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This work introduces a novel approach to quantum simulation by leveragingcontinuous-variable systems within a photonic hardware-inspired framework. Theprimary focus is on simulating static properties of the ground state ofHamiltonians associated with infinite-dimensional systems, such as thosearising in quantum field theory. We present a continuous-variable variationalquantum eigensolver compatible with state-of-the-art photonic technology. Theframework we introduce allows us to compare discrete and continuous variablesystems without introducing a truncation of the Hilbert space, opening thepossibility to investigate the scenarios where one of the two formalismsperforms better. We apply it to the study of static properties of theBose--Hubbard model and demonstrate its effectiveness and practicality,highlighting the potential of continuous-variable quantum simulations inaddressing complex problems in quantum physics.

Variational quantum simulation using non-Gaussian continuous-variable systems