Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes

The performance of error correction in the surface code can be enhanced by leveraging the knowledge of the noise model for physical qubits. To provide accurate noise information to the decoder in parallel with quantum computation, an adaptive estimation of the noise model based on syndrome measurement statistics is an effective approach. While noise model estimation based on syndrome measurement statistics is well-established for Pauli noise, it remains unexplored for more complex and realistic scenarios such as amplitude damping which cannot be represented as a Pauli channel. In this paper, we propose Bayesian inference methods for general noise models, integrating a tensor network simulator of surface code, which can efficiently simulate various noise models, with Monte Carlo sampling techniques. For stationary noise, we propose a method based on the Markov chain Monte Carlo. For time-varying noise, which is a more realistic scenario, we introduce another method based on the sequential Monte Carlo. We present numerical results of applying our proposed methods to various noise models, such as static, time-varying, and nonuniform cases, and evaluate their performance in detail.