Spectral density reconstruction with Chebyshev polynomials

TL;DR

This paper introduces a quantum algorithm using Chebyshev polynomial expansion to accurately reconstruct spectral densities in quantum many-body systems, overcoming numerical inversion issues and enabling efficient classical simulations.

Contribution

It extends a recent quantum algorithm to controllably reconstruct spectral densities with error bounds using Chebyshev polynomials, applicable to nuclear and condensed matter physics.

Findings

Successfully reconstructs a model response function as proof of principle.

Provides a method for controllable spectral density reconstruction with error estimates.

Enables efficient classical simulations of spectral properties.

Abstract

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and semi-exclusive scattering cross sections in atomic nuclei and transport properties of nuclear and neutron star matter. Integral transform techniques play an important role in accessing the spectral density in a variety of nuclear systems. However, their accuracy is in practice limited by the need to perform a numerical inversion which is often ill-conditioned. In the present work we extend a recently proposed quantum algorithm which circumvents this problem. We show how to perform controllable reconstructions of the spectral density over a finite energy resolution with rigorous error estimates. An appropriate expansion in Chebyshev polynomials allows for efficient simulations also on classical computers. We apply our idea to reconstruct a simple model -- response function as a proof of principle. This paves the way for future applications in nuclear and condensed matter physics.