[[288,12,18]] · QEC Challenge

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[[288,12,18]] d ≤

288

kd²/n

13.5

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Distance

d_X 18 · witness weight 18 (claimed upper_bound)

witness operator (support, 18 qubits)

[145, 153, 180, 181, 183, 185, 186, 187, 188, 190, 217, 219, 221, 227, 255, 256, 260, 263]

d_Z 18 · witness weight 18 (claimed upper_bound)

witness operator (support, 18 qubits)

[12, 15, 19, 20, 48, 54, 56, 58, 85, 87, 88, 89, 90, 92, 94, 95, 122, 130]

certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors Bravyi, Sergey and Cross, Andrew W. and Gambetta, Jay M. and Maslov, Dmitri and Rall, Patrick and Yoder, Theodore J.

provenance literature baseline

construction Bivariate bicycle code, orders (12, 12), A=x³ + y⁷ + y², B=x² + x + y³ (periodic boundary conditions).

model classical construction (no AI model)

reference arXiv:2308.07915

date 2023-08-15

notes Distance d=18 established in arXiv:2308.07915 (Table 3); witness here is a decoder-found logical operator of that weight (upper bound).

family bivariate bicycle (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight ≤ 6 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 144 · Z-checks 144

H_X (144 checks, sparse supports)

[2, 7, 36, 147, 156, 168] [3, 8, 37, 148, 157, 169] [4, 9, 38, 149, 158, 170] [5, 10, 39, 150, 159, 171] [6, 11, 40, 151, 160, 172] [0, 7, 41, 152, 161, 173] [1, 8, 42, 153, 162, 174] [2, 9, 43, 154, 163, 175] [3, 10, 44, 155, 164, 176] [4, 11, 45, 144, 165, 177] [0, 5, 46, 145, 166, 178] [1, 6, 47, 146, 167, 179] [14, 19, 48, 159, 168, 180] [15, 20, 49, 160, 169, 181] [16, 21, 50, 161, 170, 182] [17, 22, 51, 162, 171, 183] [18, 23, 52, 163, 172, 184] [12, 19, 53, 164, 173, 185] [13, 20, 54, 165, 174, 186] [14, 21, 55, 166, 175, 187] [15, 22, 56, 167, 176, 188] [16, 23, 57, 156, 177, 189] [12, 17, 58, 157, 178, 190] [13, 18, 59, 158, 179, 191] [26, 31, 60, 171, 180, 192] [27, 32, 61, 172, 181, 193] [28, 33, 62, 173, 182, 194] [29, 34, 63, 174, 183, 195] [30, 35, 64, 175, 184, 196] [24, 31, 65, 176, 185, 197] [25, 32, 66, 177, 186, 198] [26, 33, 67, 178, 187, 199] [27, 34, 68, 179, 188, 200] [28, 35, 69, 168, 189, 201] [24, 29, 70, 169, 190, 202] [25, 30, 71, 170, 191, 203] [38, 43, 72, 183, 192, 204] [39, 44, 73, 184, 193, 205] [40, 45, 74, 185, 194, 206] [41, 46, 75, 186, 195, 207] [42, 47, 76, 187, 196, 208] [36, 43, 77, 188, 197, 209] [37, 44, 78, 189, 198, 210] [38, 45, 79, 190, 199, 211] [39, 46, 80, 191, 200, 212] [40, 47, 81, 180, 201, 213] [36, 41, 82, 181, 202, 214] [37, 42, 83, 182, 203, 215] [50, 55, 84, 195, 204, 216] [51, 56, 85, 196, 205, 217] [52, 57, 86, 197, 206, 218] [53, 58, 87, 198, 