  Noisy intermediate-scale quantum (NISQ) computers could solve
quantum-mechanical simulation problems that are beyond the capabilities of
classical computers. However, NISQ devices experience significant errors which,
if not corrected, can render physical quantities measured in these simulations
inaccurate or meaningless. Here we describe a method of reducing these errors
which is tailored to quantum algorithms for simulating fermionic systems. The
method is based on executing quantum circuits in the model of fermionic linear
optics, which are known to be efficiently simulable classically, to infer the
relationship between exact and noisy measurement outcomes, and hence undo the
effect of noise. We validated our method by applying it to the VQE algorithm
for estimating ground state energies of instances of the Fermi-Hubbard model.
In classical numerical simulations of 12-qubit examples with physically
realistic levels of depolarising noise, errors were reduced by a factor of
around 34 compared with the uncorrected case. Smaller experiments on quantum
hardware demonstrate an average reduction in errors by a factor of 10 or more.
