Qudit-based quantum simulation of fermionic systems

Abstract

Model Hamiltonians described by fermionic operators are ubiquitous in physics and chemistry, but the quantum simulation of their properties is challenging on near-term quantum computers. Indeed, for any problem with more than two connected neighbors, standard mappings of fermions on qubits lead to many-body operators whose size increases with the size of the problem, quickly making the simulation unfeasible on noisy devices. Here we consider an alternative mapping based on qudits and the auxiliary fermion method, which leads to a significant reduction in the circuit depth and in the number of computational units to be controlled. These advantages increase for highly connected target Hamiltonians, such as lattices with long-range interactions or the molecular systems investigated in quantum chemistry. We numerically test our approach on qudits encoded in molecular spins, by performing the quantum simulation of a fermionic model on a small cluster.