111··1··11111·1111··1···111·11111··111111111··11··1··111···1··11111·1111·1·111· |
| check 46 (102) | ···1······1·1·1···1·1·1111···1·····11··1·1·11·11·11·11·1·1··11·1·11···1·11111··11111···11··1··1·111·11·1·1·1·1·1·11111·1·····111·1·1·1··111····11··11···11······1111111·11·1·11·1···1···1···111·11·1··11·1··11 |
| check 47 (106) | 1··1·1····11111··11··11···11·1··1··111····111·1111·1·11···1·1·······1···111·1·1·11···111111·111··11··11··1··1111····11········1·1·1··11111111··1111111····1·11··11·11··11·1·1111····1·11··1·11111·11·111·····1 |
| check 48 (108) | ·1·1···11····1·1·111··1·11··1·1······1·1·111·11···1111·111··111·1···1111··11111111·1·1111·11111··1···1·····11··1·111·1·1··1·11·1··1111···1·1·11··1·11····1··11·111·1111·1··1·1··11·11·111·1·11······11···1·111 |
| check 49 (122) | 11··1·1···1··1·111111·111··11··111111·11··1·1111·1·111·1·11111··11·11···11·11·1··11··1·111·1··111·1·111·1·1··1·111·1·11111·1··111·1111·11·1···1··11···1·11··11111·1·111·1111····1··11·1·11···11·1·11·11·11·11· |
| check 50 (106) | 111··1··1··1·11··1·111111·1·1··1·1·11··11·1··1·····1···1·11·1··11·11·111··11··1·11···1·1·1·111·11····1··1·1·11··1··11·11·1····1···11·11··1··11·111·11111111··111·1···1·1·1·1·111····1···11·11··1·1·11···111111 |
| check 51 (126) | 111··11··1·1·1·11·1···11·111111·111··1··1·111·····11·1·1·1·11·1111·11··111111··1··1111·11··1·1111111·11·1·1·111··1·1·111·1··1111·1·1··1111·111·1··111111·11·111·11··11·1·1111·111·1··1·111111···1·1·1·11···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
Output gate
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}
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 (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 52 single-wire gates and 496 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{S}^\dagger on output 1, \mathrm{S} on output 2, \mathrm{Z} on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{Z} on output 8, \mathrm{S}^\dagger on output 9, \mathrm{S} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{Z} on output 13, \mathrm{S}^\dagger on output 14, \mathrm{Z} on output 15, \mathrm{Z} on output 16, \mathrm{Z} on output 17, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{S}^\dagger on output 20, \mathrm{S}^\dagger on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23 and 524 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 548 correction gates
\mathrm{Z} on output 0, \mathrm{S}^\dagger on output 1, \mathrm{S} on output 2, \mathrm{Z} on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{Z} on output 8, \mathrm{S}^\dagger on output 9, \mathrm{S} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{Z} on output 13, \mathrm{S}^\dagger on output 14, \mathrm{Z} on output 15, \mathrm{Z} on output 16, \mathrm{Z} on output 17, \mathrm{Z} on output 18, \mathrm{S} on output 19, \mathrm{S}^\dagger on output 20, \mathrm{S}^\dagger on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23, \mathrm{S}^\dagger on output 24, \mathrm{Z} on output 25, \mathrm{S} on output 26, \mathrm{Z} on output 27, \mathrm{S}^\dagger on output 28, \mathrm{Z} on output 29, \mathrm{Z} on output 30, \mathrm{Z} on output 31, \mathrm{S} on output 32, \mathrm{S} on output 33, \mathrm{Z} on output 34, \mathrm{S} on output 35, \mathrm{Z} on output 36, \mathrm{Z} on output 37, \mathrm{Z} on output 38, \mathrm{Z} on output 39, \mathrm{S}^\dagger on output 40, \mathrm{S}^\dagger on output 41, \mathrm{Z} on check 42, \mathrm{S} on check 