Machine learning for predictive estimation of qubit dynamics subject to dephasing

TL;DR

This paper compares machine learning algorithms like Kalman Filters and Gaussian Process Regression for predicting qubit state evolution under dephasing, highlighting the strengths and limitations of each approach in quantum state estimation.

Contribution

It provides a detailed comparison of ML algorithms for qubit prediction, emphasizing autoregressive Kalman Filters' superior performance and analyzing GPR limitations.

Findings

Autoregressive Kalman Filter outperforms Fourier-based approaches.

GPR methods are generally unsuitable for forward prediction in this context.

Filter optimization is crucial for achieving good prediction performance.

Abstract

Decoherence remains a major challenge in quantum computing hardware and a variety of physical-layer controls provide opportunities to mitigate the impact of this phenomenon through feedback and feedforward control. In this work, we compare a variety of machine learning algorithms derived from diverse fields for the task of state estimation (retrodiction) and forward prediction of future qubit state evolution for a single qubit subject to classical, non-Markovian dephasing. Our approaches involve the construction of a dynamical model capturing qubit dynamics via autoregressive or Fourier-type protocols using only a historical record of projective measurements. A detailed comparison of achievable prediction horizons, model robustness, and measurement-noise-filtering capabilities for Kalman Filters (KF) and Gaussian Process Regression (GPR) algorithms is provided. We demonstrate superior performance from the autoregressive KF relative to Fourier-based KF approaches and focus on the role of filter optimization in achieving suitable performance. Finally, we examine several realizations of GPR using different kernels and discover that these approaches are generally not suitable for forward prediction. We highlight the underlying failure mechanism in this application and identify ways in which the output of the algorithm may be misidentified numerical artefacts.