Year: 2026
Type: preprint
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 $n \leq 37$; for inequivalent code instances with $n=144$, they are about 310 s for permutation and 16 s for local-Clifford equivalence.
Source: arXiv (Cornell University)
Authors: Bichmann, Maxie, Schmid, Ludwig, Wille, Robert
Institution: Technical University of Munich
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1929973641, G5628674369
OpenAlex ID: W7221833849