Learning spectral density functions in open quantum systems

TL;DR

This paper develops machine learning methods to accurately reconstruct spectral density functions in open quantum systems from noisy data, improving robustness and physical consistency.

Contribution

It introduces a neural network framework combined with cosine transform inversion for robust, physics-consistent spectral density estimation from noisy measurements.

Findings

Neural network approach effectively reconstructs structured spectral densities.

Cosine transform inversion provides a physically consistent spectral prior.

Method demonstrates robustness to noise in simulated data.

Abstract

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.