Symmetry-Reduced Variational Quantum Simulation of the U(5)→ SU(3) Quantum Phase Transition in the Interacting Boson Model

The spherical-to-deformed quantum phase transition of the Interacting Boson Model (IBM) is investigated using the variational quantum eigensolver (VQE). The U(5)--SU(3) transitional Hamiltonian is studied with χ=-sqrt{7}/2. We develop a symmetry-preserving, minimum-qubit VQE framework for collective nuclear models, achieving a substantial reduction in qubit requirements without compromising the finite-size quantum-phase-transition physics. The transition is characterized through the normalized d-boson occupation and ground-state energy derivatives. Finite-size results are found to approach the analytic critical point xi_c=8/17simeq0.470588, with an independent order-parameter extrapolation yielding xi_infty=0.46986(61). The VQE reproduces ground-state energies and structural observables to numerical precision. These results demonstrate the potential of symmetry-reduced VQE for efficient quantum simulations of collective nuclear dynamics and quantum phase transitions.