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

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.

arXiv comment10 pages, 2 figures; accepted at Phys. Rev. A

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• Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
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• Solving lattice gauge theories using the quantum Krylov algorithm and qubitization
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• Elucidating Many-Body Effects in Molecular Core Spectra through Real-Time Approaches: Efficient Classical Approximations and a Quantum Perspective
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