Towards Quantum Simulation of Rotating Nuclei using Quantum Variational Algorithms

Abstract: Quantum variational algorithms (QVAs) are becoming increasingly potent tools for simulating quantum many-body systems, in particular, on noisy intermediate-scale quantum (NISQ) devices. The application of QVAs, more especially the Variational Quantum Eigensolver (VQE), to schematic model simulation is examined in this work. The cranked Nilsson-Strutinsky (CNS) framework serves as a foundation for comprehending high-spin phenomena in deformed nuclei. Using single-particle level spacings, pairing correlations, cranking (rotational) terms, and particle-number conservation, we build five increasingly complex CNS-like models. Quantum-classical hybrid procedures are used to solve these Hamiltonians after mapping them to qubit operators. Key metrics such as ground state energy, angular momentum expectation values $J_x$, and entanglement entropy are used to compare the results to exact diagonalization (ED). With variational errors typically $<0.005$, our results show agreement in energy and angular momentum predictions. Notably, we find slight variances in entanglement entropy between the ED and VQE results, which are influenced by numerical precision and ansatz expressivity. These results open the door to investigating larger, more realistic CNS-type systems through more expressive ansatz and validate the use of variational quantum algorithms in modelling rotational nuclear structure.