Lanczos recursion on a quantum computer for the Green's function and ground state

TL;DR

This paper presents a quantum algorithm that efficiently computes the Green's function and ground state properties using Lanczos recursion, significantly reducing memory requirements compared to classical methods.

Contribution

It introduces a quantum counting algorithm for Lanczos recursion that preserves the state and avoids re-preparing the wavefunction, enabling efficient Green's function computation.

Findings

Exponential memory reduction over classical methods

Efficient computation of Green's functions on quantum computers

Extension to ground state determination

Abstract

A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an interacting Green's function for use in condensed matter, particle physics, and other areas. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining the ground state is also discussed.