Variational quantum simulation using non-Gaussian continuous-variable systems

This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians associated with infinite-dimensional systems, such as those arising in quantum field theory. We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space, opening the possibility to investigate the scenarios where one of the two formalisms performs better. We apply it to the study of static properties of the Bose--Hubbard model and demonstrate its effectiveness and practicality, highlighting the potential of continuous-variable quantum simulations in addressing complex problems in quantum physics.