43, \mathrm{S} on check 44, \mathrm{Z} on check 45, \mathrm{S} on check 46, \mathrm{S}^\dagger on check 47, \mathrm{Z} on check 48, \mathrm{S}^\dagger on check 49, \mathrm{S}^\dagger on check 50, \mathrm{S} on check 51, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 8, \mathrm{CZ} on output 0, output 9, \mathrm{CZ} on output 0, output 11, \mathrm{CZ} on output 0, output 13, \mathrm{CZ} on output 0, output 14, \mathrm{CZ} on output 0, output 16, \mathrm{CZ} on output 0, output 17, \mathrm{CZ} on output 0, output 18, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 24, \mathrm{CZ} on output 0, output 28, \mathrm{CZ} on output 0, output 30, \mathrm{CZ} on output 0, output 37, \mathrm{CZ} on output 0, output 40, \mathrm{CZ} on output 0, output 41, \mathrm{CZ} on output 0, check 42, \mathrm{CZ} on output 0, check 43, \mathrm{CZ} on output 0, check 44, \mathrm{CZ} on output 0, check 47, \mathrm{CZ} on output 0, check 49, \mathrm{CZ} on output 0, check 51, \mathrm{CZ} on output 1, output 3, \mathrm{CZ} on output 1, output 5, \mathrm{CZ} on output 1, output 8, \mathrm{CZ} on output 1, output 11, \mathrm{CZ} on output 1, output 12, \mathrm{CZ} on output 1, output 13, \mathrm{CZ} on output 1, output 15, \mathrm{CZ} on output 1, output 16, \mathrm{CZ} on output 1, output 17, \mathrm{CZ} on output 1, output 18, \mathrm{CZ} on output 1, output 21, \mathrm{CZ} on output 1, output 23, \mathrm{CZ} on output 1, output 25, \mathrm{CZ} on output 1, output 27, \mathrm{CZ} on output 1, output 30, \mathrm{CZ} on output 1, output 31, \mathrm{CZ} on output 1, output 34, \mathrm{CZ} on output 1, output 36, \mathrm{CZ} on output 1, output 37, \mathrm{CZ} on output 1, output 38, \mathrm{CZ} on output 1, output 39, \mathrm{CZ} on output 1, check 43, \mathrm{CZ} on output 1, check 44, \mathrm{CZ} on output 1, check 46, \mathrm{CZ} on output 1, check 48, \mathrm{CZ} on output 1, check 50, \mathrm{CZ} on output 1, check 51, \mathrm{CZ} on output 3, output 5, \mathrm{CZ} on output 3, output 9, \mathrm{CZ} on output 3, output 12, \mathrm{CZ} on output 3, output 14, \mathrm{CZ} on output 3, output 15, \mathrm{CZ} on output 3, output 20, \mathrm{CZ} on output 3, output 21, \mathrm{CZ} on output 3, output 23, \mathrm{CZ} on output 3, output 24, \mathrm{CZ} on output 3, output 25, \mathrm{CZ} on output 3, output 27, \mathrm{CZ} on output 3, output 28, \mathrm{CZ} on output 3, output 31, \mathrm{CZ} on output 3, output 34, \mathrm{CZ} on output 3, output 36, \mathrm{CZ} on output 3, output 38, \mathrm{CZ} on output 3, output 39, \mathrm{CZ} on output 3, output 40, \mathrm{CZ} on output 3, output 41, \mathrm{CZ} on output 3, check 42, \mathrm{CZ} on output 3, check 46, \mathrm{CZ} on output 3, check 47, \mathrm{CZ} on output 3, check 48, \mathrm{CZ} on output 3, check 49, \mathrm{CZ} on output 3, check 50, \mathrm{CZ} on output 5, output 9, \mathrm{CZ} on output 5, output 12, \mathrm{CZ} on output 5, output 14, \mathrm{CZ} on output 5, output 15, \mathrm{CZ} on output 5, output 20, \mathrm{CZ} on output 5, output 21, \mathrm{CZ} on output 5, output 23, \mathrm{CZ} on output 5, output 24, \mathrm{CZ} on output 5, output 25, \mathrm{CZ} on output 5, output 27, \mathrm{CZ} on output 5, output 28, \mathrm{CZ} on output 5, output 31, \mathrm{CZ} on output 5, output 34, \mathrm{CZ} on output 5, output 36, \mathrm{CZ} on output 5, output 38, \mathrm{CZ} on output 5, output 39, \mathrm{CZ} on output 