Exploiting symmetries in nuclear Hamiltonians for ground state preparation

TL;DR

This paper explores how exploiting symmetries in nuclear Hamiltonians, specifically the Lipkin and Agassi models, can improve ground state preparation using quantum algorithms like VQE, and discusses classical approaches inspired by quantum methods.

Contribution

It demonstrates the importance of symmetry-aware ansätze and initialization strategies in VQE for nuclear models, and discusses classical quantum-inspired methods for ground state learning.

Findings

Symmetry-aware ansätze improve VQE performance.

Symmetry exploitation reduces quantum resource requirements.

Classical quantum-inspired methods show promise for nuclear ground states.

Abstract

The Lipkin and Agassi models are simplified nuclear models that provide natural test beds for quantum simulation methods. Prior work has investigated the suitability of the Variational Quantum Eigensolver (VQE) to find the ground state of these models. There is a growing awareness that if VQE is to prove viable, we will need problem inspired ans\"{a}tze that take into account the symmetry properties of the problem and use clever initialization strategies. Here, by focusing on the Lipkin and Agassi models, we investigate how to do this in the context of nuclear physics ground state problems. We further use our observations to discus the potential of new classical, but quantum-inspired, approaches to learning ground states in nuclear problems.