Deterministically prepare highly entangled ground states for Fermi-Hubbard model on digital quantum computers

One apparent advantage of quantum computers in solving the problems in quantum physics and chemistry is their ability to handle exponentially large Hilbert space with a linear growth in the number of required qubits as the system size increases. Currently, all practical demonstrations on real digital quantum hardware have only seen certain successes for relatively small system sizes and shallow circuit depths with the state of the art being up to tens of qubits and hundreds of CNOT gates. In this work, we prepare entangled ground states for a small Fermi-Hubbard cluster (of a 4-site ring) on digital quantum computers by constructing the analytically-exact factorized unitary coupled cluster variational ansatzes for two physically important but computationally hard cases: the half-filling (4 electrons) and the single-hole-doping (3 electrons), respectively. With strong Hubbard interactions, the first case resembles Mott insulator phase while the second case exhibits Nagaoka ferromagnetism. Our numerical and quantum hardware simulations exemplify the particular challenge even in small systems using noisy intermediate-scale quantum (NISQ) devices to prepare highly entangled states in strongly correlated phenomena when deep circuits are potentially unavoidable.