Variance minimisation on a quantum computer for nuclear structure

TL;DR

This paper introduces a variance minimization algorithm using a variational quantum eigensolver to determine nuclear excitation spectra on quantum computers, demonstrated with a Lipkin-Meshkov-Glick model.

Contribution

It develops a variance-based VQE method with reduced-qubit encoding for nuclear structure calculations on quantum computers, enabling excited state spectrum determination.

Findings

Successfully applied to Lipkin-Meshkov-Glick model

Demonstrated feasibility on limited-qubit quantum hardware

Provided a new approach for nuclear excitation spectra

Abstract

Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This presents a challenge when performing calculations on large systems when using classical computing methods. By using a quantum computer, one may be able to overcome this difficulty thanks to the exponential way the Hilbert space of a quantum computer grows with the number of quantum bits (qubits). Our aim is to develop quantum computing algorithms which can reproduce and predict nuclear structure such as level schemes and level densities. As a sample Hamiltonian, we use the Lipkin-Meshkov-Glick model. We use an efficient encoding of the Hamiltonian onto many-qubit systems, and have developed an algorithm allowing the full excitation spectrum of a nucleus to be determined with a variational algorithm capable of implementation on today's quantum computers with a limited number of qubits. Our algorithm uses the variance of the Hamiltonian, $\langle H^2\rangle - \langle H\rangle ^2$, as a cost function for the widely-used variational quantum eigensolver (VQE). In this work we present a variance based method of finding the excited state spectrum of a small nuclear system using a quantum computer, using a reduced-qubit encoding method.