Digital quantum simulation of lattice fermion theories with local encoding

Abstract

We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and two-qubit gates and is scalable since integrating each Hamiltonian term requires a finite (non-scaling) cost. The exact local fermion encoding we adopt relies on auxiliary ${\mathbb{Z}}_2$ lattice gauge fields by adding a pure gauge Hamiltonian term akin to the Toric Code. By numerically emulating the quantum simulator real-time dynamics, we observe a timescale separation for spin- and charge-excitations in a spin-$\frac{1}{2}$ Hubbard ladder in the $t-J$ model limit.

24 pages, 9 figures

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• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Local fermion-to-qudit mappings: a practical recipe for four-level systems