Quantum simulation of one-dimensional fermionic systems with Ising Hamiltonians

In recent years, analog quantum simulators have reached unprecedented quality, both in qubit numbers and coherence times. Most of these simulators natively implement Ising-type Hamiltonians, which limits the class of models that can be simulated efficiently. We propose a method to overcome this limitation and simulate the time evolution of a large class of spinless fermionic systems in one dimension (1D) using simple Ising-type Hamiltonians with local transverse fields. Our method is based on domain wall encoding, which is implemented via strong (anti)ferromagnetic couplings $|J|$. We show that in the limit of strong $|J|$, the domain walls behave like spinless fermions in 1D. The Ising Hamiltonians are one-dimensional chains with nearest-neighbor and, optionally, next-nearest-neighbor interactions. As a proof of concept, we perform numerical simulations of various 1D fermionic systems using domain wall evolution and accurately reproduce the systems' properties, such as topological edge states, Anderson localization, quantum chaotic time evolution, and time-reversal symmetry breaking via Floquet engineering. Our approach makes the simulation of a large class of fermionic many-body systems feasible on analog quantum hardware that natively implements Ising-type Hamiltonians with transverse fields.