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面向测量诱导信息丢失场景的量子传感量子机器学习（QML）研究

文章背景与核心概要

本研究探讨了量子机器学习（QML）在金刚石氮-空位（NV）色心磁场估计中的应用。作为高灵敏度固态磁力测量的重要平台，NV色心在含噪声中等规模量子（NISQ）时代面临着从有限次测量和噪声数据中提取可靠参数的严峻挑战。

研究将磁场传感建模为监督回归任务，对比了基于测量后经典数据的传统机器学习模型与基于测量前相干量子态的量子核模型。核心目标在于量化测量诱导的信息丢失对传感性能的影响，并确立理论性能上限。研究结果表明，直接利用相干量子态信息能显著提升QML的传感性能，这强调了在实际量子传感应用中，将量子传感器与QML流水线深度集成的必要性。

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摘要

金刚石中的氮-空位（NV）色心可作为高灵敏度固态量子传感器，用于高精度磁力测量。然而，在含噪声中等规模量子（NISQ）时代，从噪声大、有限次测量且受限于测量过程的传感数据中提取可靠信息，仍然是一项巨大的挑战。量子机器学习（QML）通过学习量子传感数据与底层物理信号之间的非线性关系，为改进参数估计提供了一条潜在途径。

在这项工作中，我们研究了QML在受NV色心启发的磁力测量场景中进行磁场估计的作用。我们将磁场传感表述为一项监督回归任务。我们比较了基于测量后的经典数据训练的几种经典机器学习模型，与基于测量前的相干量子态训练的量子核模型之间的性能。我们的目标是分离出测量诱导的信息丢失所产生的影响，从而为传感性能提供一个理论上限。只有当学习模型能够直接获取相干量子信息时，该上限才是可实现的。

我们的结果表明，基于QML的传感性能随着相干量子态信息的引入而显著提高，而模型复杂度或学习范式的改变对其影响有限。这一观察结果强调了构建紧密集成量子传感器与QML模型的学习流水线，对于在现实约束下增强磁场传感能力的重要性。

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.