  As the search continues for useful applications of noisy intermediate scale
quantum devices, variational simulations of fermionic systems remain one of the
most promising directions. Here, we perform a series of quantum simulations of
chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and
114 one-qubit gates. We model the binding energy of ${\rm H}_6$, ${\rm H}_8$,
${\rm H}_{10}$ and ${\rm H}_{12}$ chains as well as the isomerization of
diazene. We also demonstrate error-mitigation strategies based on
$N$-representability which dramatically improve the effective fidelity of our
experiments. Our parameterized ansatz circuits realize the Givens rotation
approach to non-interacting fermion evolution, which we variationally optimize
to prepare the Hartree-Fock wavefunction. This ubiquitous algorithmic primitive
corresponds to a rotation of the orbital basis and is required by many
proposals for correlated simulations of molecules and Hubbard models. Because
non-interacting fermion evolutions are classically tractable to simulate, yet
still generate highly entangled states over the computational basis, we use
these experiments to benchmark the performance of our hardware while
establishing a foundation for scaling up more complex correlated quantum
simulations of chemistry.
