A matching decoder for bivariate bicycle codes

• URL: http://arxiv.org/abs/2602.22770v1
• Date: Thu, 26 Feb 2026 09:00:20 GMT
• Title: A matching decoder for bivariate bicycle codes
• Authors: Kaavya Sahay, Dominic J. Williamson, Benjamin J. Brown,
• Abstract summary: We propose a method we call the 'cylinder trick' to rapidly find a correction using matching on code symmetries.<n>We benchmark our decoder on the gross code family, cyclic hypergraph-product codes, generalized toric codes, and recently proposed directional codes.<n>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'
• Score: 0.8739101659113153
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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