5, output 40, \mathrm{CZ} on output 5, output 41, \mathrm{CZ} on output 5, check 42, \mathrm{CZ} on output 5, check 46, \mathrm{CZ} on output 5, check 47, \mathrm{CZ} on output 5, check 48, \mathrm{CZ} on output 5, check 49, \mathrm{CZ} on output 5, check 50, \mathrm{CZ} on output 8, output 9, \mathrm{CZ} on output 8, output 11, \mathrm{CZ} on output 8, output 13, \mathrm{CZ} on output 8, output 14, \mathrm{CZ} on output 8, output 16, \mathrm{CZ} on output 8, output 17, \mathrm{CZ} on output 8, output 18, \mathrm{CZ} on output 8, output 20, \mathrm{CZ} on output 8, output 24, \mathrm{CZ} on output 8, output 28, \mathrm{CZ} on output 8, output 30, \mathrm{CZ} on output 8, output 37, \mathrm{CZ} on output 8, output 40, \mathrm{CZ} on output 8, output 41, \mathrm{CZ} on output 8, check 42, \mathrm{CZ} on output 8, check 43, \mathrm{CZ} on output 8, check 44, \mathrm{CZ} on output 8, check 47, \mathrm{CZ} on output 8, check 49, \mathrm{CZ} on output 8, check 51, \mathrm{CZ} on output 9, output 11, \mathrm{CZ} on output 9, output 12, \mathrm{CZ} on output 9, output 13, \mathrm{CZ} on output 9, output 15, \mathrm{CZ} on output 9, output 16, \mathrm{CZ} on output 9, output 17, \mathrm{CZ} on output 9, output 18, \mathrm{CZ} on output 9, output 21, \mathrm{CZ} on output 9, output 23, \mathrm{CZ} on output 9, output 25, \mathrm{CZ} on output 9, output 27, \mathrm{CZ} on output 9, output 30, \mathrm{CZ} on output 9, output 31, \mathrm{CZ} on output 9, output 34, \mathrm{CZ} on output 9, output 36, \mathrm{CZ} on output 9, output 37, \mathrm{CZ} on output 9, output 38, \mathrm{CZ} on output 9, output 39, \mathrm{CZ} on output 9, check 43, \mathrm{CZ} on output 9, check 44, \mathrm{CZ} on output 9, check 46, \mathrm{CZ} on output 9, check 48, \mathrm{CZ} on output 9, check 50, \mathrm{CZ} on output 9, check 51, \mathrm{CZ} on output 11, output 13, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 16, \mathrm{CZ} on output 11, output 17, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 20, \mathrm{CZ} on output 11, output 24, \mathrm{CZ} on output 11, output 28, \mathrm{CZ} on output 11, output 30, \mathrm{CZ} on output 11, output 37, \mathrm{CZ} on output 11, output 40, \mathrm{CZ} on output 11, output 41, \mathrm{CZ} on output 11, check 42, \mathrm{CZ} on output 11, check 43, \mathrm{CZ} on output 11, check 44, \mathrm{CZ} on output 11, check 47, \mathrm{CZ} on output 11, check 49, \mathrm{CZ} on output 11, check 51, \mathrm{CZ} on output 12, output 14, \mathrm{CZ} on output 12, output 15, \mathrm{CZ} on output 12, output 20, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, output 23, \mathrm{CZ} on output 12, output 24, \mathrm{CZ} on output 12, output 25, \mathrm{CZ} on output 12, output 27, \mathrm{CZ} on output 12, output 28, \mathrm{CZ} on output 12, output 31, \mathrm{CZ} on output 12, output 34, \mathrm{CZ} on output 12, output 36, \mathrm{CZ} on output 12, output 38, \mathrm{CZ} on output 12, output 39, \mathrm{CZ} on output 12, output 40, \mathrm{CZ} on output 12, output 41, \mathrm{CZ} on output 12, check 42, \mathrm{CZ} on output 12, check 46, \mathrm{CZ} on output 12, check 47, \mathrm{CZ} on output 12, check 48, \mathrm{CZ} on output 12, check 49, \mathrm{CZ} on output 12, check 50, \mathrm{CZ} on output 13, output 14, \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 20, \mathrm{CZ} on output 13, output 24, \mathrm{CZ} on output 13, output 