QML for Quantum Sensing under Measurement-Induced Information Loss

Sounak Bhowmik; Himanshu Thapliyal

quant-phAug 25, 2026

QML for Quantum Sensing under Measurement-Induced Information Loss

Authors: Sounak Bhowmik, Himanshu Thapliyal

Organizations: Department of Electrical and Computer Engineering Southern Methodist University, Dallas, TX, USA

Abstract

Nitrogen-vacancy (NV) centers in diamond can serve as highly sensitive solid-state quantum sensors for high-sensitivity magnetometry. However, in the noisy intermediate-scale quantum (NISQ) era, extracting reliable information from noisy, finite-shot, and measurement-limited sensing data remains a considerable challenge. Whereas, quantum machine learning (QML) offers a potential path to improve parameter estimation by learning nonlinear relationships between quantum-sensing data and the underlying physical signal. In this work, we investigate the role of QML in magnetic-field estimation within an NV center-inspired magnetometry setting. We formulated magnetic field sensing as a supervised regression task. We compared the performance of several classical machine learning models trained on measurement-based classical data with that of quantum kernel-based models trained on pre-measurement coherent quantum states. Our objective is to isolate the impact of measurement-induced information loss and therefore provide a theoretical upper bound on the sensing performance. The upper bound is achievable only when coherent quantum information is directly available to the learning model. Our results show that QML-based sensing performance improves significantly with coherent quantum-state information, and not much with changes in model complexity or learning paradigm. This observation underscores the importance of learning pipelines that tightly integrate quantum sensors and QML models to enhance magnetic field sensing under realistic constraints.

Figures & tables

Fig. 1 : Level diagram of a nitrogen-vacancy center in diamond, where a substitutional nitrogen atom and an adjacent vacancy form a spin defect used for nanoscale magnetometry. Without any external magnetic field, the energies of the orbital ground states, $\in\{\ket{0},\ket{\pm 1}\}$ , split, called zero field splitting (ZFS). In the presence of an external magnetic field, $B_{NV}$ along the quantization axis of the crystal, the degenerate ground states, $\ket{+1}$ and $\ket{-1}$ , split up, which is referred to as Zeeman splitting. Once optically excited, the $\ket{\pm 1}$ states decay through metastable singlet states to the ground state, $\ket{0}$ , leading to optical initialization and spin-dependent fluorescence to be read optically to estimate the unknown magnetic field.

Fig. 2 : Magnetic field estimation using NV center-inspired quantum sensing simulation. (A) Ramsey Interferometry simulation: $\theta_{i}=\gamma B_{i}t_{k}$ ; $\rho_{i}(t_{k})$ is the corresponding density matrix, after the system evolves under a magnetic field $B_{i}$ for time $t_{k}$ ; $\mathbf{x_{i}}$ is the corresponding expectation value of the observable. (B) Regression problem to estimate the unknown magnetic field: $\hat{B}^{\rho}$ and $\hat{B}^{\braket{x}}$ are the estimated magnetic field values based on coherent-state and classical measurement statistics, respectively.

Parameter	Value
Magnetic field range	$B\in[0,2]~\mu T$
Training samples	800
Test samples	100
Evolution times	$\{5,10,20,40,60\}~\mu s$
Random seeds	$3$
Dephasing time	$T_{2}=100~\mu s$

TABLE I : Simulation and learning parameters used in the NV center-inspired sensing benchmark.

Fig. 3 : NV center-inspired magnetometry regression (mean $\pm$ std over seeds): Depicts the theoretical upper bound, and its performance gap with the models learning from the measurement data. The estimation error in the latter is $100$ times more. Sensing pipelines that are more closely integrated with the coherent quantum states, or a more sophisticated measurement strategy, can help to close this gap and provide more accurate results.

Fig. 4 : Test RMSE ( $\mu$ T) at 2048 shots (mean $\pm$ std): The RMSE is significantly lower in the theoretical upper bound, which highlights its gap with the measurement-based learning models.

Quantum Machine Learning

Quantum machine learning uses quantum circuits and quantum data to build learning algorithms and study their computational and statistical limits.

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Bayesian quantum sensing using graybox machine learning

Akram Youssry, Stefan Todd, Patrick Murton, Muhammad Junaid Arshad+3

Quantum Photonics Laboratory and Centre for Quantum Computation and Communication Technology, RMIT University, Melbourne, VIC 3000, Australia · School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia · Institute of Photonics and Quantum Sciences, SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK+1

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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.

Abstract

Quantum Machine Learning

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