Quantum algorithms for generator coordinate methods

TL;DR

This paper introduces quantum algorithms for the generator coordinate method (GCM) that leverage low-depth circuits to efficiently probe large sub-spaces in molecular systems, enabling improved ground and excited state energy calculations.

Contribution

It presents a quantum algorithm for discretizing the Hill-Wheeler equation and extends GCM to a multi-product form for systematic symmetry restoration and higher rank effects.

Findings

Demonstrates quantum algorithm performance for ground and excited states.

Shows GCM quantum algorithms as an alternative to variational quantum eigensolvers.

Introduces multi-product GCM extension for symmetry purification.

Abstract

This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. The GCM formalism defined by exponential operators with exponents defined through generators of the Fermionic U(N) Lie algebra (Thouless theorem) offers a possibility of probing large sub-spaces using low-depth quantum circuits. In the present studies, we illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground and excited state energies. We also generalize the standard GCM formulation to multi-product extension that when collective paths are properly probed, can systematically introduce higher rank effects and provide elementary mechanisms for symmetry purification when generator states break the spatial or spin symmetries. The GCM quantum algorithms also can be viewed as an alternative to existing variational quantum eigensolvers, where multi-step classical optimization algorithms are replaced by a single-step procedure for solving the Hill-Wheeler eigenvalue problem.