Fast and Accurate Decoder for the XZZX Code Using Simulated Annealing

Abstract

The XZZX code is a variant of the surface code tailored to address biased noise in realistic quantum devices. We propose a simulated annealing (SA) decoder for the XZZX code. Our SA decoder is amenable to parallelization because its MCMC updates are simple and local. To initialize SA, we use a recovery configuration produced by our greedy matching decoder. Although $Z$-biased noise is commonly assumed in realistic quantum devices, we instead focus on $Y$-biased noise, where MWPM becomes suboptimal because it neglects correlations induced by $Y$ errors. Our numerical simulations for the code capacity noise model, where only data qubits suffer errors, show that our SA decoder achieves higher accuracy than the MWPM decoder. Furthermore, our SA decoder achieves an accuracy comparable to that of the optimal minimum-energy (MAP-configuration) decoder formulated as an integer programming problem, called the CPLEX decoder. In our greedy matching decoder, we randomize the tie-breaking among equal-weight pairs. This randomness generates a variety of initial configurations for SA, which can lead to faster convergence of our SA decoder. By comparing decoding times of our SA decoder, the CPLEX decoder, and the matrix product state (MPS) decoder, all of which can handle $Y$-biased noise appropriately, we estimate that our SA decoder could be competitive in runtime under an idealized assumption of near-perfect parallel efficiency. These results suggest that combining SA with our greedy matching initializer is a practical approach toward fault-tolerant quantum computation.