The interaction between a quantum system and its environment can be characterized by the spectral density function: knowing its structure is important for optimizing applications of quantum technologies such as quantum sensing protocols. In this work, we present the first experimental demonstration of a machine learning-based reconstruction of reaction-coordinate spectral density parameters from NV centre Rabi dynamics. Unlike the previous work, we recover all spectral density parameters rather than only the central frequency, and benchmark the performance of the neural network against the Cramér-Rao bound and maximum likelihood estimator. Our results demonstrate that the model predicted by the neural network can reliably reproduce the NV dynamics over the estimation window, and can produce estimates for some parameters with variances comparable to that of maximum likelihood.
The interaction between a quantum system and its environment can be characterized by the spectral density function: knowing its structure is important for optimizing applications of quantum technologies such as quantum sensing protocols. In this work, we present the first experimental demonstration of a machine learning-based reconstruction of reaction-coordinate spectral density parameters from NV centre Rabi dynamics. Unlike the previous work, we recover all spectral density parameters rather than only the central frequency, and benchmark the performance of the neural network against the Cramér-Rao bound and maximum likelihood estimator. Our results demonstrate that the model predicted by the neural network can reliably reproduce the NV dynamics over the estimation window, and can produce estimates for some parameters with variances comparable to that of maximum likelihood.
Spectral densities encode essential information that characterises the interaction between a system and its environment in an open-quantum system problem. This information is crucial for determining the system's dynamics. In this work, we leverage the potential of machine learning techniques to reconstruct the features of the environment. Specifically, we show that, given the time evolution of a system observable, an artificial neural network can infer the main features of the spectral density. Firstly, for relevant examples of exactly solvable and weakly-coupled spin-boson models, we demonstrate that the neural network can classify the Ohmicity parameter of the environment as either Ohmic, sub-Ohmic, or super-Ohmic, with high accuracy, effectively distinguishing between different forms of dissipation. Additionally, we extend our approach to a regression task, where the neural network accurately predicts continuous values of the Ohmicity parameter, the coupling strength and the cut-off frequency, providing a comprehensive characterisation of the spectral density. Furthermore, to address scenarios beyond the weak coupling regime, we employ the reaction coordinate mapping. For a dissipative spin-boson model with a structured spectral density comprising one, two, or three Lorentzian peaks, we demonstrate that a neural network can classify the spectral density based on the number of peaks and accurately predict their positions. The methodology developed in this thesis, along with the case studies analysed, demonstrates the effectiveness of machine learning techniques for characterising environments with arbitrary spectral densities across a broad range of coupling regimes.
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we use exactly solvable spin-boson models with pure-dephasing and amplitude-damping channels to reconstruct spectral density functions from noisy simulated data. First, we introduce a parameter estimation approach based on machine learning regressors to infer Lorentzian and Ohmic-like spectral density parameters, quantifying robustness to noise. Second, we show that a cosine transform inversion yields a physics-consistent spectral prior estimation, which is refined by a constrained neural network enforcing positivity and correct asymptotic behaviour. Our neural network framework robustly reconstructs structured spectral densities by filtering simulated noisy signals and learning general functional dependencies.
Non-Markovian quantum state diffusion provides a wavefunction-based framework for modeling open quantum systems. In this work, we introduce a novel machine learning approach based on an operator construction algorithm. This algorithm employs a neural network as a universal generator to reconstruct the stochastic time evolution operator from an ensemble of quantum trajectories. Unlike conventional machine learning methods that approximate time-dependent wavefunctions or expectation values, our operator-based approach offers broader applicability to stochastic processes. We benchmark the algorithm on the spin-boson model across diverse spectral densities, demonstrating its accuracy. Furthermore, we showcase the operator's utility in calculating absorption spectra and reconstructing reduced density matrices at extended timescales. These results establish a new paradigm for the application of machine learning in quantum dynamics.
Abstract The undesired interaction of a quantum system with its environment generally leads to a coherence decay of superposition states in time. A precise knowledge of the spectral content of the noise induced by the environment is crucial to protect qubit coherence and optimize its employment in quantum device applications. We experimentally show that the use of neural networks (NNs) can highly increase the accuracy of noise spectroscopy, by reconstructing the power spectral density that characterizes an ensemble of carbon impurities around a nitrogen-vacancy (NV) center in diamond. NNs are trained over spin coherence functions of the NV center subjected to different Carr–Purcell sequences, typically used for dynamical decoupling (DD). As a result, we determine that deep learning models can be more accurate than standard DD noise-spectroscopy techniques, by requiring at the same time a much smaller number of DD sequences.
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 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× 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 0.10-0.19. By reducing both the required data volume and acquisition time, \textsc{NVRNet} enables up to ∼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 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.