Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm

TL;DR

This paper demonstrates that the ADAPT-VQE quantum algorithm can effectively solve nuclear structure problems, including models with phase transitions and symmetry breaking, with linear scaling in quantum operations and robustness to noise.

Contribution

It shows that the adaptive variational quantum eigensolver can handle complex nuclear models with realistic interactions, maintaining efficiency and robustness.

Findings

Linear scaling of quantum operations with qubits

Successful application to realistic nuclear shell models

Weak noise does not impair algorithm efficiency

Abstract

We use the Lipkin-Meshkov-Glick (LMG) model and the valence-space nuclear shell model to examine the likely performance of variational quantum eigensolvers in nuclear-structure theory. The LMG model exhibits both a phase transition and spontaneous symmetry breaking at the mean-field level in one of the phases, features that characterize collective dynamics in medium-mass and heavy nuclei. We show that with appropriate modifications, the ADAPT-VQE algorithm, a particularly flexible and accurate variational approach, is not troubled by these complications. We treat up to 12 particles and show that the number of quantum operations needed to approach the ground-state energy scales linearly with the number of qubits. We find similar scaling when the algorithm is applied to the nuclear shell model with realistic interactions in the $sd$ and $pf$ shells. Although most of these simulations contain no noise, we use a noise model from real IBM hardware to show that for the LMG model with four particles, weak noise has no effect on the efficiency of the algorithm.