Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm
Abstract
The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it can be used to perform matrix inversion, which is an important step in calculating the single-particle Green's function in the Lehmann representation. Due to the inverse function not being defined at zero, we explore the effect of approximating f(x)=1/x with a polynomial. This is carried out by calculating the single-particle Green's function of the two-site single-impurity Anderson model. We also propose a new circuit construction for the linear combination of unitaries block encoding technique, that reduces the number of single and two-qubit gates required.
Cite
@article{arxiv.2307.13583,
title = {Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm},
author = {Alexis Ralli and Gabriel Greene-Diniz and David Muñoz Ramo and Nathan Fitzpatrick},
journal= {arXiv preprint arXiv:2307.13583},
year = {2023}
}
Comments
22 pages, 16 Figures, quantum signal processing (QSP) phi angles in anc folder