Optimizing compiler for Fermion simulation circuits

Jordan-Wigner and Bravyi-Kitaev transformations are the two widely known examples of the Fermion $\rightarrow$ qubit operator mappings. There exist however at least $O(2^{n^2})$ possible such mappings. Thus, an appropriate choice of the mapping can result in the reduction of quantum resource cost in practice, such as two-qubit gate counts in Fermion-simulation circuits. In this talk, I will present a methodology that may be used to optimize these simulation circuits, leveraging the vastly large space from which a suitable mapping may be drawn. A series of heuristics will be explored to arrive at the post-optimization quantum circuits.