An application benchmark for fermionic quantum simulations

It is expected that the simulation of correlated fermions in chemistry and material science will be one of the first practical applications of quantum processors. Given the rapid evolution of quantum hardware, it is increasingly important to develop robust benchmarking techniques to gauge the capacity of quantum hardware specifically for the purpose of fermionic simulation.
Here we propose using the one-dimensional Fermi-Hubbard model as an application benchmark for variational quantum simulations on near-term quantum devices. Since the one-dimensional Hubbard model is both strongly correlated and exactly solvable with the Bethe ansatz, it provides a reference ground state energy that a given device with limited coherence will be able to approximate up to a maximal size. The length of the largest chain that can be simulated provides an effective fermionic length. We use variational quantum eigensolver to approximate the ground state energy values of Fermi-Hubbard instances and show how the fermionic length benchmark can be used in practice to assess the performance of bounded-depth devices in a scalable fashion.