Bayesian Inference of General Noise Model Parameters from Surface Code's Syndrome Statistics

Active research on the surface code shows that its decoding performance can be significantly enhanced by utilizing the information of the noise model and optimizing the grid shape and decoding algorithm. Usually, the parameters in the noise model for the quantum error correction code must be prepared separately using some method, such as the quantum process tomography. There is a strong need to perform noise model estimation in parallel with the syndrome measurement during decoding to avoid the demanding prior tomography procedure. While noise model estimation based on syndrome measurement statistics is well-explored for Pauli noise, it remains under-studied for more complex noise models like amplitude damping. In this paper, we propose general noise model Bayesian inference methods that integrate the surface code's tensor network simulator, which can efficiently simulate various noise models, with Monte Carlo sampling techniques. For stationary noise, where the noise parameters are constant and do not change, we propose a method based on the Markov chain Monte Carlo. For time-varying noise, which is a more realistic situation, we introduce another method based on the sequential Monte Carlo. We present the numerical results of applying the proposed methods to various noise models, such as static, time-varying, and non-uniform cases, and evaluate their performance in detail.