207, 219] [54, 59, 88, 199, 208, 220] [48, 55, 89, 200, 209, 221] [49, 56, 90, 201, 210, 222] [50, 57, 91, 202, 211, 223] [51, 58, 92, 203, 212, 224] [52, 59, 93, 192, 213, 225] [48, 53, 94, 193, 214, 226] [49, 54, 95, 194, 215, 227] [62, 67, 96, 207, 216, 228] [63, 68, 97, 208, 217, 229] [64, 69, 98, 209, 218, 230] [65, 70, 99, 210, 219, 231] [66, 71, 100, 211, 220, 232] [60, 67, 101, 212, 221, 233] [61, 68, 102, 213, 222, 234] [62, 69, 103, 214, 223, 235] [63, 70, 104, 215, 224, 236] [64, 71, 105, 204, 225, 237] [60, 65, 106, 205, 226, 238] [61, 66, 107, 206, 227, 239] [74, 79, 108, 219, 228, 240] [75, 80, 109, 220, 229, 241] [76, 81, 110, 221, 230, 242] [77, 82, 111, 222, 231, 243] [78, 83, 112, 223, 232, 244] [72, 79, 113, 224, 233, 245] [73, 80, 114, 225, 234, 246] [74, 81, 115, 226, 235, 247] [75, 82, 116, 227, 236, 248] [76, 83, 117, 216, 237, 249] [72, 77, 118, 217, 238, 250] [73, 78, 119, 218, 239, 251] [86, 91, 120, 231, 240, 252] [87, 92, 121, 232, 241, 253] [88, 93, 122, 233, 242, 254] [89, 94, 123, 234, 243, 255] [90, 95, 124, 235, 244, 256] [84, 91, 125, 236, 245, 257] [85, 92, 126, 237, 246, 258] [86, 93, 127, 238, 247, 259] [87, 94, 128, 239, 248, 260] [88, 95, 129, 228, 249, 261] [84, 89, 130, 229, 250, 262] [85, 90, 131, 230, 251, 263] [98, 103, 132, 243, 252, 264] [99, 104, 133, 244, 253, 265] [100, 105, 134, 245, 254, 266] [101, 106, 135, 246, 255, 267] [102, 107, 136, 247, 256, 268] [96, 103, 137, 248, 257, 269] [97, 104, 138, 249, 258, 270] [98, 105, 139, 250, 259, 271] [99, 106, 140, 251, 260, 272] [100, 107, 141, 240, 261, 273] [96, 101, 142, 241, 262, 274] [97, 102, 143, 242, 263, 275] [0, 110, 115, 255, 264, 276] [1, 111, 116, 256, 265, 277] [2, 112, 117, 257, 266, 278] [3, 113, 118, 258, 267, 279] [4, 114, 119, 259, 268, 280] [5, 108, 115, 260, 269, 281] [6, 109, 116, 261, 270, 282] [7, 110, 117, 262, 271, 283] [8, 111, 118, 263, 272, 284] [9, 112, 119, 252, 273, 285] [10, 108, 113, 253, 274, 286] [11, 109, 114, 254, 275, 287] [12, 122, 127, 144, 267, 276] [13, 123, 128, 145, 268, 277] [14, 124, 129, 146, 269, 278] [15, 125, 130, 147, 270, 279] [16, 126, 131, 148, 271, 280] [17, 120, 127, 149, 272, 281] [18, 121, 128, 150, 273, 282] [19, 122, 129, 151, 274, 283] [20, 123, 130, 152, 275, 284] [21, 124, 131, 153, 264, 285] [22, 120, 125, 154, 265, 286] [23, 121, 126, 155, 266, 287] [24, 134, 139, 144, 156, 279] [25, 135, 140, 145, 157, 280] [26, 136, 141, 146, 158, 281] [27, 137, 142, 147, 159, 282] [28, 138, 143, 148, 160, 283] [29, 132, 139, 149, 161, 284] [30, 133, 140, 150, 162, 285] [31, 134, 141, 151, 163, 286] [32, 135, 142, 152, 164, 287] [33, 136, 143, 153, 165, 276] [34, 132, 137, 154, 166, 277] [35, 133, 138, 155, 167, 278]

