Quantum simulation of fermions: geometric locality and error mitigation

We consider mappings from fermionic systems to spin systems that preserve geometric locality in more than one spatial dimension. Such mappings are useful for simulating lattice fermion models (e.g., the Hubbard model) on a quantum computer. Locality-preserving mappings avoid the overhead associated with non-local parity terms in conventional mappings, such as the Jordan-Wigner transformation. As a result, they often provide solutions with lower circuit depth. Moreover, locality-preserving mappings are likely to be more resistant to qubit noises by avoiding encoding the fermionic correlation functions in non-local Pauli operators. Here, we discuss how to detect/correct single-qubit errors with two known locality-preserving maps. We then go beyond that by constructing new mappings with better error detecting/correcting performance than the existing ones. Our methods do no introduce extra physical qubits beyond those required by the original mappings. Being able to detect/correct errors in initial state preparations is crucial to the success of near-term quantum algorithms such as the variational quantum eigensolver. Our results also provide systematic methods to constructing quantum error-detecting/correcting codes with Majorana fermion operators.