  Present quantum computers often work with distinguishable qubits as their
computational units. In order to simulate indistinguishable fermionic
particles, it is first required to map the fermionic state to the state of the
qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish
this mapping. The BKSF mapping has connections to quantum error correction and
opens the door to new ways of understanding fermionic simulation in a
topological context. Here, we present the first detailed exposition of BKSF
algorithm for molecular simulation. We provide the BKSF transformed qubit
operators and report on our implementation of the BKSF fermion-to-qubits
transform in OpenFermion. In this initial study of the hydrogen molecule, we
have compared BKSF, Jordan-Wigner and Bravyi-Kitaev transforms under the
Trotter approximation. We considered different orderings of the exponentiated
terms and found lower Trotter errors than previously reported for Jordan-Wigner
and Bravyi-Kitaev algorithms. These results open the door to further study of
the BKSF algorithm for quantum simulation.
