Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm

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.

10 pages, 7 figures. Identical in content to published version. Now incudes analysis of noise

References in corpus (5)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Variational approaches to constructing the many-body nuclear ground state for quantum computing
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
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