  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.