H_Z (144 checks, sparse supports)

[9, 120, 132, 149, 154, 252] [10, 121, 133, 150, 155, 253] [11, 122, 134, 144, 151, 254] [0, 123, 135, 145, 152, 255] [1, 124, 136, 146, 153, 256] [2, 125, 137, 147, 154, 257] [3, 126, 138, 148, 155, 258] [4, 127, 139, 144, 149, 259] [5, 128, 140, 145, 150, 260] [6, 129, 141, 146, 151, 261] [7, 130, 142, 147, 152, 262] [8, 131, 143, 148, 153, 263] [0, 21, 132, 161, 166, 264] [1, 22, 133, 162, 167, 265] [2, 23, 134, 156, 163, 266] [3, 12, 135, 157, 164, 267] [4, 13, 136, 158, 165, 268] [5, 14, 137, 159, 166, 269] [6, 15, 138, 160, 167, 270] [7, 16, 139, 156, 161, 271] [8, 17, 140, 157, 162, 272] [9, 18, 141, 158, 163, 273] [10, 19, 142, 159, 164, 274] [11, 20, 143, 160, 165, 275] [0, 12, 33, 173, 178, 276] [1, 13, 34, 174, 179, 277] [2, 14, 35, 168, 175, 278] [3, 15, 24, 169, 176, 279] [4, 16, 25, 170, 177, 280] [5, 17, 26, 171, 178, 281] [6, 18, 27, 172, 179, 282] [7, 19, 28, 168, 173, 283] [8, 20, 29, 169, 174, 284] [9, 21, 30, 170, 175, 285] [10, 22, 31, 171, 176, 286] [11, 23, 32, 172, 177, 287] [12, 24, 45, 144, 185, 190] [13, 25, 46, 145, 186, 191] [14, 26, 47, 146, 180, 187] [15, 27, 36, 147, 181, 188] [16, 28, 37, 148, 182, 189] [17, 29, 38, 149, 183, 190] [18, 30, 39, 150, 184, 191] [19, 31, 40, 151, 180, 185] [20, 32, 41, 152, 181, 186] [21, 33, 42, 153, 182, 187] [22, 34, 43, 154, 183, 188] [23, 35, 44, 155, 184, 189] [24, 36, 57, 156, 197, 202] [25, 37, 58, 157, 198, 203] [26, 38, 59, 158, 192, 199] [27, 39, 48, 159, 193, 200] [28, 40, 49, 160, 194, 201] [29, 41, 50, 161, 195, 202] [30, 42, 51, 162, 196, 203] [31, 43, 52, 163, 192, 197] [32, 44, 53, 164, 193, 198] [33, 45, 54, 165, 194, 199] [34, 46, 55, 166, 195, 200] [35, 47, 56, 167, 196, 201] [36, 48, 69, 168, 209, 214] [37, 49, 70, 169, 210, 215] [38, 50, 71, 170, 204, 211] [39, 51, 60, 171, 205, 212] [40, 52, 61, 172, 206, 213] [41, 53, 62, 173, 207, 214] [42, 54, 63, 174, 208, 215] [43, 55, 64, 175, 204, 209] [44, 56, 65, 176, 205, 210] [45, 57, 66, 177, 206, 211] [46, 58, 67, 178, 207, 212] [47, 59, 68, 179, 208, 213] [48, 60, 81, 180, 221, 226] [49, 61, 82, 181, 222, 227] [50, 62, 83, 182, 216, 223] [51, 63, 72, 183, 217, 224] [52, 64, 73, 184, 218, 225] [53, 65, 74, 185, 219, 226] [54, 66, 75, 186, 220, 227] [55, 67, 76, 187, 216, 221] [56, 68, 77, 188, 217, 222] [57, 69, 78, 189, 218, 223] [58, 70, 79, 190, 219, 224] [59, 71, 80, 191, 220, 225] [60, 72, 93, 192, 233, 238] [61, 73, 94, 193, 234, 239] [62, 74, 95, 194, 228, 235] [63, 75, 84, 195, 229, 236] [64, 76, 85, 196, 230, 237] [65, 77, 86, 197, 231, 238] [66, 78, 87, 198, 232, 239] [67, 79, 88, 199, 228, 233] [68, 80, 89, 200, 229, 234] [69, 81, 90, 201, 230, 235] [70, 82, 91, 202, 231, 236] [71, 83, 92, 203, 232, 237] [72, 84, 105, 204, 245, 250] [73, 85, 106, 205, 246, 251] [74, 86, 107, 206, 240, 247] [75, 87, 96, 207, 241, 248] [76, 88, 97, 208, 242, 249] [77, 89, 98, 209, 243, 250] [78, 90, 99, 210, 244, 251] [79, 91, 100, 211, 240, 245] [80, 92, 101, 212, 241, 246] [81, 93, 102, 213, 242, 247] [82, 94, 103, 214, 243, 248] [83, 95, 104, 215, 244, 249] [84, 96, 117, 216, 257, 262] [85, 97, 118, 217, 258, 263] [86, 98, 119, 218, 252, 259] [87, 99, 108, 219, 253, 260] [88, 100, 109, 220, 254, 261] [89, 101, 110, 221, 255, 262] [90, 102, 111, 222, 256, 263] [91, 103, 112, 223, 252, 257] [92, 104, 113, 224, 253, 258] [93, 105, 114, 225, 254, 259] [94, 106, 115, 226, 255, 260] [95, 107, 116, 227, 256, 261] [96, 108, 129, 228, 269, 274] [97, 109, 130, 229, 270, 275] [98, 110, 131, 230, 264, 271] [99, 111, 120, 231, 265, 272] [100, 112, 121, 232, 266, 273] [101, 113, 122, 233, 267, 274] [102, 114, 123, 234, 268, 275] [103, 115, 124, 235, 264, 269] [104, 116, 125, 236, 265, 270] [105, 117, 126, 237, 266, 271] [106, 118, 127, 238, 267, 272] [107, 119, 128, 239, 268, 273] [108, 120, 141, 240, 281, 286] [109, 121, 142, 241, 282, 287] [110, 122, 143, 242, 276, 283] [111, 123, 132, 243, 277, 284] [112, 124, 133, 244, 278, 285] [113, 125, 134, 245, 279, 286] [114, 126, 135, 246, 280, 287] [115, 127, 136, 247, 276, 281] [116, 128, 137, 248, 277, 282] [117, 129, 138, 249, 278, 283] [118, 130, 139, 250, 279, 284] [119, 131, 140, 251, 280, 285]

raw submission JSON