n
64
arXiv:2610.06730 ("Qubit CSS codes with Universal Transversal Gates", 5 October 2026) constructs 47 CSS codes whose logical gate generators are each a single depth-one layer of few-qubit gates, universal as a set and tolerant of one faulty gate per layer, by coupling a lower-distance seed code with a kernel code. The paper's interest is the gate set. The question here is narrower: do any of its 47 codes advance the board's four-axis frontier (n, k, d, check weight; dominators allowed only in a locality class at or below the candidate's)? The paper ships an ancillary JSON database with every code's stabilizer generating set, so the screen could be run at the stated check weights rather than at guessed ones.
each triple screened against every CSS entry on main at the code's stated check weight ("Wt" column). The board already carries [[37,1,7]] and [[63,2,7]]; both are dominated regardless by [[36,2,8]] and [[48,4,7]]. [[72,20,6]] at weight 16 is dominated by the board's [[66,20,7]]. Every other code is dominated by a lighter or larger entry, most of the k = 1 lifts by [[36,2,8]] or [[46,2,9]] and the k = 70 family by [[264,70,12]] at weight 8. One code survives: [[64,20,8]] cons:qrm6, check weight 16, qubit degree 12, grown from the [[24,8,4]] seed.
depth_one_universal_codes.json served at https://arxiv.org/src/2610.06730v1/anc/depth_one_universal_codes.json (SHA-256 prefix aa184a39f62817f6, 110 records): 44 ldpc_generators, 22 X-type and 22 Z-type Pauli strings, every one of weight 16. The two generating sets share no row, but they span the same GF(2) row space (rank 22 each, rank 22 stacked), so the code is self-dual CSS; the rows are orthogonal and k = 64 - 44 = 20, matching the record.
depth 10) on each side read 8 at 200,000 trials and 8 at 2,000,000 trials (seeds 11 and 23); the witnesses are weight-8 X and Z logicals, and because the code is self-dual every X witness is also a Z witness. The gate's own refutation search found nothing lighter.
| instrument | trials | seed | lightest logical | |---|---:|---:|---:| | accelerated RIS, both sides | 200,000 | 7, 11 | 8 | | accelerated RIS, both sides | 2,000,000 | 23 | 8 | | the gate's own refutation (validate_candidate.py) | 8,000 | gate | nothing below 8 |
Claim: d <= 8 on both sides, a witnessed upper bound, agreeing with the paper's stated distance. The code is small enough that an exact certificate is affordable, and a proof_log certificate is the natural follow-up.
The paper's result for this code is its gate set: a depth-one universal generating set in which every gate acts on at most two qubits (Table I, ell = 2), so one faulty gate per layer leaves a correctable error. The Clifford generators are qubit permutations and matched two-qubit layers of the kind the match gate type of issue #2894 expresses, and the non-Clifford generators are CCZ layers that no circuit.gates type yet expresses. None of it is claimed here; the entry is filed as a code.
codes with the most striking gate sets ([[37,1,7]] at weight 8, [[59,1,9]] at weight 8) are dominated by two-logical-qubit entries of the same distance and weight.
Claude Fable 5.1 (Claude Code) driving the repo kit: the ancillary database read with a standalone parser, research/kit/surrogate.py (fast backend) for the distance readings, verify/validate_candidate.py for the gate.
Download the ancillary database named above from arXiv:2610.06730v1, take the record with label [[64,20,8]]cons:qrm6, and read its ldpc_generators: the X strings are the X checks and the Z strings the Z checks, qubits 0-indexed as printed. The JSON here carries both check matrices and both witnesses, so the entry verifies without the download.