[[160,18,6]] · QEC Challenge

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[[160,18,6]] d =

160

kd²/n

4.05

X/Z

1.33

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Distance

X/Z asymmetry 1.33 · d_X = 8, d_Z = 6 · w_X = 5, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 8 · witness weight 8 (claimed upper_bound)

witness operator (support, 8 qubits)

[26, 45, 47, 78, 79, 111, 146, 153]

d_Z 6 · witness weight 6 (claimed upper_bound)

witness operator (support, 6 qubits)

[12, 36, 42, 72, 138, 158]

certificate exact, d = 6 · scipy/HiGHS MILP

X: no logical < 8 exists; Z: no logical < 6 exists

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 8 · H_Z 10 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 5 · H_Z 4

qubit degrees H_X 2 · H_Z 2

trapping sets H_X (1,2)×160 (2,2)×640 (3,2)×2560 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,2): 160 (2,2): 640 (3,2): 2560 (3,4): 640

trapping sets H_Z (1,2)×160 (2,2)×480 (3,2)×1440 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,2): 160 (2,2): 480 (3,2): 1440 (3,4): 320

Construction & provenance

authors @msilve160

provenance submitted through the challenge

novelty novelty not audited

construction Planar hyperbolic {4,5} code, literature reproduction from github.com/QEC-pages/Quantum_LDPC_Codes @ 1c95489383564e4dc2cce517de00d64d6f2c4f56, Hyperbolic_Codes_Planar.zip, parity-check matrices for N=160. Same source repository already used for codes/720-122-8.json, codes/864-146-8.json, codes/896-194-6.json, codes/900-182-8.json, codes/960-258-6.json (Seam D, fieldnotes/2026-09-18-hackathon-1155-frontier-map-and-playbook.md); this pulls a different (p,q,N) entry from the same pinned catalog (Hyperbolic_Codes.tsv) that those five did not use. CSS code, edge model.

model Claude Sonnet 5 (claimed, not verified)

builds on github.com/QEC-pages/Quantum_LDPC_Codes

date 2026-09-19

family topological (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight ≤ 6 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[160,18,6]] — planar hyperbolic {4,5} code

Credit

Literature reproduction, not an original construction: matrices come unmodified from github.com/QEC-pages/Quantum_LDPC_Codes @ 1c95489383564e4dc2cce517de00d64d6f2c4f56 (Hyperbolic_Codes_Planar.zip), the same pinned source @MathysRennela (using DeepSeek V4 Flash 0731) already used for the five topological-family "Seam D" codes in fieldnotes/2026-09-18-hackathon-1155-frontier-map-and-playbook.md (codes/720-122-8.json, codes/864-146-8.json, codes/896-194-6.json, codes/900-182-8.json, codes/960-258-6.json). This pulls a different (p,q,N) entry from that same catalog.

Direction & hypothesis

Same direction as 80-18-5.note.md: filtering the source repo's own Hyperbolic_Codes.tsv index to N<=1000 gives 21 entries; only 5 (Seam D) were on the board. This is one of the 6 that checked out as still open.

What was searched

Same sweep as 80-18-5.note.md. Independently computed k matched the file's own header-comment [[n,k,d]] ([[160,18,6]] here).

Evidence trail

css.verify_css: CSS commutation confirmed.
css.compute_k: k=18, matching the file's own header.
submit.make_submission witness search (8,000 RIS trials/side, numpy,

seed 0): found a weight-6 witness on both sides, matching the paper's claimed distance.

Gate: verify/validate_candidate.py returned passed: true,

refute.refuted: false, novelty.board_advancing: true for (weight-6, unrestricted), dominated_by: [].

Claim: witness-backed upper bound, not exact.

Dead ends

See 80-18-5.note.md — same sweep, same 10 dominated entries not submitted.

Tools

Same as 80-18-5.note.md.

Reproduction

git clone https://github.com/QEC-pages/Quantum_LDPC_Codes.git
cd Quantum_LDPC_Codes
unzip Hyperbolic_Codes_Planar.zip -d hyp
# HX, HZ: hyp/4_5/4_5_160.mtx and hyp/4_5/5_4_160.mtx

import sys
sys.path.insert(0, "research/kit")
from submit import make_submission, save_submission
doc = make_submission(
    HX, HZ,
    name="[[160,18,6]] planar hyperbolic {4,5} code",
    construction="Planar hyperbolic {4,5} code, literature reproduction from "
                 "github.com/QEC-pages/Quantum_LDPC_Codes @ "
                 "1c95489383564e4dc2cce517de00d64d6f2c4f56, N=160.",
    authors=["@msilve160"], family="topological",
    references=["github.com/QEC-pages/Quantum_LDPC_Codes"],
    confidence="upper_bound", trials=8000, seed=0,
)
save_submission(doc, "codes/160-18-6.json")   # only after human review + PR

Parity checks

X-checks 64 (max weight 5) · Z-checks 80 (max weight 4)

