Faster spectral density calculation using energy moments

TL;DR

This paper introduces a quantum-computer-friendly reformulation of spectral density calculations using energy moments, significantly reducing computational costs for nuclear response simulations.

Contribution

It presents a novel approach that reformulates the Gaussian Integral Transform in terms of Fourier moments, enabling more efficient spectral density calculations on quantum computers.

Findings

Expected 125x speed-up for giant dipole response calculations.

Approximately 50x reduction in computation time for quasi-elastic electron scattering.

Framework exploits prior knowledge of energy moments to optimize performance.

Abstract

Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate the recently proposed Gaussian Integral Transform technique in terms of Fourier moments of the system Hamiltonian which can be computed efficiently on a quantum computer. One of the main advantages of this framework is that it allows for an important reduction of the computational cost by exploiting previous knowledge about the energy moments of the spectral density. For a simple model of medium mass nucleus like $^{40}$Ca and target energy resolution of $1$ MeV we find an expected speed-up of $\approx 125$ times for the calculation of the giant dipole response and of $\approx 50$ times for the simulation of quasi-elastic electron scattering at typical momentum transfers.