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We numerically analyze the feasibility of a platform-neutral, generalstrategy to perform quantum simulations of fermionic lattice field theoriesunder open boundary conditions. The digital quantum simulator requires solelyone- and two-qubit gates and is scalable since integrating each Hamiltonianterm requires a finite (non-scaling) cost. The exact local fermion encoding weadopt relies on auxiliary $\mathbb{Z}_2$ lattice gauge fields by adding a puregauge Hamiltonian term akin to the Toric Code. By numerically emulating thequantum simulator real-time dynamics, we observe a timescale separation forspin- and charge-excitations in a spin-$\frac{1}{2}$ Hubbard ladder in the$t-J$ model limit. Additionally, we show that such local fermion encoding isalso useful in tensor network numerical simulations.

Scalable digital quantum simulation of lattice fermion theories with local encoding