[[47,23,3]] · QEC Challenge

[[47,23,3]] d =

kd²/n

4.40426

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 10, w_Z = 10 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 3 · witness weight 3 (claimed upper_bound)

witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-01

witness operator (support, 3 qubits)

[5, 15, 17]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-01

witness operator (support, 3 qubits)

[22, 34, 38]

certificate exact, d = 3 · CryptoMiniSat 5.14 SAT · level proof_log: the refutation was re-checked by drat-trim and is replayed by CI

X: no logical < 3 exists; Z: no logical < 3 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 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 10 · H_Z 10

qubit degrees H_X 1–5 (mean 2.553) · H_Z 1–5 (mean 2.553)

trapping sets H_X (1,1)×6 (2,1)×37 (3,0)×23 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 6 (1,2): 17 (1,3): 19 (1,4): 2 (1,5): 3 (2,1): 37 (2,2): 83 (2,3): 142 (2,4): 128 (2,5): 37 (2,6): 22 (2,7): 2 (2,8): 1 (3,0): 23 (3,1): 189 (3,2): 598 (3,3): 1117 (3,4): 1406 (3,5): 1056 (3,6): 582 (3,7): 241 (3,8): 50 (3,9): 14

trapping sets H_Z (1,1)×6 (2,1)×37 (3,0)×23 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction priced calculus E-PUNCTURE transform of codes/48-20-4.json

model Beam 1.0 (claimed, not verified)

date 2026-11-01

family other (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (computed)

How this code was found

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

[[47,23,3]] — priced calculus E-PUNCTURE transform of 48-20-4.json

Direction & hypothesis

Weight-10 unrestricted CSS cell. Transform a connected CSS parent (48-20-4.json, a board entry) with the priced construction calculus to obtain a connected child that is not dominated by any existing entry in its track cell.

What was searched

Single-step and depth-2 deletion (C-DELETE-CHECK), peel (E-PEEL), and puncture (E-PUNCTURE) moves enumerated with machine.planner.plan from github.com/MathysRennela/code-calculus-dev. Parent: codes/48-20-4.json. Rule used for this survivor: E-PUNCTURE. Connected children only; bare-qubit children and dominated candidates dropped. Witness search at 1000 RIS trials per side (research/kit/surrogate.lightest_logical, seeds 0/1), then verify/validate_candidate.py with full refutation.

Evidence trail

The submitted distance is a witness-backed upper bound: d = min(d_X, d_Z) with explicit X and Z logical witnesses carried in the JSON. The gate's random-seed refutation found no lighter logical. Parent entry: codes/48-20-4.json.

Dead ends

Other single-step moves from the same parents were discarded as disconnected, bare-qubit children, dominated candidates, or refuted by the gate.

Tools

Model: Beam 1.0. Harness: research/kit (coordination, submit, prescreen), code-calculus consumer. Approx compute: CPU only.

Reproduction

Rebuild H_X/H_Z from codes/48-20-4.json by applying the E-PUNCTURE move of the priced calculus as recorded above; re-run the witness search at the stated budget.

Parity checks

X-checks 12 (max weight 10) · Z-checks 12 (max weight 10)

H_X (12 checks, sparse supports)

[0, 3, 7, 12, 19, 23, 31, 41, 43, 45] [1, 2, 6, 13, 20, 24, 32, 42, 44, 46] [1, 2, 5, 14, 21, 25, 33, 39, 43, 45] [0, 3, 4, 15, 22, 26, 34, 40, 44, 46] [3, 4, 7, 8, 16, 27, 35, 39, 41, 45] [2, 5, 6, 9, 17, 28, 36, 40, 42, 46] [1, 5, 6, 10, 18, 29, 37, 39, 41, 43] [4, 8, 11, 15, 19, 25, 27, 29, 31, 39] [5, 9, 10, 14, 20, 26, 28, 30, 32, 40] [6, 9, 10, 13, 21, 23, 27, 29, 33, 41] [5, 13, 17, 18, 21, 24, 34, 36, 38, 40] [6, 14, 17, 18, 20, 25, 31, 35, 37, 41]

H_Z (12 checks, sparse supports)

[0, 10, 12, 14, 16, 23, 26, 30, 35, 43] [1, 11, 13, 15, 17, 24, 25, 29, 36, 44] [2, 8, 12, 14, 18, 24, 25, 28, 37, 45] [4, 8, 10, 14, 19, 26, 27, 30, 31, 39] [5, 9, 11, 15, 20, 25, 28, 29, 32, 40] [6, 8, 10, 12, 21, 24, 28, 29, 33, 41] [7, 9, 11, 13, 22, 23, 27, 30, 34, 42] [0, 8, 18, 19, 21, 27, 31, 34, 38, 43] [2, 10, 16, 19, 21, 29, 32, 33, 36, 45] [2, 4, 6, 8, 16, 27, 35, 39, 42, 46] [3, 5, 7, 9, 17, 28, 36, 40, 41, 45] [0, 4, 6, 10, 18, 29, 37, 40, 41, 44]

Code ID 47-23-3 · download JSON · raw on GitHub