\subsection{Methods}
The FCI Hamiltonian in the basis of configuration states of the $\mathrm{A_g}$ irreducible representation of F$_{2}$ using the STO-3G atomic basis set\cite{Pople69_2657} was obtained from Psi4.\cite{Sherrill17_3185} This matrix was then decomposed into a sum of tensor products of Pauli operators to give the qubit representations (the qubit Hamiltonians are given in the SI). All of the quantum computer experiments were run via Qiskit,\cite{qiskit} and the trial state variational parameters were optimized via the simultaneous perturbation stochastic approximation algorithm with method parameters $a=1.2$, $A=20$, $c=0.06$, $\alpha=0.602$, and $\gamma=0.101$.\cite{Spall98_817} The 132 terms in the qubit Hamiltonians were grouped into 40 tensor product basis states via OpenFermion.\cite{openfermion} For the optimization, 200 iterations were performed and 1,024 shots were used for the energy evaluations at the perturbed parameters at each iteration. The readout error calibration matrix was calculated at the beginning of the optimization, and then every 10 iterations thereafter. We used 8,192 shots for the construction of the calibration matrix. During the last 25 iterations, the energies at the current parameters were also evaluated, again using 8,192 shots. The reported energies correspond to the average over these last 25 evaluations.

\subsection{Acknowledgements}
This work has been supported by the U.S. Naval Research Laboratory and its Naval Innovation Science and Engineering (NISE) programs. We acknowledge IBM Q resources through a collaboration with AFRL/RI and thank Steve Hellberg, Steve Policastro, and Sergio Tafur for discussions.

