Quantum simulation of 1D-fermionic systems with Ising Hamiltonians

In recent years, programmable, analogue quantum simulators have become capable of simulating quantum critical phenomena in many-body systems, including dynamical phase transitions. However, many of these quantum simulations are focused on Ising-type Hamiltonians with transverse fields, as these are native to quantum hardware platforms like superconducting flux qubits or neutral atoms. The simulation of 1D systems of spinless fermions, or quantum spin chains, poses a challenge to these platforms due to the lack of non-stoquastic couplings or limited control thereof. We propose a method to simulate the time- evolution of certain spinless fermionic systems in 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 fermions in 1D. This approach makes the simulation of certain fermionic many- body systems accessible to contemporary analogue quantum hardware that natively implements Ising-type Hamiltonians with transverse fields. The Ising Hamiltonians are 1D chains of spins with nearestneighbor and, optionally, next-nearest-neighbor interactions. As a proof-of-concept, we perform numerical simulations of various fermionic systems, such as the AubryAndre model, using domain-wall evolution and accurately reproduce various properties, such as phase diagrams and dynamical phase transitions. Ultimately, we discuss the feasibility of the approach to yield experimental results in the near future.