Comparison of variational quantum eigensolvers in light nuclei

TL;DR

This paper compares two variational quantum eigensolver algorithms, UCC and ADAPT, for simulating light nuclei in the nuclear shell model, highlighting their relative efficiencies and resource usage.

Contribution

It introduces a new metric for quantum resource quantification and provides a comparative analysis of UCC and ADAPT in nuclear structure calculations.

Findings

ADAPT is more efficient near magic numbers.

UCC requires fewer resources in the mid shell.

Slater determinants are effective reference states.

Abstract

Quantum computing is one of the most promising technologies of the near future, and the simulation of quantum many-body systems is a natural application. In this work, we present classical simulations of the ground states of light atomic nuclei within the $p$ shell, from $^{6}$He to $^{10}$B, calculated within the nuclear shell model. We compare the performance of two leading variational quantum eigensolver algorithms: the Unitary Coupled Cluster (UCC) and the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) methods, introducing a new metric to quantify the use of quantum resources in each simulation. We find that Slater determinants are the most useful reference states for both approaches. Our analysis suggests that ADAPT is more efficient for nuclei close to magic numbers, while UCC tends to require fewer resources toward the mid shell. This work lays the groundwork for robust benchmarking of quantum algorithms in nuclear structure studies.