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

Abstract

The technique of quantum counting is used to obtain coefficients from a Lanczos recursion from a single ground-state wavefunction on the quantum computer. This is used to compute the continued fraction representation of a general Green's function, which can be useful in condensed matter, particle physics, and others. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory required over classical methods.