Preserving MWPM-Decodability in Fault-Equivalent Rewrites
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908902045515776 |
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| author | Schweikart, Maximilian Grans-Samuelsson, Linnea Kissinger, Aleks Rodatz, Benjamin |
| author_facet | Schweikart, Maximilian Grans-Samuelsson, Linnea Kissinger, Aleks Rodatz, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19522 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Preserving MWPM-Decodability in Fault-Equivalent Rewrites Schweikart, Maximilian Grans-Samuelsson, Linnea Kissinger, Aleks Rodatz, Benjamin Quantum Physics 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. |
| title | Preserving MWPM-Decodability in Fault-Equivalent Rewrites |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.19522 |