Adaptive Estimation of Drifting Noise in Quantum Error Correction

TL;DR

This paper introduces a novel adaptive estimation framework for tracking time-dependent drifting noise in quantum error correction, improving decoding accuracy and logical error suppression by exploiting syndrome data.

Contribution

It develops a rigorous analytical framework and sliding-window algorithms to accurately estimate multi-frequency noise drifts in quantum systems, surpassing traditional static models.

Findings

Robust tracking of multi-frequency noise drifts demonstrated in simulations.

Estimated models' logical error rates align with ground-truth, showing improved accuracy.

Suppression of logical errors compared to static error models achieved.

Abstract

Advancing quantum information processors and building fault-tolerant architectures rely on the ability to accurately characterize the noise sources and suppress their impact on quantum devices. In practice, noise often drifts over time, whereas conventional noise characterization and decoding methods typically assume stationarity or provide only a time-average behavior of the noise. This treatment can result in suboptimal decoding performance. In this work, we present a rigorous analytical framework to capture time-dependent Pauli noise, by exploiting the syndrome statistics of quantum error correction experiments. We propose a sliding-window estimation method which allows us to recover the frequency components of the noise, by using optimal window sizes that we derive analytically. We prove the noise-filtering behavior of sliding windows, linking window size to spectral cutoff frequencies, and provide an iterative algorithm that captures multiple drift frequencies. We further introduce an overlapping window algorithm that enables us to capture rapid multi-frequency noise drifts in a single-pass fashion. Simulations for both phenomenological and circuit-level noise models validate our framework, demonstrating robust tracking of multi-frequency drift. The logical error rate obtained from our estimated models consistently align with the ground-truth logical error rate, and we find suppression of logical errors compared to static error models. Our window-based estimation methods and adaptive decoding offer new insights into noise spectroscopy and decoder optimization under drift using only syndrome data.