28, \mathrm{CZ} on output 13, output 30, \mathrm{CZ} on output 13, output 37, \mathrm{CZ} on output 13, output 40, \mathrm{CZ} on output 13, output 41, \mathrm{CZ} on output 13, check 42, \mathrm{CZ} on output 13, check 43, \mathrm{CZ} on output 13, check 44, \mathrm{CZ} on output 13, check 47, \mathrm{CZ} on output 13, check 49, \mathrm{CZ} on output 13, check 51, \mathrm{CZ} on output 14, output 15, \mathrm{CZ} on output 14, output 16, \mathrm{CZ} on output 14, output 17, \mathrm{CZ} on output 14, output 18, \mathrm{CZ} on output 14, output 21, \mathrm{CZ} on output 14, output 23, \mathrm{CZ} on output 14, output 25, \mathrm{CZ} on output 14, output 27, \mathrm{CZ} on output 14, output 30, \mathrm{CZ} on output 14, output 31, \mathrm{CZ} on output 14, output 34, \mathrm{CZ} on output 14, output 36, \mathrm{CZ} on output 14, output 37, \mathrm{CZ} on output 14, output 38, \mathrm{CZ} on output 14, output 39, \mathrm{CZ} on output 14, check 43, \mathrm{CZ} on output 14, check 44, \mathrm{CZ} on output 14, check 46, \mathrm{CZ} on output 14, check 48, \mathrm{CZ} on output 14, check 50, \mathrm{CZ} on output 14, check 51, \mathrm{CZ} on output 15, output 20, \mathrm{CZ} on output 15, output 21, \mathrm{CZ} on output 15, output 23, \mathrm{CZ} on output 15, output 24, \mathrm{CZ} on output 15, output 25, \mathrm{CZ} on output 15, output 27, \mathrm{CZ} on output 15, output 28, \mathrm{CZ} on output 15, output 31, \mathrm{CZ} on output 15, output 34, \mathrm{CZ} on output 15, output 36, \mathrm{CZ} on output 15, output 38, \mathrm{CZ} on output 15, output 39, \mathrm{CZ} on output 15, output 40, \mathrm{CZ} on output 15, output 41, \mathrm{CZ} on output 15, check 42, \mathrm{CZ} on output 15, check 46, \mathrm{CZ} on output 15, check 47, \mathrm{CZ} on output 15, check 48, \mathrm{CZ} on output 15, check 49, \mathrm{CZ} on output 15, check 50, \mathrm{CZ} on output 16, output 17, \mathrm{CZ} on output 16, output 18, \mathrm{CZ} on output 16, output 20, \mathrm{CZ} on output 16, output 24, \mathrm{CZ} on output 16, output 28, \mathrm{CZ} on output 16, output 30, \mathrm{CZ} on output 16, output 37, \mathrm{CZ} on output 16, output 40, \mathrm{CZ} on output 16, output 41, \mathrm{CZ} on output 16, check 42, \mathrm{CZ} on output 16, check 43, \mathrm{CZ} on output 16, check 44, \mathrm{CZ} on output 16, check 47, \mathrm{CZ} on output 16, check 49, \mathrm{CZ} on output 16, check 51, \mathrm{CZ} on output 17, output 18, \mathrm{CZ} on output 17, output 20, \mathrm{CZ} on output 17, output 24, \mathrm{CZ} on output 17, output 28, \mathrm{CZ} on output 17, output 30, \mathrm{CZ} on output 17, output 37, \mathrm{CZ} on output 17, output 40, \mathrm{CZ} on output 17, output 41, \mathrm{CZ} on output 17, check 42, \mathrm{CZ} on output 17, check 43, \mathrm{CZ} on output 17, check 44, \mathrm{CZ} on output 17, check 47, \mathrm{CZ} on output 17, check 49, \mathrm{CZ} on output 17, check 51, \mathrm{CZ} on output 18, output 20, \mathrm{CZ} on output 18, output 24, \mathrm{CZ} on output 18, output 28, \mathrm{CZ} on output 18, output 30, \mathrm{CZ} on output 18, output 37, \mathrm{CZ} on output 18, output 40, \mathrm{CZ} on output 18, output 41, \mathrm{CZ} on output 18, check 42, \mathrm{CZ} on output 18, check 43, \mathrm{CZ} on output 18, check 44, \mathrm{CZ} on output 18, check 47, \mathrm{CZ} on output 18, check 49, \mathrm{CZ} on output 18, check 51, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 23, \mathrm{CZ} on output 20, output 25, \mathrm{CZ} on output 20, output 27, \mathrm{CZ} on output 20, output 30, \mathrm{CZ} on output 20, output 31, \mathrm{CZ} on output 20, output 34, \mathrm{CZ} on output 20, output 36, \mathrm{CZ} on output 20, output 37, \mathrm{CZ} on output 20, output 38, \mathrm{CZ} on output 20, output 39, \mathrm{CZ} on output 20, check 43, \mathrm{CZ} on output 20, check 44, \mathrm{CZ} on output 20, check 46, \mathrm{CZ} on output 20, check 48, \mathrm{CZ} on output 20, check 50, \mathrm{CZ} on output 20, check 51, \mathrm{CZ} on output 21, output 23, \mathrm{CZ} on output 21, output 24, \mathrm{CZ} on output 21, output 25, \mathrm{CZ} on output 21, output 27, \mathrm{CZ} on output 21, output 28, \mathrm{CZ} on output 21, output 31, \mathrm{CZ} on output 21, output 34, \mathrm{CZ} on output 21, output 36, \mathrm{CZ} on output 21, output 38, \mathrm{CZ} on output 21, output 39, \mathrm{CZ} on output 21, output 40, \mathrm{CZ} on output 21, output 41, \mathrm{CZ} on output 21, check 42, \mathrm{CZ} on output 21, check 45, \mathrm{CZ} on output 21, check 46, \mathrm{CZ} on output 21, check 48, \mathrm{CZ} on output 21, check 49, \mathrm{CZ} on output 23, output 24, \mathrm{CZ} on output 23, output 25, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 28, \mathrm{CZ} on output 23, output 31, \mathrm{CZ} on output 23, output 34, \mathrm{CZ} on output 23, output 36, \mathrm{CZ} on output 23, output 38, \mathrm{CZ} on output 23, output 39, \mathrm{CZ} on output 23, output 40, \mathrm{CZ} on output 23, output 41, \mathrm{CZ} on output 23, check 42, \mathrm{CZ} on output 23, check 46, \mathrm{CZ} on output 23, check 47, \mathrm{CZ} on output 23, check 48, \mathrm{CZ} on output 23, check 49, \mathrm{CZ} on output 23, check 50, \mathrm{CZ} on output 24, output 25, \mathrm{CZ} on output 24, output 27, \mathrm{CZ} on output 24, output 30, \mathrm{CZ} on output 24, output 31, \mathrm{CZ} on output 24, output 34, \mathrm{CZ} on output 24, output 36, \mathrm{CZ} on output 24, output 37, \mathrm{CZ} on output 24, output 38, \mathrm{CZ} on output 24, output 39, \mathrm{CZ} on output 24, check 43, \mathrm{CZ} on output 24, check 44, \mathrm{CZ} on output 24, check 46, \mathrm{CZ} on output 24, check 48, \mathrm{CZ} on output 24, check 50, \mathrm{CZ} on output 24, check 51, \mathrm{CZ} on output 25, output 27, \mathrm{CZ} on output 25, output 28, \mathrm{CZ} on output 25, output 31, \mathrm{CZ} on output 25, output 34, \mathrm{CZ} on output 25, output 36, \mathrm{CZ} on output 25, output 38, \mathrm{CZ} on output 25, output 39, \mathrm{CZ} on output 25, output 40, \mathrm{CZ} on output 25, output 41, \mathrm{CZ} on output 25, check 42, \mathrm{CZ} on output 25, check 46, \mathrm{CZ} on output 25, check 47, \mathrm{CZ} on output 25, check 48, \mathrm{CZ} on output 25, check 49, \mathrm{CZ} on output 25, check 50, \mathrm{CZ} on output 27, output 28, \mathrm{CZ} on output 27, output 31, \mathrm{CZ} on output 27, output 34, \mathrm{CZ} on output 27, output 36, \mathrm{CZ} on output 27, output 38, \mathrm{CZ} on output 27, output 39, \mathrm{CZ} on output 27, output 40, \mathrm{CZ} on output 27, output 41, \mathrm{CZ} on output 27, check 42, \mathrm{CZ} on output 27, check 46, \mathrm{CZ} on output 27, check 47, \mathrm{CZ} on output 27, check 48, \mathrm{CZ} on output 27, check 49, \mathrm{CZ} on output 