Quantum circuits for solving local fermion-to-qubit map- pings

Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the lo-cality of the operators comes at the ex-pense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the lower-dimensional physical Hilbert space that represents fermionic de-grees of freedom, one must satisfy a set of constraints. In this work, we intro-duce quantum circuits that exactly satisfy these stringent constraints. We demon-strate how maintaining locality allows one to carry out a Trotterized time-evolution with constant circuit depth per time step. Our construction is particularly advanta-geous to simulate the time evolution op-erator of fermionic systems in d>1 di-mensions. We also discuss how these families of circuits can be used as vari-ational quantum states, focusing on two approaches: a first one based on gen-eral constant-fermion-number gates, and a second one based on the Hamiltonian variational ansatz where the eigenstates are represented by parametrized time -evolution operators. We apply our meth-ods to the problem of finding the ground state and time-evolved states of the t -V model.

Automated summary

Local Hamiltonians of fermionic systems on a lattice can be mapped onto qubit Hamiltonians with auxiliary degrees of freedom to maintain locality. This work introduces quantum circuits that exactly satisfy the constraints of the fermionic degrees of freedom, allowing for Trotterized time-evolution with constant circuit depth per time step. The construction is advantageous for simulating fermionic systems in dimensions greater than one and can be used as variational quantum states.