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The widespread use of the noninteracting ground state as the initial statefor the digital quantum simulation of the Fermi-Hubbard model is largely due tothe scarcity of alternative easy-to-prepare approximations to the exact groundstate in the literature. Exploiting the fact that the spin-$\frac{1}{2}$Heisenberg model is the effective low-energy theory of the Fermi-Hubbard modelat half-filling in the strongly interacting limit, here we propose a three-stepdeterministic quantum routine to prepare an educated guess of the ground stateof the Fermi-Hubbard model through a shallow circuit suitable for near-termquantum hardware. First, the ground state of the Heisenberg model isinitialized via a hybrid variational method using an ansatz that explores onlythe correct symmetry subspace. Second, a general method is devised to convert amulti-spin-$\frac{1}{2}$ wave function into its fermionic version. Third,taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameterlayer that adds doublon-holon pairs is applied to this fermionic state.Numerical simulations on chains and ladders with up to 12 sites confirm theimprovement over the noninteracting ground state of the overlap with the exactground state for the intermediate values of the interaction strength at whichquantum simulation is bound to be most relevant.

From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons