A Quantum Annealing Protocol to Solve the Nuclear Shell Model

TL;DR

This paper introduces a quantum annealing protocol tailored for the nuclear shell model, enabling efficient approximation of nuclear ground states with polynomial cost, potentially advancing the study of heavier nuclei.

Contribution

The authors develop a specialized quantum annealing method with a unique driver Hamiltonian, validated through classical simulations on large basis sizes, addressing scalability issues in nuclear physics.

Findings

Validated in a dozen nuclei with basis sizes up to 10^5

Spectral gap analysis correlates with annealing time and accuracy

Polynomial estimated cost suggests feasibility for studying heavier nuclei

Abstract

The nuclear shell model accurately describes the structure and dynamics of atomic nuclei. However, the exponential scaling of the basis size with the number of degrees of freedom hampers a direct numerical solution for heavy nuclei. In this work, we present a quantum annealing protocol to obtain nuclear ground states. We propose a tailored driver Hamiltonian that preserves a large gap and validate our approach in a dozen nuclei with basis sizes up to $10^5$ using classical simulations of the annealing evolution. We explore the relation between the spectral gap and the total time of the annealing protocol, assessing its accuracy by comparing the fidelity and energy relative error to classical benchmarks. While the nuclear Hamiltonian is non-local and thus challenging to implement in current setups, the estimated computational cost of our annealing protocol on quantum circuits is polynomial in the single particle basis size, paving the way to study heavier nuclei.