  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.
