Methods for Automated Equivalence Checking of Quantum Error-Correction Codes
Abstract
Quantum error-correction code and circuit construction is an active field of research, motivating automated methods for identifying equivalent designs. We develop and evaluate automated strategies for deciding whether two descriptions of quantum error-correction codes are equivalent under specified transformations. We formalize permutation equivalence for stabilizer and CSS codes and local-Clifford equivalence for stabilizer codes within a unified framework that separates physical from representation freedom. We develop three decision strategies (group-action search, isomorphism-based methods, and constraint solving), together with invariants and signatures for preprocessing. The empirical evaluation shows that no paradigm dominates across equivalence notions, code families, and parameter ranges. We therefore combine their complementary strengths in input-dependent hybrid checkers following a staged Refute-Refine-Decide architecture. Mean hybrid runtimes remain below 10 s for most evaluated structured-code cases with n ≤ 37; for inequivalent code instances with n=144, they are about 310 s for permutation and 16 s for local-Clifford equivalence.
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BibTeX
@misc{bichmann2026methods,
title = {{Methods for Automated Equivalence Checking of Quantum Error-Correction Codes}},
author = {Maxie Bichmann and Ludwig Schmid and Robert Wille},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18218},
eprint = {2610.18218},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18218},
}
RIS
TY - UNPB
TI - Methods for Automated Equivalence Checking of Quantum Error-Correction Codes
AU - Maxie Bichmann
AU - Ludwig Schmid
AU - Robert Wille
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18218
UR - https://arxiv.org/abs/2610.18218
AB - Quantum error-correction code and circuit construction is an active field of research, motivating automated methods for identifying equivalent designs. We develop and evaluate automated strategies for deciding whether two descriptions of quantum error-correction codes are equivalent under specified transformations. We formalize permutation equivalence for stabilizer and CSS codes and local-Clifford equivalence for stabilizer codes within a unified framework that separates physical from representation freedom. We develop three decision strategies (group-action search, isomorphism-based methods, and constraint solving), together with invariants and signatures for preprocessing. The empirical evaluation shows that no paradigm dominates across equivalence notions, code families, and parameter ranges. We therefore combine their complementary strengths in input-dependent hybrid checkers following a staged Refute-Refine-Decide architecture. Mean hybrid runtimes remain below 10 s for most evaluated structured-code cases with n ≤ 37; for inequivalent code instances with n=144, they are about 310 s for permutation and 16 s for local-Clifford equivalence.
ER -