[[150,32,6]] · QEC Challenge

[[150,32,6]] d ≤

150

kd²/n

7.68

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 6, d_Z ≤ 6 · w_X = 5, w_Z = 5 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 6 · witness weight 6 (claimed upper_bound)

witness operator (support, 6 qubits)

[0, 10, 14, 42, 56, 133]

d_Z 6 · witness weight 6 (claimed upper_bound)

witness operator (support, 6 qubits)

[41, 46, 49, 65, 94, 116]

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

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

check weights H_X 5 · H_Z 5

qubit degrees H_X 2 · H_Z 2

trapping sets H_X (1,2)×150 (2,2)×600 (3,2)×2400 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,2): 150 (2,2): 600 (3,2): 2400 (3,4): 600

trapping sets H_Z (1,2)×150 (2,2)×600 (3,2)×2400 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,2): 150 (2,2): 600 (3,2): 2400 (3,4): 600

Construction & provenance

authors @msilve160

provenance submitted through the challenge

novelty novelty not audited

construction Planar hyperbolic {5,5} code, literature reproduction from github.com/QEC-pages/Quantum_LDPC_Codes @ 1c95489383564e4dc2cce517de00d64d6f2c4f56, Hyperbolic_Codes_Planar.zip, parity-check matrices for N=150. 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

[[150,32,6]] — planar hyperbolic {5,5} 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: the source repo's own index, Hyperbolic_Codes.tsv, lists every (p,q,N) it provides matrices for. Filtering 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: cloned the source repo at the pinned commit, read the full catalog, unzipped the matrix archive, loaded all 15 untouched candidates. Independently computed k matched the file's own header-comment [[n,k,d]] on every one ([[150,32,6]] here). All 15 were checked against the live board; 6 were open.

Evidence trail

css.verify_css: CSS commutation confirmed.
css.compute_k: k=32, 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: Claude Sonnet 5, git clone of the pinned source, a from-scratch .mtx reader cross-checked against research/kit/css.py, research/kit/submit.py, verify/validate_candidate.py.

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/5_5/5_5_150_X.mtx and hyp/5_5/5_5_150_Z.mtx

import sys
sys.path.insert(0, "research/kit")
from submit import make_submission, save_submission
doc = make_submission(
    HX, HZ,
    name="[[150,32,6]] planar hyperbolic {5,5} code",
    construction="Planar hyperbolic {5,5} code, literature reproduction from "
                 "github.com/QEC-pages/Quantum_LDPC_Codes @ "
                 "1c95489383564e4dc2cce517de00d64d6f2c4f56, N=150.",
    authors=["@msilve160"], family="topological",
    references=["github.com/QEC-pages/Quantum_LDPC_Codes"],
    confidence="upper_bound", trials=8000, seed=0,
)
save_submission(doc, "codes/150-32-6.json")   # only after human review + PR

Parity checks

X-checks 60 (max weight 5) · Z-checks 60 (max weight 5)

H_X (60 checks, sparse supports)

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

H_Z (60 checks, sparse supports)

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

Code ID 150-32-6 · download JSON · raw on GitHub