27, check 50, \mathrm{CZ} on output 28, output 30, \mathrm{CZ} on output 28, output 31, \mathrm{CZ} on output 28, output 34, \mathrm{CZ} on output 28, output 36, \mathrm{CZ} on output 28, output 37, \mathrm{CZ} on output 28, output 38, \mathrm{CZ} on output 28, output 39, \mathrm{CZ} on output 28, check 43, \mathrm{CZ} on output 28, check 44, \mathrm{CZ} on output 28, check 46, \mathrm{CZ} on output 28, check 48, \mathrm{CZ} on output 28, check 50, \mathrm{CZ} on output 28, check 51, \mathrm{CZ} on output 29, check 45, \mathrm{CZ} on output 29, check 48, \mathrm{CZ} on output 29, check 49, \mathrm{CZ} on output 29, check 50, \mathrm{CZ} on output 30, output 37, \mathrm{CZ} on output 30, output 40, \mathrm{CZ} on output 30, output 41, \mathrm{CZ} on output 30, check 42, \mathrm{CZ} on output 30, check 43, \mathrm{CZ} on output 30, check 44, \mathrm{CZ} on output 30, check 47, \mathrm{CZ} on output 30, check 49, \mathrm{CZ} on output 30, check 51, \mathrm{CZ} on output 31, output 34, \mathrm{CZ} on output 31, output 36, \mathrm{CZ} on output 31, output 38, \mathrm{CZ} on output 31, output 39, \mathrm{CZ} on output 31, output 40, \mathrm{CZ} on output 31, output 41, \mathrm{CZ} on output 31, check 42, \mathrm{CZ} on output 31, check 46, \mathrm{CZ} on output 31, check 47, \mathrm{CZ} on output 31, check 48, \mathrm{CZ} on output 31, check 49, \mathrm{CZ} on output 31, check 50, \mathrm{CZ} on output 34, output 36, \mathrm{CZ} on output 34, output 38, \mathrm{CZ} on output 34, output 39, \mathrm{CZ} on output 34, output 40, \mathrm{CZ} on output 34, output 41, \mathrm{CZ} on output 34, check 42, \mathrm{CZ} on output 34, check 46, \mathrm{CZ} on output 34, check 47, \mathrm{CZ} on output 34, check 48, \mathrm{CZ} on output 34, check 49, \mathrm{CZ} on output 34, check 50, \mathrm{CZ} on output 36, output 38, \mathrm{CZ} on output 36, output 39, \mathrm{CZ} on output 36, output 40, \mathrm{CZ} on output 36, output 41, \mathrm{CZ} on output 36, check 42, \mathrm{CZ} on output 36, check 46, \mathrm{CZ} on output 36, check 47, \mathrm{CZ} on output 36, check 48, \mathrm{CZ} on output 36, check 49, \mathrm{CZ} on output 36, check 50, \mathrm{CZ} on output 37, output 40, \mathrm{CZ} on output 37, output 41, \mathrm{CZ} on output 37, check 42, \mathrm{CZ} on output 37, check 43, \mathrm{CZ} on output 37, check 44, \mathrm{CZ} on output 37, check 47, \mathrm{CZ} on output 37, check 49, \mathrm{CZ} on output 37, check 51, \mathrm{CZ} on output 38, output 39, \mathrm{CZ} on output 38, output 40, \mathrm{CZ} on output 38, output 41, \mathrm{CZ} on output 38, check 42, \mathrm{CZ} on output 38, check 46, \mathrm{CZ} on output 38, check 47, \mathrm{CZ} on output 38, check 48, \mathrm{CZ} on output 38, check 49, \mathrm{CZ} on output 38, check 50, \mathrm{CZ} on output 39, output 40, \mathrm{CZ} on output 39, output 41, \mathrm{CZ} on output 39, check 42, \mathrm{CZ} on output 39, check 46, \mathrm{CZ} on output 39, check 47, \mathrm{CZ} on output 39, check 48, \mathrm{CZ} on output 39, check 49, \mathrm{CZ} on output 39, check 50, \mathrm{CZ} on output 40, check 43, \mathrm{CZ} on output 40, check 44, \mathrm{CZ} on output 40, check 46, \mathrm{CZ} on output 40, check 48, \mathrm{CZ} on output 40, check 50, \mathrm{CZ} on output 40, check 51, \mathrm{CZ} on output 41, check 43, \mathrm{CZ} on output 41, check 44, \mathrm{CZ} on output 41, check 46, \mathrm{CZ} on output 