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arXiv:2603.14144

Fast Single Nitrogen-Vacancy Center Ramsey Characterization using a Physics-Informed Neural Network

Chao Shang, Gregory D. Fuchs

quant-phSubmitted Mar 14, 2026• Announced Mar 17, 2026• 0 citations• Revised Apr 3, 2026 (v2)
v1 · Mar 14, 2026v2 · Apr 3, 2026
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Abstract

Precise characterization of the local spin environment of single diamond nitrogen-vacancy (NV) centers is crucial for advancing quantum sensing, quantum networking, and the optimization of quantum materials. However, single NV center fluorescence measurements requires long averaging times to obtain clean data that is suitable for conventional model fitting, and that constitutes a key experimental bottleneck for high-throughput characterization. To address this, we introduce \textsc{NVRNet}, a physics-informed simulation-to-reality machine learning pipeline that maps minimal-sweep, noisy Ramsey data to a denoised waveform while directly estimating the hyperfine coupling to proximal ${}^{13}\mathrm{C}$ nuclear spins. The pipeline's denoiser utilizes a two-stage time-frequency U-Net and an attention-augmented time-domain U-Net, pretrained on Hamiltonian-based spin-dynamics simulations with experimentally calibrated noise. To effectively bridge the simulation-to-reality gap, parameter-efficient adapters are attached to the backbone and fine-tuned on targeted experimental data. Across three distinct NV centers, this experimentally fine-tuned model reduces the median reconstruction error on held-out, few-sweep traces to $0.44\text{-}0.67\times$ of the raw experimental noise level. Subsequently, a transformer-based estimator extracts the underlying hyperfine parameters. Forward reconstructions derived from these inferred parameters faithfully reproduce the dominant experimental time- and frequency-domain features, yielding representative normalized fast Fourier transform (FFT) reconstruction errors of $0.10\text{-}0.19$. By reducing both the required data volume and acquisition time, \textsc{NVRNet} enables up to $\sim 40\times$ acceleration of the measurement process, establishing a fast, hardware-compatible pathway for robust hyperfine inference and autonomous qubit characterization.

