Fast and accurate decoder for the XZZX code using simulated annealing

The XZZX code is a variant of the surface code to incorporate biased noise in realistic quantum device. Although, as decoders of surface codes, minimum-weight perfect matching (MWPM) algorithm is widely used, it can take into account only X (bit-flip) and Z (phase-flip) errors, not Y (bit-flip and phase-flip) errors. To handle Y errors appropriately, Markov chain Monte Carlo (MCMC) decoders and matrix product state (MPS) decoders have been researched, and however, these decoders are too slow. For the XZZX code, we formulate decoding as energy minimization problem of Ising model, and apply simulated annealing (SA) to solve them. Specifically, to prepare an initial configuration of SA, we propose to employ recovery chains obtained by a greedy matching decoder, which brings us fast convergence of SA. By numerical simulation for code capacity noise model where only data qubits suffer errors, we confirmed that our SA decoder is more accurate than the MWPM decoder. Furthermore, our SA decoder attained the accuracy, equivalent to the optimal decoder formulated by integer programming. By comparing decoding times of our SA decoder, the decoder by the integer programming, and the MPS decoder, we confirmed that our SA decoder is fastest if parallelized. This result implies a possibility of the combination of our greedy matching and SA decoders in quantum error correction.