Bayesian quantum sensing using graybox machine learning

TL;DR

This paper demonstrates a graybox machine learning approach for quantum sensing that combines physics-based models with data-driven techniques, significantly improving magnetic field estimation accuracy in solid-state quantum sensors.

Contribution

The work introduces the first experimental graybox modeling strategy for a solid-state quantum system, enhancing sensor fidelity with fewer training data compared to deep learning.

Findings

Graybox model outperforms physics-only models in magnetic field estimation

Achieves several orders of magnitude reduction in mean squared error

Requires fewer training data than fully deep-learning approaches

Abstract

Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often constrained by unmodelled effects, including noise, imperfect state preparation, and non-ideal control fields. In this work, we report the first experimental implementation of a graybox modelling strategy for a solid-state open quantum system. The graybox framework integrates a physics-based system model with a data-driven description of experimental imperfections, achieving higher fidelity than purely analytical (whitebox) approaches while requiring fewer training resources than fully deep-learning models. We experimentally validate the method on the task of estimating a static magnetic field using a single-spin quantum sensor, performing Bayesian inference with a graybox model trained on prior experimental data. Using roughly 10,000 training datapoints, the graybox model yields several orders of magnitude improvement in mean squared error over the corresponding physics-only model. These results are broadly applicable to a wide range of quantum sensing platforms, not limited to single-spin systems, and are particularly valuable for real-time adaptive protocols, where model inaccuracies can otherwise lead to suboptimal control and degraded performance.