# Bayesian quantum sensing using graybox machine learning

arXiv: https://arxiv.org/abs/2601.17465 · HTML: https://mlsanity.com/paper/2601.17465/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 92 references that are in the map.
- First posted on arXiv 24 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [Hardware Conditioned Policies for Multi-Robot Transfer Learning](https://mlsanity.com/paper/1811.09864/) (2018)
- [Learning models of quantum systems from experiments](https://mlsanity.com/paper/2002.06169/) (2020)
- [Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation](https://mlsanity.com/paper/2502.00782/) (2025)
- [Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows](https://mlsanity.com/paper/2211.00214/) (2022)
- [Experimental graybox quantum system identification and control](https://mlsanity.com/paper/2206.12201/) (2022)
- [Quantum Geometric Machine Learning for Quantum Circuits and Control](https://mlsanity.com/paper/2006.11332/) (2020)
- [Noise Detection with Spectator Qubits and Quantum Feature Engineering](https://mlsanity.com/paper/2103.13018/) (2021)
- [Multi-Axis Control of a Qubit in the Presence of Unknown Non-Markovian Quantum Noise](https://mlsanity.com/paper/2208.03058/) (2022)
- [Quantum control in the presence of strongly coupled non-Markovian noise](https://mlsanity.com/paper/2404.19251/) (2024)
- [Quantum Feature Space of a Qubit Coupled to an Arbitrary Bath](https://mlsanity.com/paper/2505.03397/) (2025)
- [Resource-efficient adaptive Bayesian tracking of magnetic fields with a quantum sensor](https://mlsanity.com/paper/2008.08891/) (2020)
- [Singularity-free dynamical invariants-based quantum control](https://mlsanity.com/paper/2510.15340/) (2025)

## Abstract (arXiv)

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 blackbox 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, as well as significant improvement over a blackbox model with comparable size. 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.