Simulated-annealing decoder for the XZZX code with greedy-matching initialization

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 Markov chain Monte Carlo 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. Under $Y$-biased noise, the minimum-weight perfect matching (MWPM) decoder becomes suboptimal because it cannot take into account the fact that a $Y$ error contains both $X$ and $Z$ components on the same qubit. 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. They also show that, under moderately $Y$-biased noise, our SA decoder achieves accuracy comparable to that of a decoder based on IBM ILOG CPLEX Optimizer (CPLEX), which uses integer programming to find a minimum-energy error configuration consistent with the measured syndrome. 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 improves the convergence of our SA decoder. These results suggest that combining SA with our greedy-matching initializer is a promising approach to decoding the XZZX code under $Y$-biased noise in the code capacity noise model.

arXiv comment26 pages, 15 figures; revised to match the published version

References in corpus (25)

• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Topological quantum memory
• Multiple Particle Interference and Quantum Error Correction
• Suppressing quantum errors by scaling a surface code logical qubit
• Quantum error correction below the surface code threshold
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Quantum Low-Density Parity-Check Codes
• The XZZX Surface Code
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Towards practical classical processing for the surface code
• Tailoring surface codes for highly biased noise
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes
• High threshold error correction for the surface code
• Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
• Statistical mechanical models for quantum codes with correlated noise
• An efficient Markov chain Monte Carlo algorithm for the surface code
• High threshold codes for neutral atom qubits with biased erasure errors
• Measurement-free topological protection using dissipative feedback
• Pipelined correlated minimum weight perfect matching of the surface code
• Tailored cluster states with high threshold under biased noise
• Ising model formulation for highly accurate topological color codes decoding
• Error-rate-agnostic decoding of topological stabilizer codes