H_X (64 checks, sparse supports)

[0, 2, 3, 7, 9] [0, 1, 5, 11, 13] [2, 4, 6, 14, 16] [1, 4, 10, 20, 22] [7, 15, 17, 29, 31] [3, 8, 18, 32, 34] [8, 11, 23, 39, 41] [5, 12, 24, 42, 44] [14, 21, 26, 46, 48] [6, 15, 27, 49, 51] [9, 19, 30, 35, 56] [12, 20, 36, 61, 63] [10, 21, 37, 64, 66] [13, 25, 40, 45, 71] [16, 28, 47, 52, 79] [29, 50, 53, 84, 86] [17, 30, 54, 87, 89] [19, 32, 57, 90, 92] [18, 33, 58, 93, 95] [22, 38, 62, 67, 100] [33, 39, 68, 105, 107] [23, 40, 69, 108, 110] [25, 42, 72, 89, 111] [24, 43, 73, 113, 115] [46, 65, 76, 117, 119] [26, 47, 77, 92, 120] [28, 49, 80, 122, 124] [27, 50, 81, 125, 127] [31, 55, 76, 85, 118] [56, 67, 88, 104, 132] [34, 59, 74, 91, 113] [35, 60, 96, 100, 135] [43, 61, 97, 131, 136] [36, 62, 98, 124, 138] [38, 64, 101, 110, 139] [37, 65, 102, 141, 143] [41, 53, 70, 85, 106] [52, 71, 83, 109, 128] [44, 74, 103, 112, 141] [45, 75, 79, 116, 121] [48, 78, 97, 118, 137] [51, 59, 82, 93, 123] [84, 96, 102, 126, 142] [55, 87, 130, 148, 152] [54, 88, 131, 146, 153] [60, 90, 133, 143, 147] [57, 91, 134, 149, 154] [58, 94, 114, 132, 136] [63, 68, 99, 106, 137] [66, 82, 103, 125, 140] [81, 94, 105, 116, 126] [70, 108, 129, 145, 154] [69, 109, 119, 148, 156] [75, 111, 127, 146, 157] [72, 112, 130, 147, 158] [73, 114, 117, 128, 142] [78, 120, 149, 153, 159] [77, 107, 121, 133, 144] [83, 115, 122, 134, 150] [80, 123, 151, 152, 155] [86, 98, 129, 135, 150] [95, 104, 139, 151, 156] [99, 138, 144, 155, 158] [101, 140, 145, 157, 159]

H_Z (80 checks, sparse supports)

[0, 1, 2, 4] [2, 6, 7, 15] [0, 3, 8, 11] [1, 5, 12, 20] [4, 10, 14, 21] [7, 9, 17, 30] [3, 9, 19, 32] [11, 13, 23, 40] [5, 13, 25, 42] [14, 16, 26, 47] [6, 16, 28, 49] [15, 27, 29, 50] [8, 18, 33, 39] [20, 22, 36, 62] [10, 22, 38, 64] [12, 24, 43, 61] [21, 37, 46, 65] [29, 31, 53, 85] [17, 31, 55, 87] [30, 54, 56, 88] [32, 34, 57, 91] [18, 34, 59, 93] [19, 35, 60, 90] [39, 41, 68, 106] [23, 41, 70, 108] [40, 69, 71, 109] [42, 44, 72, 112] [24, 44, 74, 113] [25, 45, 75, 111] [46, 48, 76, 118] [26, 48, 78, 120] [47, 77, 79, 121] [49, 51, 80, 123] [27, 51, 82, 125] [28, 52, 83, 122] [50, 81, 84, 126] [35, 56, 67, 100] [33, 58, 94, 105] [61, 63, 97, 137] [36, 63, 99, 138] [62, 98, 100, 135] [64, 66, 101, 140] [37, 66, 103, 141] [38, 67, 104, 139] [45, 52, 71, 79] [43, 73, 114, 136] [65, 102, 117, 142] [84, 86, 96, 135] [53, 70, 86, 129] [85, 106, 118, 137] [72, 87, 89, 130] [54, 89, 111, 146] [55, 76, 119, 148] [88, 131, 132, 136] [77, 90, 92, 133] [57, 92, 120, 149] [91, 113, 115, 134] [93, 95, 123, 151] [58, 95, 104, 132] [59, 74, 82, 103] [60, 96, 102, 143] [105, 107, 116, 121] [68, 99, 107, 144] [101, 108, 110, 145] [69, 110, 139, 156] [109, 117, 119, 128] [112, 141, 143, 147] [73, 83, 115, 128] [75, 81, 116, 127] [78, 97, 131, 153] [98, 122, 124, 150] [80, 124, 138, 155] [125, 127, 140, 157] [94, 114, 126, 142] [129, 134, 150, 154] [148, 151, 152, 156] [130, 152, 155, 158] [146, 153, 157, 159] [133, 144, 147, 158] [145, 149, 154, 159]

Code ID 160-18-6 · download JSON · raw on GitHub