  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.
