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

A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground-state wave function 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 wave function does not need to be reprepared 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.

Automated summary

The state-preserving quantum counting algorithm efficiently obtains coefficients of a Lanczos recursion from a single ground-state wave function on a quantum computer. This enables the computation of the continued fraction representation of an interacting Green's function with exponential reduction in memory compared to classical methods. The algorithm also discusses an extension for determining the ground state.