[\![156,\,28,\,3]\!] factory

\mathrm{S}^\dagger on output 0, \mathrm{S}^\dagger on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{S}^\dagger on output 5, \mathrm{S}^\dagger on output 8, \mathrm{Z} on output 9, \mathrm{S} on output 10, \mathrm{S}^\dagger on output 12, \mathrm{S}^\dagger on output 13, \mathrm{Z} on output 14, \mathrm{Z} on output 16, \mathrm{S} on output 17, \mathrm{S}^\dagger on output 19, \mathrm{S} on output 20, \mathrm{S}^\dagger on output 21, \mathrm{S}^\dagger on output 22, \mathrm{S}^\dagger on output 23, \mathrm{Z} on output 24, \mathrm{S} on output 25, \mathrm{Z} on output 26, \mathrm{S}^\dagger on output 27, \mathrm{S} on check 28, \mathrm{Z} on check 29, \mathrm{Z} on check 30, \mathrm{S} on check 31, \mathrm{S} on check 32, \mathrm{Z} on check 33, \mathrm{S}^\dagger on check 34, \mathrm{S}^\dagger on check 35, \mathrm{Z} on check 36, \mathrm{S}^\dagger on check 37, \mathrm{CZ} on output 0, check 36, \mathrm{CZ} on output 1, check 36, \mathrm{CZ} on output 2, output 4, \mathrm{CZ} on output 2, output 6, \mathrm{CZ} on output 2, output 7, \mathrm{CZ} on output 2, output 9, \mathrm{CZ} on output 2, output 11, \mathrm{CZ} on output 2, output 14, \mathrm{CZ} on output 2, output 15, \mathrm{CZ} on output 2, output 18, \mathrm{CZ} on output 2, output 24, \mathrm{CZ} on output 2, output 26, \mathrm{CZ} on output 2, check 28, \mathrm{CZ} on output 2, check 31, \mathrm{CZ} on output 2, check 33, \mathrm{CZ} on output 2, check 34, \mathrm{CZ} on output 2, check 35, \mathrm{CZ} on output 2, check 36, \mathrm{CZ} on output 4, output 6, \mathrm{CZ} on output 4, output 7, \mathrm{CZ} on output 4, output 9, \mathrm{CZ} on output 4, output 11, \mathrm{CZ} on output 4, output 14, \mathrm{CZ} on output 4, output 15, \mathrm{CZ} on output 4, output 18, \mathrm{CZ} on output 4, output 24, \mathrm{CZ} on output 4, output 26, \mathrm{CZ} on output 4, check 28, \mathrm{CZ} on output 4, check 31, \mathrm{CZ} on output 4, check 33, \mathrm{CZ} on output 4, check 34, \mathrm{CZ} on output 4, check 35, \mathrm{CZ} on output 5, check 36, \mathrm{CZ} on output 6, output 7, \mathrm{CZ} on output 6, output 9, \mathrm{CZ} on output 6, output 11, \mathrm{CZ} on output 6, output 14, \mathrm{CZ} on output 6, output 15, \mathrm{CZ} on output 6, output 18, \mathrm{CZ} on output 6, output 24, \mathrm{CZ} on output 6, output 26, \mathrm{CZ} on output 6, check 28, \mathrm{CZ} on output 6, check 31, \mathrm{CZ} on output 6, check 33, \mathrm{CZ} on output 6, check 34, \mathrm{CZ} on output 6, check 35, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, output 11, \mathrm{CZ} on output 7, output 14, \mathrm{CZ} on output 7, output 15, \mathrm{CZ} on output 7, output 18, \mathrm{CZ} on output 7, output 24, \mathrm{CZ} on output 7, output 26, \mathrm{CZ} on output 7, check 28, \mathrm{CZ} on output 7, check 31, \mathrm{CZ} on output 7, check 33, \mathrm{CZ} on output 7, check 34, \mathrm{CZ} on output 7, check 35, \mathrm{CZ} on output 8, check 36, \mathrm{CZ} on output 9, output 11, \mathrm{CZ} on output 9, output 14, \mathrm{CZ} on output 9, output 15, \mathrm{CZ} on output 9, output 18, \mathrm{CZ} on output 9, output 24, \mathrm{CZ} on output 9, output 26, \mathrm{CZ} on output 9, check 28, \mathrm{CZ} on output 9, check 31, \mathrm{CZ} on output 9, check 33, \mathrm{CZ} on output 9, check 34, \mathrm{CZ} on output 9, check 35, \mathrm{CZ} on output 9, check 36, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 15, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 24, \mathrm{CZ} on output 11, output 26, \mathrm{CZ} on output 11, check 28, \mathrm{CZ} on output 11, check 31, \mathrm{CZ} on output 11, check 33, \mathrm{CZ} on output 11, check 34, \mathrm{CZ} on output 11, check 35, \mathrm{CZ} on output 12, check 36, \mathrm{CZ} on output 13, check 36, \mathrm{CZ} on output 14, output 15, \mathrm{CZ} on output 14, output 18, \mathrm{CZ} on output 14, output 24, \mathrm{CZ} on output 14, output 26, \mathrm{CZ} on output 14, check 28, \mathrm{CZ} on output 14, check 31, \mathrm{CZ} on output 14, check 33, \mathrm{CZ} on output 14, check 34, \mathrm{CZ} on output 14, check 35, \mathrm{CZ} on output 14, check 36, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 24, \mathrm{CZ} on output 15, output 26, \mathrm{CZ} on output 15, check 28, \mathrm{CZ} on output 15, check 31, \mathrm{CZ} on output 15, check 33, \mathrm{CZ} on output 15, check 34, \mathrm{CZ} on output 15, check 35, \mathrm{CZ} on output 16, check 32, \mathrm{CZ} on output 16, check 33, \mathrm{CZ} on output 16, check 37, \mathrm{CZ} on output 18, output 24, \mathrm{CZ} on output 18, output 26, \mathrm{CZ} on output 18, check 28, \mathrm{CZ} on output 18, check 31, \mathrm{CZ} on output 18, check 33, \mathrm{CZ} on output 18, check 34, \mathrm{CZ} on output 18, check 35, \mathrm{CZ} on output 19, check 36, \mathrm{CZ} on output 21, check 36, \mathrm{CZ} on output 22, check 36, \mathrm{CZ} on output 23, check 36, \mathrm{CZ} on output 24, output 26, \mathrm{CZ} on output 24, check 28, \mathrm{CZ} on output 24, check 31, \mathrm{CZ} on output 24, check 33, \mathrm{CZ} on output 24, check 34, \mathrm{CZ} on output 24, check 35, \mathrm{CZ} on output 24, check 36, \mathrm{CZ} on output 26, check 28, \mathrm{CZ} on output 26, check 31, \mathrm{CZ} on output 26, check 33, \mathrm{CZ} on output 26, check 34, \mathrm{CZ} on output 26, check 35, \mathrm{CZ} on output 26, check 36, \mathrm{CZ} on output 27, check 36, \mathrm{CZ} on check 28, check 31, \mathrm{CZ} on check 28, check 33, \mathrm{CZ} on check 28, check 34, \mathrm{CZ} on check 28, check 35, \mathrm{CZ} on check 28, check 36, \mathrm{CZ} on check 29, check 36, \mathrm{CZ} on check 30, check 36, \mathrm{CZ} on check 31, check 33, \mathrm{CZ} on check 31, check 34, \mathrm{CZ} on check 31, check 35, \mathrm{CZ} on check 31, check 36, \mathrm{CZ} on check 32, check 33, \mathrm{CZ} on check 32, check 37, \mathrm{CZ} on check 33, check 34, \mathrm{CZ} on check 33, check 35, \mathrm{CZ} on check 33, check 36, \mathrm{CZ} on check 33, check 37, \mathrm{CZ} on check 34, check 35, \mathrm{CZ} on check 36, check 37

