Tracking and adapting to non-stationary noise in quantum channels

Errors in quantum computing stem from various sources e.g. qubit cross-talk, environmental coupling, pulse distortion, and electromagnetic shielding issues. Non-stationary statistics however challenge reproducibility of error mitigated outcomes obtained using probabilistic error cancellation. We present results that quantify the importance of well-characterized hardware for ensuring outcome stability. We evaluate circuit performance in non-stationary conditions, comparing expected outcomes to those observed on transmon devices. We establish performance bounds based on characterization data.Our results indicate that outcome stability is bounded by the Hellinger distance between the joint distribution of noise parameters. We also explore Bayesian inference for adaptive noise estimation to enhance PEC accuracy in the Bernstein-Vazirani test circuit using decoherence data from the ibm_kolkata device. We establish a direct connection between inference efficiency and PEC accuracy in the presence of non-stationary amplitude and phase damping noise affecting CNOT gates. When Bayesian inference is 90% accurate, PEC mitigated observable error stays below 20%. If accuracy drops to 66%, the error rises to 35%. These results enable better understanding of the variations observed in quantum computing experiments and underscore the need for adaptive approaches in quantum error mitigation for ensuring reproducibility on near term devices within the quantum computing community.