Quantum error-correcting code parameters, checkable by a certificate of provable size
Abstract
Quantum error correction protects quantum information by encoding it in a code described by three numbers: how many physical qubits it uses, how many logical qubits it protects, and the smallest error it cannot detect. The last is an optimum over exponentially many candidates, so it is read off a solver rather than checked. Here we show that code parameters can be certified by a short certificate, a list or a pairing or a symbolic instance, whose correctness the kernel of a proof assistant decides by computation, and whose size is itself a theorem rather than an estimate. Two published code families have distances settled here: the bivariate bicycle code's $[[144,12,12]]$, certified, and the affine-permutation codes printed at [[1152,580,≤ 12]] and [[2304,1156,≤ 14]], settled at twelve and fourteen. Eleven code families and thirty-nine parameter sets follow, with nothing beyond three standard axioms trusted and the pipeline's specification step preset to twenty columns.
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BibTeX
@misc{an2026quantum,
title = {{Quantum error-correcting code parameters, checkable by a certificate of provable size}},
author = {Shuoming An and Fusheng Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03214},
eprint = {2610.03214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03214},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum error-correcting code parameters, checkable by a certificate of provable size
AU - Shuoming An
AU - Fusheng Yang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.03214
UR - https://arxiv.org/abs/2610.03214
AB - Quantum error correction protects quantum information by encoding it in a code described by three numbers: how many physical qubits it uses, how many logical qubits it protects, and the smallest error it cannot detect. The last is an optimum over exponentially many candidates, so it is read off a solver rather than checked. Here we show that code parameters can be certified by a short certificate, a list or a pairing or a symbolic instance, whose correctness the kernel of a proof assistant decides by computation, and whose size is itself a theorem rather than an estimate. Two published code families have distances settled here: the bivariate bicycle code's $[[144,12,12]]$, certified, and the affine-permutation codes printed at [[1152,580,≤ 12]] and [[2304,1156,≤ 14]], settled at twelve and fourteen. Eleven code families and thirty-nine parameter sets follow, with nothing beyond three standard axioms trusted and the pipeline's specification step preset to twenty columns.
ER -