  Quantum computing has the potential to significantly speed up complex
computational tasks, and arguably the most promising application area for
near-term quantum computers is the simulation of quantum mechanics. To make the
most of our limited quantum computing resources, we need new and more compact
algorithms and mappings. Whereas previous work, including recent
demonstrations, has focused primarily on general mappings for fermionic
systems, we propose instead to construct customized mappings tailored to the
considered quantum mechanical systems. Specifically, we take advantage of
existing symmetry, which we build into the mappings a priori to obtain optimal
compactness. To demonstrate this approach, we have performed quantum computing
calculations of the fluorine molecule, in which we have mapped 16 active
spin-orbitals to 4 qubits. This is a four-fold reduction in the qubit
requirement, as compared to the standard general mappings. Moreover, our
compact system-to-qubits mappings are robust against noise that breaks
symmetry, thereby reducing non-statistical errors in the computations.
Furthermore, many systems, including F2, are described by real Hamiltonians,
allowing us to also reduce the number of single-qubit operations in the
hardware-efficient ansatz for the quantum variational eigensolver by roughly a
factor of three.