41, check 48, \mathrm{CZ} on output 41, check 50, \mathrm{CZ} on output 41, check 51, \mathrm{CZ} on check 42, check 43, \mathrm{CZ} on check 42, check 44, \mathrm{CZ} on check 42, check 46, \mathrm{CZ} on check 42, check 48, \mathrm{CZ} on check 42, check 50, \mathrm{CZ} on check 42, check 51, \mathrm{CZ} on check 43, check 44, \mathrm{CZ} on check 43, check 47, \mathrm{CZ} on check 43, check 49, \mathrm{CZ} on check 43, check 51, \mathrm{CZ} on check 44, check 47, \mathrm{CZ} on check 44, check 49, \mathrm{CZ} on check 44, check 51, \mathrm{CZ} on check 45, check 47, \mathrm{CZ} on check 45, check 48, \mathrm{CZ} on check 45, check 49, \mathrm{CZ} on check 46, check 47, \mathrm{CZ} on check 46, check 48, \mathrm{CZ} on check 46, check 49, \mathrm{CZ} on check 46, check 50, \mathrm{CZ} on check 47, check 48, \mathrm{CZ} on check 47, check 51, \mathrm{CZ} on check 49, check 51
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 17, 18, 27, 32, 34, 51, 55, 57, 62, 65, 67, 71, 72, 74, 76, 80, 82, 85, 86, 88, 91, 94, 95, 96 and 47 more (listed below); \mathrm{T}^5 on rotations 1, 2, 3, 5, 9, 11, 13, 15, 19, 21, 23, 29, 42, 43, 102, 103, 109; \mathrm{T}^\dagger on rotations 4, 6, 8, 10, 12, 20, 24, 33, 38, 53, 104, 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 71 rotations at T³
17, 18, 27, 32, 34, 51, 55, 57, 62, 65, 67, 71, 72, 74, 76, 80, 82, 85, 86, 88, 91, 94, 95, 96, 97, 98, 101, 106, 108, 110, 112, 114, 117, 118, 119, 130, 131, 135, 136, 139, 141, 142, 144, 145, 146, 153, 159, 160, 162, 164, 166, 168, 171, 174, 176, 177, 179, 180, 183, 184, 185, 191, 192, 194, 195, 196, 198, 199, 201, 202, 203
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/206.42.3.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-206.42.3.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.
Exactly 1,282 faults of weight 3 are undetectable and damaging, so A_{3}=1{,}282. 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 [0,3,57].
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
built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows
Found by: AI search (gamma frontier): from Wills parent codes
Discovery: AI search
1 recorded source
[
{
"regime": "AI search (gamma frontier): from Wills parent codes",
"file": "gamma_frontier_release/protocols/paired_column_contraction_206_42_3_d293f2254ed0.json",
"label": "paired_column_contraction_206_42_3_d293f2254ed0",
"N": 52,
"d": 3,
"d_is_exact": true,
"origin": "Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 4 paired-column contractions",
"provenance": "gamma frontier release record paired_column_contraction_206_42_3_d293f2254ed0 (source catalogue id paired_column_contraction_206_42_3_d293f2254ed0); construction: Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 4 paired-column contractions; matrix d293f2254ed0b64e...; the release states d=3 (exact), gamma=1.447468380709706 (exact)",
"notes": "matrix gamma_frontier_release/matrices/d293f2254ed0b64e72e271b02ab1f34e0fd86a34eda59a79f937da1406117e06.matrix"
}
]Use it in code
Load this factory and re-derive every number from its circuit with the catalogue's own verifier.
# git clone https://github.com/shubhamj810/magic-state-factory-repo
# cd magic-state-factory-repo/master_catalog
import json, urllib.request
import verify_catalog as VC
url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/206.42.3.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[842].