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.
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.
Quantum machine learning (QML) provides a transformative approach to data analysis by integrating the principles of quantum computing with classical machine learning methods. With the exponential growth of data and the increasing complexity of computational tasks, quantum algorithms offer tremendous advantages in terms of processing speed, memory efficiency, and the ability to resolve issues intractable for classical systems. In this work, the use of QML techniques for both supervised and unsupervised learning problems is explored. Quantum-enhanced models such Quantum Support Vector Machines (QSVMs) and Quantum Neural Networks (QNNs) show outstanding performance in classification and regression tasks by using quantum kernels and entanglement in supervised learning. Moreover, hybrid quantum-classical solutions offer useful implementations on noisy intermediate-scale quantum (NISQ) devices, hence bridging the gap between present quantum technology and practical uses. By means of comparative analysis, this paper emphasizes the possible benefits and drawbacks of QML, thereby providing understanding of its future importance in sectors including material science, finance, and healthcare. In the end, QML opens the path for a new era of intelligent data processing and solves until unthinkable difficult challenges.
Quantum Machine Learning (QML) is an exciting frontier applying the philosophy of quantum computation to classical machine learning for improved learning performance of complicated tasks. However, QML is greatly challenged by realistic issues like noisy quantum measurements and limited labeled quantum data caused by the high cost and technological limitations. This paper explores the novel transfer-learning mechanisms to tackle these issues, which allow the reuse of the knowledge from related quantum tasks for improving model performance and generalization in resource-limited scenarios. Transfer learning, one of the great and successful concepts of classical machine learning, is to transfer the learned parameters or features from the source domain (or task) to the target domain (or task). We further develop and investigate, in quantum, a methodology where parameterized quantum circuits (PQCs) learnt on a source quantum data set have certain parts partially re-used or fine-tuned for a target task, given limited amount of target data. This strategy also avoids large quantum training runs that are not scalable on state-of-the-art noisy intermediate-scale quantum (NISQ) processors. The suggested methods are layerwise quantum adaptation, quantum kernel reuse and hybrid quantum-classical feature transfer. We investigate the robustness of these mechanisms in presence of noise by simulating quantum circuits using depolarizing and readout noise models. Moreover, we show that pretraining of quantum models on synthetic (or simulated) data sets (which are generated using larger, less noisy systems) can be instrumental in learning on real, small-sized quantum devices. Experiment results in quantum classification tasks demonstrate the effectiveness of transfer learning in boosting the accuracy, accelerating the convergence, and lowering the quantum circuit depth of successfully trained model. It is interesting to mention that transfer using layer-wise models became very resistant to quantum noise, as its performance did not degrade significantly for noisy inputs. These results demonstrate that transfer learning can overcome the scarce quantum data and suppress the harmful impact of measurement noise. This work presents a potential venue for enhancing the applicability of QML in the NISQ era. By transferring knowledge from theoretical quantum learning models to actual quantum hardware constraints, transfer learning allows quantum algorithms to learn faster and generalize better across tasks.
Quantum sensing offers sensitivities surpassing classical limits, yet practical deployment is often constrained by noise and inefficient signal extraction. This systematic review synthesizes literature from 2015 to 2025 and maps the landscape of data-driven signal processing across diverse platforms, including nitrogen-vacancy (NV) centers and cold atom interferometers. Emerging methodologies are categorized and emphasis is placed on the dominance of hybrid quantum-classical architectures where classical machine learning manages high-dimensional data processing while quantum processors execute specific primitives like feature mapping. Our findings demonstrate that advanced statistical frameworks such as Variational Bayesian Inference (VBI) enable scalable multi-parameter estimation with polynomial complexity, allowing dozens of sensor parameters to be estimated within minutes. Meanwhile, quantum sensing missions in GPS-denied navigation have achieved operational gains through AI-automated software designed to manage quantum hardware drifts and environmental noise, despite a persistent reality gap for generalized quantum machine learning. We further analyze the critical sensitivity-robustness dilemma inherent in entangled sensors and discuss mitigation strategies such as covariant quantum error-correcting codes. We also distinguish between theoretical Quantum Fisher Information (QFI) and realized Mean Squared Error (MSE) of sensor outputs to resolve benchmarking inconsistencies in quantum metrology, and propose a "Gold Standard" reproducibility framework tailored for the Noisy Intermediate-Scale Quantum (NISQ) era to promote automated workflows and hardware calibration transparency. This review provides a strategic roadmap for researchers to bridge the gap between theoretical sensitivity and reliable, software-defined operational utility in quantum sensing.
