  In our recent work, we have examined various fermion to qubit mappings in the
context of quantum simulation including the original Bravyi-Kitaev Superfast
encoding (OSE) as well as a generalized version (GSE). We return to OSE and
compare it against the Jordan-Wigner (JW) transform for quantum chemistry
considering the number of qubits required, the Pauli weight of terms in the
transformed Hamiltonians, and the $L_1$ norm of the Hamiltonian. We considered
a test set of molecular systems known as the Atomization Energy 6 (AE6) as well
as Hydrogen lattices. Our results showed that the resource efficiency of OSE is
strongly affected by the spatial locality of the underlying single-particle
basis. We find that OSE is outperformed by JW when the orbitals in the
underlying single-particle basis are highly overlapping, which limits its
applicability to near-term quantum chemistry simulations utilizing standard
basis sets. In contrast, when orbitals are overlapping with only few others, as
is the case of Hydrogen lattices with very tight orbitals, OSE fares
comparatively better. Our results illustrate the importance of choosing the
right combination of basis sets and fermion to qubit mapping to get the most
out of a quantum device when simulating physical systems.
