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arXiv:2308.00831 · Machine Learning Science and Technology

Spectral density classification for environment spectroscopy

J Barr, Giorgio Zicari, Alessandro Ferraro, Mauro Paternostro

Published Feb 26, 2024• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2632-2153/ad2cf1

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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.
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.
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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.
Abstract A probing scheme is considered with an accessible and controllable qubit, used to probe an out‐of equilibrium system consisting of a second qubit interacting with an environment. Quantum spontaneous synchronization between the probe and the system emerges in this model and, by tuning the probe frequency, can occur both in‐phase and in anti‐phase. The capability of machine learning in this probing scheme is analyzed based on quantum synchronization. An artificial neural network is used to infer, from a probe observable, main dissipation features, such as the environment Ohmicity index. The efficiency of the algorithm in the presence of some noise in the dataset is also considered. It is shown that the performance in either classification and regression is significantly improved due to the in/anti‐phase synchronization transition. This opens the way to the characterization of environments with arbitrary spectral densities.
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.