Preserving MWPM-Decodability in Fault-Equivalent Rewrites

Quantum Physics [Submitted on 19 Mar 2026] Preserving MWPM-Decodability in Fault-Equivalent Rewrites Maximilian Schweikart, Linnea Grans-Samuelsson, Aleks Kissinger, Benjamin Rodatz Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to efficiently, approximately solve the decoding problem through minimum-weight perfect matching (MWPM). However, this efficiency-enabling property can be lost when constructing implementations for fault-tolerant gadgets such as syndrome-extraction circuits or logical operations. In this work, we take a circuit-centric perspective to formalise how the decoding problem changes when applying ZX rewrites to a ZX diagram with a given detector basis. We demonstrate a set of rewrites that preserve MWPM-decodability of circuits and show that these matchability-preserving rewrites can be used to fault-tolerantly extract quantum circuits from phase-free ZX diagrams. In particular, this allows us to build efficiently decodable, fault-tolerant syndrome-extraction circuits for matchable codes. Comments: 23 pages. Submitted to QPL 2026 Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.19522 [quant-ph]   (or arXiv:2603.19522v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.19522 Focus to learn more Submission history From: Maximilian Tim Schweikart [view email] [v1] Thu, 19 Mar 2026 23:23:28 UTC (80 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)