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.
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.
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.
Abstract Spectral densities encode the relevant information characterizing the system–environment interaction in an open-quantum system problem. Such information is key to 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 the time evolution of a system observable can be used by an artificial neural network to infer the main features of the spectral density. In particular, for relevant examples of spin-boson models, we can classify with high accuracy the Ohmicity parameter of the environment as either Ohmic, sub-Ohmic or super-Ohmic, thereby distinguishing between different forms of dissipation.
We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which prior knowledge is encoded in the training data and the inverse transformation manifold is explicitly parametrized through a neural network. We systematically investigate this novel reconstruction approach, providing a detailed analysis of its performance on physically motivated mock data, and compare it to established methods of Bayesian inference. The reconstruction accuracy is found to be at least comparable and potentially superior in particular at larger noise levels. We argue that the use of labeled training data in a supervised setting and the freedom in defining an optimization objective are inherent advantages of the present approach and may lead to significant improvements over state-of-the-art methods in the future. Potential directions for further research are discussed in detail.
Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in many-body physics. However, the inversion is proved to be ill-posed in the realistic systems with noisy Green's functions. In this paper we propose an automatic differentiation (AD) framework as a generic tool for the spectral reconstruction from propagator observable. Exploiting the neural networks' regularization as a nonlocal smoothness regulator of the spectral function, we represent spectral functions by neural networks and use the propagator's reconstruction error to optimize the network parameters unsupervisedly. In the training process, except for the positive-definite form for the spectral function, there are no other explicit physical priors embedded into the neural networks. The reconstruction performance is assessed through relative entropy and mean square error for two different network representations. Compared to the maximum entropy method, the AD framework achieves better performance in the large-noise situation. It is noted that the freedom of introducing nonlocal regularization is an inherent advantage of the present framework and may lead to substantial improvements in solving inverse problems.
Modeling the dynamics of open quantum systems on noisy intermediate-scale quantum (NISQ) devices constitutes a major challenge, as high noise levels and environmental degradations lead to the decay of pure quantum states (decoherence) and energy losses. This situation represents one of the most important problems in the field of quantum information technologies. While existing data-driven methods struggle to generalize beyond the training data (extrapolation), physics-informed neural networks (PINNs) require predefined governing equations, which limit their discovery capability when the underlying physics is incomplete or unknown. In this work, we present the ParaQNN (ParaQuantum neural network) architecture, an equation-free framework for physical discovery. ParaQNN disentangles multi-scale dynamics without relying on a priori laws by employing a dialetheist logic layer that models coherent signal and decoherent noise as independent yet interacting channels. Through extensive benchmark tests performed on Rabi oscillations, Lindblad dynamics, and particularly complex "mixed regimes" where relaxation and dephasing processes compete, we show that ParaQNN exhibits a consistent performance advantage compared to Random Forest, XGBoost, and PINN models with incomplete physical information. Unlike its competitors, ParaQNN succeeds in maintaining oscillatory and damping dynamics with high accuracy even in extrapolation regions where training data are unavailable, by "discovering" the underlying structural invariants from noisy measurements. These results demonstrate that paraconsistent logic provides a structurally more stable epistemic foundation than classical methods for learning quantum behavior in situations where mathematical equations prove insufficient.
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.