Estimation and Decoding of Drifting Noise in Quantum Error Correction

Abstract

Reliable and fault-tolerant quantum computation requires precise modeling and correction of noise affecting quantum devices. In practice, noise processes often vary over time, whereas many existing characterization and decoding methods assume stationary or time averaged error models. This treatment can result in suboptimal decoding performance. This thesis develops an analytical framework for identifying time-dependent Pauli noise directly from syndrome statistics generated during quantum error correction. We introduce a sliding-window estimation approach that extracts the frequency components of drifting noise. By analytically deriving optimal window lengths, we establish a clear relationship between window size and its effective spectral filtering properties, linking window parameters to corresponding cutoff frequencies. To capture more complex temporal behavior, we propose an iterative method for isolating multiple drift frequencies and an overlapping-window scheme that enables efficient single-pass tracking of rapidly varying, multi-frequency noise. Numerical simulations under both phenomenological and circuit-level noise models demonstrate accurate recovery of time-varying noise dynamics. Logical error rates computed using the estimated models closely match those from the true noise processes and show improved performance relative to static error models. Overall, the proposed window-based estimationand adaptive decoding strategies provide a systematic approach to noise spectroscopy and decoder optimization under temporal drift using only syndrome data