Simulating Fermionic Hamiltonians requires a mapping from fermionic to qubit operators. This mapping must obey the underlying algebra of fermionic operators; in particular, their specific anticommutation relations. The traditional mapping is the Jordan-Wigner encoding, which is simple and qubit minimal, but can incur significant overheads during simulation. This is because the qubit weight of fermionic operators is high, i.e. operators typically must involve many qubits. New mappings address this trade-off and hold other intriguing features. For example, the Bravyi-Kitaev mapping reduces operator weight via a translation into the parity basis. Recent work even integrates error detection and correction properties into the mapping, exploiting the native conservation of parity required in these systems. This tutorial will serve as an introduction to recent innovations in fermion-qubit mappings. I will summarize the algebraic criteria when constructing fermion-qubit mappings and describe recently explored mappings.
Bio: Christopher Kang is a PhD student advised by Fred Chong at the University of Chicago. His work focuses on the design of quantum architectures for Hamiltonian simulation.
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