Aspects of Symmetry in Nuclear Quantum Computing Variational Algorithms

Variational Quantum Eigensolvers (VQEs) have become a standard tool for use in preparing eigenstates in quantum simulations of many-body systems. In the case of the nuclear shell model, various adaptations of the VQE have been shown to be able to produce ground and excited states of nuclei. The VQE algorithm works by seeking minima in a cost function, which is often the expectation value of the energy. For a well-formulated problem, symmetries that are respected by the Hamiltonian should appear in the final converged solution provided by the VQE, even if those symmetries are broken by the wave function ansatz. We demonstrate explicit appearance of the particle–hole symmetry, and explicit recovery of angular momentum conservation due to rotational symmetry, during VQE runs in the case of the nuclear shell model. We conduct analyses of how the symmetry convergence appears in different ansatz formulations, and suggest that information obtained could be used in future VQE design.