Fermion-to-Qubit Encodings for Quantum Simulation

Quantum simulation of fermionic many-body systems is an important application of quantum computing, with relevance to problems in the fields of quantum chemistry and condensed matter. One challenge in implementing these simulations is that they require mapping the indistinguishable fermions to distinguishable qubits. Several schemes for accomplishing this fermion to qubit mapping have been proposed. In this presentation we provide an overview of progress in the field. We will highlight a number of fermionic encodings, ranging from the well-known Jordan-Wigner mapping to the recent Custom Fermionic Codes scheme developed by R. Chien and J. Whitfield (arXiv:2009.11860).