Document Type
Article
Publication Date
1-2017
Publication Title
Physical Review A - Atomic, Molecular, and Optical Physics
Department
Department of Physics and Astronomy
Abstract
Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the Auxiliary Fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical data structure and generalized to achieve a further locality improvement for local fermionic models on a rectangular lattice. We conclude that the most compact encoding of the fermionic operators can be done using ancilla qubits with the Auxiliary Fermion scheme. Without introducing ancillas, a variant of the Bravyi-Kitaev transform provides the most compact fermion-to-qubit mapping for Hubbard-like models.
DOI
10.1103/PhysRevA.95.032332
Dartmouth Digital Commons Citation
Havlíček, Vojtěch; Troyer, Matthias; and Whitfield, James D., "Operator Locality in the Quantum Simulation of Fermionic Models" (2017). Dartmouth Scholarship. 3021.
https://digitalcommons.dartmouth.edu/facoa/3021
