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.

• Received 12 August 2020
• Revised 26 January 2021
• Accepted 18 February 2021

DOI:https://doi.org/10.1103/PhysRevA.103.032404