Comments
25 pages, two column, 14 figures

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Precise characterization of the local spin environment of single diamond nitrogen-vacancy (NV) centers is crucial for advancing quantum sensing, quantum networking, and the optimization of quantum materials. However, single NV center fluorescence measurements requires long averaging times to obtain clean data that is suitable for conventional model fitting, and that constitutes a key experimental bottleneck for high-throughput characterization. To address this, we introduce \textsc{NVRNet}, a physics-informed simulation-to-reality machine learning pipeline that maps minimal-sweep, noisy Ramsey data to a denoised waveform while directly estimating the hyperfine coupling to proximal 13C{}^{13}\mathrm{C}13C nuclear spins. The pipeline's denoiser utilizes a two-stage time-frequency U-Net and an attention-augmented time-domain U-Net, pretrained on Hamiltonian-based spin-dynamics simulations with experimentally calibrated noise. To effectively bridge the simulation-to-reality gap, parameter-efficient adapters are attached to the backbone and fine-tuned on targeted experimental data. Across three distinct NV centers, this experimentally fine-tuned model reduces the median reconstruction error on held-out, few-sweep traces to 0.44-0.67×0.44\text{-}0.67\times0.44-0.67× of the raw experimental noise level. Subsequently, a transformer-based estimator extracts the underlying hyperfine parameters. Forward reconstructions derived from these inferred parameters faithfully reproduce the dominant experimental time- and frequency-domain features, yielding representative normalized fast Fourier transform (FFT) reconstruction errors of 0.10-0.190.10\text{-}0.190.10-0.19. By reducing both the required data volume and acquisition time, \textsc{NVRNet} enables up to ∼40×\sim 40\times∼40× acceleration of the measurement process, establishing a fast, hardware-compatible pathway for robust hyperfine inference and autonomous qubit characterization.
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.
Nitrogen-vacancy (NV) centers in diamond are a solid-state platform for quantum sensing 1 and information processing due to their spin-dependent optical transitions at room temperature 2. Accurate characterization of NV spin dynamics, including hyperfine interactions with nuclear spins, is essential both for optimizing sensing performance and for designing high-fidelity quantum controls. In this work, we use the open-source package/ library Quantum Toolbox in Python (QuTiP) 3, 4 to simulate two readout protocols (continuous-wave ODMR, pulsed ODMR) with and without the hyperfine coupling. By comparing simulated resonance positions and population dynamics against experimental and simulation profiles from the literature, we demonstrate that our QuTiP model reproduces the characteristic profiles present in other works. We analyze the computational cost of including hyperfine terms to the model via execution time averaging and show that built-in parallelization accelerates the no-hyperfine model but provides small returns when the coupling is included. Finally, we illustrate how simulation parameters align with predictions of DC magnetometry 5. We also provide some ideas for extending this framework to GPU-accelerated and/or machine learning assisted parameter estimation and calibration 6, 7. Our soon-to-be open-source code 8 provides a flexible foundation for both quantum sensing characterization and the development of NV-based quantum information protocols.
Abstract We present a variational quantum circuit (VQC) that utilizes the architecture of a quantum neural network (QNN) to simulate hyperfine interactions in diamond nitrogen vacancy (NV) centers, which is typically a challenging task for traditional computation methods. Isotopes of 13 C, though naturally rare, possess a nuclear spin ( l = 1 2 ) which anisotropically interacts with the NV center’s electron spin, resulting in distinct hyperfine structure and coherence properties. The VQC’s ansatz unitary was implemented stepwise (through optimization Trotter steps) to mimic a multi-layered QNN configuration. The dynamical evolution of the 14 NV- 13 C Hamiltonian was simulated while maintaining flexibility for optimization on noisy intermediate-scale quantum (NISQ) platforms. Qiskit SDK was used to design and execute the circuit on 127-qubit IBM quantum hardware. Ansatz parameters were optimized using six classical optimization algorithms initialized with pseudo-random parameter vectors. We successfully determined optimal ansatz parameters for estimating the minimum energy eigenvalues of the 14 NV- 13 C observable using the VQC’s cost function, enabling us to model the system’s ground state dynamics. Our findings show that gradient-free optimizers are efficient for the designed Hardware Efficient SU(2) 2-local circuit (ESU2) ansatz, characterized by a barren plateau landscape. We further established that a maximally entangled VQC initialization (i.e., GHZ 3 ) retains its entanglement scheme irrespective of the optimization pathway. Hence, this approach highlights the effectiveness of QNN-inspired VQC circuits for accurately simulating NV centers coupled with strongly interacting nearest-neighbor nuclear spins. Our work lays down a foundational step for realizing precise control on near-term quantum hardware that utilizes NV centers, leading to high fidelities.
Ensemble nitrogen-vacancy (NV) centers in diamond enable robust vector magnetometry in unshielded environments, yet deployment remains bottlenecked by complex calibration and a reliance on external data references. Conventional statistical machine learning requires an exorbitantly large volume of training data and suffers from severe simulation-to-reality mismatches. To address this, we introduce a physics-guided hybrid machine learning framework that embeds the Zeeman splitting directly into the learning pipeline. Our physics-guided model significantly reduces the average tracking error demonstrating a 372-fold precision improvement over purely statistical baselines. Furthermore, our hybrid architecture pairs a sparse physical measurement with scalable synthetic data generation, seamlessly incorporating real-world hardware non-idealities. When deployed to decode uncalibrated, raw experimental ODMR data, our framework delivers exceptional predictive accuracy for the scalar magnetic field. This work paves the way toward self-calibrated sensors while establishing a machine learning training method applicable to other data-scarce physical systems
Quantum sensors leverage matter's quantum properties to enable measurements with unprecedented spatial and spectral resolution. Among these sensors, those utilizing nitrogen-vacancy (NV) centers in diamond offer the distinct advantage of operating at room temperature. Nevertheless, signals received from NV centers are often complex, making interpretation challenging. This is especially relevant in low magnetic field scenarios, where standard approximations for modeling the system fail. Additionally, NV signals feature a prominent noise component. In this Letter, we present a signal-to-image deep learning model capable of automatically inferring the number of nuclear spins surrounding a NV sensor and the hyperfine couplings between the sensor and the nuclear spins. Our model is trained to operate effectively across various magnetic field scenarios, requires no prior knowledge of the involved nuclei, and is designed to handle noisy signals, leading to fast characterization of nuclear environments in real experimental conditions. With detailed numerical simulations, we test the performance of our model in scenarios involving varying numbers of nuclei, achieving an average error of less than 2 kHz in the estimated hyperfine constants.
Inverse problems in scientific sensing are often solved with either hand-designed regularizers or supervised networks trained on simulated labels, yet both can fail when the forward model is nonlinear, spectrally coupled, and physically delicate. We study this issue for noise sensing based on nitrogen-vacancy (NV) centers in diamond, where a quantum sensor measures magnetic-noise spectra generated by sparse spin sources. We show that replacing a common scalar/coherent forward approximation with a tensor power-summed dipolar operator changes the inverse landscape and exposes a center-collapse failure mode in free-density optimization. We propose NeTMY, an amortization-free coordinate neural field coupled to the differentiable NV forward model, with annealed positional encoding, multiscale optimization, sparsity/gating, and spectrum-fidelity losses. Across sparse synthetic reconstructions generated by the corrected operator, NeTMY achieves the best localization and distributional metrics in the tested benchmark. Mechanism experiments show that NeTMY does not directly execute the raw density-space gradient; its parameterization smooths and redistributes updates, mitigating the center-collapse pathology. These results position NV quantum sensing as a useful testbed for physics-faithful neural inverse problems.