Towards Quantum Simulation of Rotating Nuclei using Quantum Variational Algorithms

Abstract

Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE) to four progressively complex models based on the cranked Nilsson-Strutinsky (CNS) framework. By incorporating single-particle spacings, pairing correlations, and rotational cranking terms, we evaluate VQE performance against exact diagonalization (ED) benchmarks. We provide a systematic benchmarking of VQE across a hierarchy of CNS-inspired Hamiltonians, explicitly identifying where hardware-efficient ansatz succeed and fail, and introducing quantum information diagnostics, the entanglement spectrum and Quantum Fisher Information, as novel probes of the pairing-rotation. Our results demonstrate that with a properly optimised multi-restart warm-starting strategy, VQE achieves near-machine-precision convergence ($|ΔE| < 10^{-4}$) across the full cranking frequency range $ω\in [0,1.2]$ and we confirm that the same strategy reproduces an established $^{6}$He shell-model pairing benchmark, demonstrating that the RealAmplitudes ansatz is expressively sufficient for this problem class. The entanglement spectrum confirms the product-state character of the exact ground state throughout the pairing-rotation transition, while the Quantum Fisher Information identifies a finite-size precursor to the critical pair-breaking frequency. These results establish a systematic methodological baseline and provide a reproducible framework for the nuclear physics community.