Efficient Fermi-Hubbard model ground-state preparation by coupling to a classical reservoir

Preparing the ground state of the Fermi-Hubbard model presents a substantial challenge due to the exponential expansion of the Hilbert space, which complicates the search for an efficient route from an initial state to the ground state using the variational principle. In this work, we introduce an algorithm that uses a classical reservoir in the instantaneous limit, applying time-dependent operators to the initial quantum state without enlarging the Hilbert space. The time dependence of these operators is carefully chosen to drive the initial state toward the ground state in a minimal number of time steps. Numerical optimization is employed to fine-tune the operator amplitudes, effectively minimizing the system’s energy. This approach shares a mathematical expression with the Variational Hamiltonian Ansatz(VHA) but enforces additional total spin symmetry for enhanced accuracy.