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 1D using simple Ising-type Hamiltonians with local transverse fields. The time complexity of the simulation scales with the square root of the inverse error, and thus favorably compared to the worst-case error of first-order product formulas. 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 analogue quantum hardware that natively implements Ising-type Hamiltonians with transverse fields.