In modern-day quantum metrology, quantum sensors are widely employed to detect weak magnetic fields or nanoscale signals. Quantum devices, exploiting quantum coherence, are inevitably connected to physical constants and can achieve accuracy, repeatability, and precision approaching fundamental limits. As a result, these sensors have shown utility in a wide range of research domains spanning both science and technology. A rapidly emerging quantum sensing platform employs atomic-scale defects in crystals. In particular, magnetometry using nitrogen-vacancy (NV) color centers in diamond has garnered increasing interest. NV systems possess a combination of remarkable properties, optical addressability, long coherence times, and biocompatibility. Sensors based on NV centers excel in spatial resolution and magnetic sensitivity. These diamond-based sensors promise comparable combination of high spatial resolution and magnetic sensitivity without cryogenic operation. The above properties of NV magnetometers promise increasingly integrated quantum measurement technology, as a result, they have been extensively developed with various protocols and find use in numerous applications spanning materials characterization, nuclear magnetic resonance (NMR), condensed matter physics, paleomagnetism, neuroscience and living systems biology, and industrial vector magnetometry. In this chapter, NV centers are explored for magnetic sensing in a number of contexts. In general, we introduce novel regimes for magnetic-field probes with NV ensembles. Specifically, NV centers are developed for sensitive magnetometers for applications where microwaves (MWs) are prohibitively invasive and operations need to be carried out under zero ambient magnetic field. The primary goal of our discussion is to improve the utility of these NV center-based magnetometers.
Nitrogen-vacancy (NV) centers in diamond are a versatile quantum sensing platform for high sensitivity measurements of magnetic fields, temperature and strain with nanoscale spatial resolution. A common bottleneck is the analysis of optically detected magnetic resonance (ODMR) spectra, where target quantities are encoded in resonance features. Conventional nonlinear fitting is often computationally expensive, sensitive to initialization, and prone to failure at low signal-to-noise ratio (SNR). Here we introduce a robust, efficient machine learning (ML) framework for real-time ODMR analysis based on a one-dimensional convolutional neural network (1D-CNN). The model performs direct parameter inference without initial guesses or iterative optimization, and is naturally parallelizable on graphics processing units (GPU) for high-throughput processing. We validate the approach on both synthetic and experimental datasets, showing improved throughput, accuracy and robustness than standard nonlinear fitting, with the largest gains in the low-SNR regime. We further validate our methods in two representative sensing applications: diagnosing intracellular temperature changes using nanodiamond probes and widefield magnetic imaging of superconducting vortices in a high-temperature superconductor. This deep-learning inference framework enables fast and reliable extraction of physical parameters from complex ODMR data and provides a scalable route to real-time quantum sensing and imaging.
Quantum sensing is an emerging field with the potential to outperform classical methods in both precision and spatial resolution. However, the sensitivity of the underlying quantum platform also makes the sensors highly susceptible to their environmental noise. To address this issue, techniques from the field of quantum error mitigation use information about the noise to improve measurement results. We present a novel mitigation technique for quantum sensors to efficiently reverse the effects of any noise that can be described by a completely positive trace preserving map. The method leverages the knowledge acquired by a pre-characterization step of the device to automatically adapt to the complexity of the dissipative evolution and to indicate optimal sensing times τ to achieve the most accurate results. We demonstrate that our method reaches the best achievable sensitivity in noisy single-NV-center magnetometry.
This work marks a further step toward more resilient quantum sensors with the smallest scale of resolution.