Towards Quantum Simulation of Rotating Nuclei using Quantum Variational Algorithms

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. Our results demonstrate that while simpler models achieve high precision (errors $<0.005$), the transition to 8-spin-orbital Hamiltonians reveals significant scaling and optimization challenges. Notably, we show that Model IV, which employs a more expressive RealAmplitudes ansatz, successfully captures the qualitative physics of rotational alignment and reduces energy deviations compared to intermediate benchmarks. These results establish a systematic methodological baseline, identifying the breaking points of hardware-efficient ansatz while validating the potential of QVAs to model the complex competition between pairing and rotation in deformed nuclei.