1, 10, 24, 28, 37, 39, 42, 44, 45, 47, 50, 54, 56, 59, 61, 62, 64, 66, 67, 68, 80, 83, 84, 85, 91, 93, 96, 100, 102, 103, 104, 109, 111, 113, 114, 115, 116, 117, 121, 126, 127, 128, 132, 135, 136, 137, 141, 142, 144, 148, 152, 153, 154, 155

[
 {
  "regime": "AI search (gamma frontier): contraction of an existing code",
  "file": "gamma_frontier_release/protocols/paired_column_contraction_158_28_3_ae811a8b250b.json",
  "label": "paired_column_contraction_158_28_3_ae811a8b250b",
  "N": 38,
  "d": 3,
  "d_is_exact": true,
  "origin": "Existing triorthogonal code with physical paired-column contraction",
  "provenance": "gamma frontier release record paired_column_contraction_158_28_3_ae811a8b250b (source catalogue id paired_column_contraction_158_28_3_ae811a8b250b); construction: Existing triorthogonal code with physical paired-column contraction; matrix ae811a8b250bde21...; the release states d=3 (exact), gamma=1.5750693312829973 (exact); the release matrix has 158 columns of which 2 are a repeated pair -- equal columns cancel to a diagonal Clifford and deposit nothing, so they are deleted here and this circuit is the reduced one, with 156 injections for the same gate and distance",
  "notes": "matrix gamma_frontier_release/matrices/ae811a8b250bde210d743f4144b516a709296d59b9911c4e7a03688bc609cde8.matrix"
 }
]