2017/12/31 by Mark Steudtner, Stephanie Wehner · 110 citations
Computer Science · Mathematics · Physics and Astronomy · #Fock space #Hamiltonian (control theory) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum circuit #Quantum computer #Quantum error correction #Quantum gate #Quantum mechanics #Qubit #Theoretical physics #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1088/1367-2630/aac54f
published in New Journal of Physics 20(6), 063010 (IOP Publishing) · 11+13 pages, 5 figures, 2 tables, see ArXiv files for Mathematica code (text file) and documentation (pdf); fixed typos in this new version
openalex publication_date 2018/05/16 · arxiv created 2018/10/11 · arxiv updated 2018/10/12 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. Interestingly, the minimal requirement of qubits for simulating Fermions seems to be agnostic of the actual number of particles as well as other symmetries. This leads to qubit requirements that are well above the minimal requirements as suggested by combinatorial considerations. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a nonlinear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with a more modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.