A matching decoder for bivariate bicycle codes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912928124370944 |
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| author | Sahay, Kaavya Williamson, Dominic J. Brown, Benjamin J. |
| author_facet | Sahay, Kaavya Williamson, Dominic J. Brown, Benjamin J. |
| contents | The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the minimum-weight perfect matching algorithm, a subroutine invaluable to decoding topological codes, to decode bivariate bicycle codes. Using the equivalence of bivariate bicycle codes to copies of the toric code, we propose a method we call the 'cylinder trick' to rapidly find a correction using matching on code symmetries. We benchmark our decoder on the gross code family, cyclic hypergraph-product codes, generalized toric codes, and recently proposed directional codes, demonstrating the general applicability of our protocol. For a subset of these codes, we find that our decoder can be significantly improved by augmenting matching with strategies including belief propagation and 'over-matching', thus achieving performance competitive with state-of-the-art approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22770 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A matching decoder for bivariate bicycle codes Sahay, Kaavya Williamson, Dominic J. Brown, Benjamin J. Quantum Physics The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the minimum-weight perfect matching algorithm, a subroutine invaluable to decoding topological codes, to decode bivariate bicycle codes. Using the equivalence of bivariate bicycle codes to copies of the toric code, we propose a method we call the 'cylinder trick' to rapidly find a correction using matching on code symmetries. We benchmark our decoder on the gross code family, cyclic hypergraph-product codes, generalized toric codes, and recently proposed directional codes, demonstrating the general applicability of our protocol. For a subset of these codes, we find that our decoder can be significantly improved by augmenting matching with strategies including belief propagation and 'over-matching', thus achieving performance competitive with state-of-the-art approaches. |
| title | A matching decoder for bivariate bicycle codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.22770 |