https://doi.org/10.1140/epja/s10050-023-00952-6
Regular Article - Theoretical Physics
Faster spectral density calculation using energy moments
1
Physics Department, University of Trento, Via Sommarive 14, 38123, Trento, Italy
2
InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, 98195, Seattle, WA, USA
3
INFN-TIFPA Trento Institute of Fundamental Physics and Applications, Trento, Italy
Received:
27
October
2022
Accepted:
12
February
2023
Published online:
9
March
2023
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 
Ca and target energy resolution of 1 MeV we find an expected speed-up of 
times for the calculation of the giant dipole response and of 
times for the simulation of quasi-elastic electron scattering at typical momentum transfers.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
