2017/01/24 by Vojtěch Havlíček, Matthias Troyer, James Whitfield +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Biology #Linguistics #Locality #Mathematical physics #Mathematics #Operator (biology) #Philosophy #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical physics #quant-ph
paper · pdf · doi:10.1103/physreva.95.032332
published as Phys. Rev. A 95, 032332 (2017)
arxiv created 2017/01/24 · openalex publication_date 2017/03/29 · arxiv updated 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.