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

How can quantum computing resources be optimized to simulate collective nuclear dynamics and quantum phase transitions? Specifically, this paper investigates whether rotational symmetry can be exploited to reduce the qubit requirements for the Interacting Boson Model (IBM) without losing the physical accuracy needed to describe the spherical-to-deformed phase transition.

The author employs the Variational Quantum Eigensolver (VQE) to study the U(5) to SU(3) transitional Hamiltonian. A key innovation is the use of rotational symmetry to project the IBM Hilbert space onto the L=0 sector before encoding. This symmetry-preserving approach allows for a minimum-qubit binary encoding that is significantly more efficient than a direct encoding of the full IBM space. The author validates this approach by comparing VQE results against exact diagonalization, focusing on ground-state energy, structural observables like d-boson occupation, and the identification of pseudocritical points in the finite-size transition.

The symmetry-reduced VQE framework successfully reproduces the exact IBM ground-state energies and structural observables to numerical precision. The author finds that the finite-size pseudocritical points converge toward the analytical critical point (ξ_c = 8/17) as the boson number increases. Furthermore, the study confirms that the VQE can capture the sharpening of the phase transition—quantified by the maximum response of the order parameter—demonstrating that the quantum algorithm effectively captures the underlying physics of the collective shape evolution.

This work provides a scalable, symmetry-aware workflow for nuclear structure calculations on quantum computers. By demonstrating that rotational symmetry can be used to drastically reduce qubit requirements, the paper offers a viable path for simulating larger, more complex nuclear systems that would otherwise be computationally prohibitive. It establishes the IBM as a robust benchmark for testing quantum algorithms in the context of nuclear phase transitions.