Quantum simulation of fermionic systems using qubits will play an important role in current and emerging quantum computing architectures. Limitations of small scale quantum computers will help inform the roadmap to the future and here we present new tools for creating qubit operators for fermionic systems.
The Fenwick tree approach to fermion-to-qubit mappings is implemented in the Julia Language. A similar Python implementation found in https://github.com/quantumlib/OpenFermion as contributed by https://github.com/VojtaHavlicek.
In the technical note, we give an introduction and a summary of our generalized approach to Jordan-Wigner and Bravyi-Kitaev transforms and beyond. In particular, the parity tree forms the crux of our general approach. The primary reference for this work is:
Operator Locality in Quantum Simulation of Fermionic Models
Vojtěch Havlíček, Matthias Troyer, James D. Whitfield
Phys. Rev. A 95, 032332 (2017)
https://arxiv.org/pdf/1701.07072.pdf
James. D. Whitfield @ Dartmouth.Edu