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arXiv · 2603.19522

Preserving MWPM-Decodability in Fault-Equivalent Rewrites

Maximilian Schweikart·Linnea Grans-Samuelsson·Aleks Kissinger·Benjamin Rodatz
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Abstract

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.

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Maximilian Schweikart, Linnea Grans-Samuelsson, Aleks Kissinger, Benjamin Rodatz. 2026-03-19. Preserving MWPM-Decodability in Fault-Equivalent Rewrites. https://arxiv.org/abs/2603.19522

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