Continuous-variable ADAPT-VQE for bosonic lattice models

We present a continuous-variable adaptive variational quantum eigensolver (CV-ADAPT-VQE). As concrete examples, we consider the ground-state preparation for (i) the Bose-Hubbard model and (ii) the bosonic Kitaev chain, including its extension with an on-site Kerr interaction. The former conserves the total boson number, while the latter conserves global parity. We construct symmetry-preserving operator pools tailored to each case and show, using GPU-based classical simulations, that CV-ADAPT-VQE results in significantly shallower circuits compared to Hamiltonian-based VQE approaches. Our results point toward direct applications in quantum simulations of condensed-matter systems, quantum chemistry, and high-energy physics.