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Local Hamiltonians of fermionic systems on a lattice can be mapped onto localqubit Hamiltonians. Maintaining the locality of the operators comes at theexpense of increasing the Hilbert space with auxiliary degrees of freedom. Inorder to retrieve the lower-dimensional physical Hilbert space that representsfermionic degrees of freedom, one must satisfy a set of constraints. In thiswork, we introduce quantum circuits that exactly satisfy these stringentconstraints. We demonstrate how maintaining locality allows one to carry out aTrotterized time-evolution with constant circuit depth per time step. Ourconstruction is particularly advantageous to simulate the time evolutionoperator of fermionic systems in d>1 dimensions. We also discuss how thesefamilies of circuits can be used as variational quantum states, focusing on twoapproaches: a first one based on general constant-fermion-number gates, and asecond one based on the Hamiltonian variational ansatz where the eigenstatesare represented by parametrized time-evolution operators. We apply our methodsto the problem of finding the ground state and time-evolved states of the$t$-$V$ model.

Quantum circuits for solving local fermion-to-qubit mappings