Ultrafast Hybrid Fermion-to-Qubit mapping

Fermion-to-qubit mappings play a crucial role in representing fermionic interactions on a quantum computer. Efficient mappings translate fermionic modes of a system to qubit interactions with a high degree of locality while using few auxiliary resources. We present a family of locality-preserving fe...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: O'Brien, Oliver, Strelchuk, Sergii
Format: Article
Language:English
Subjects:
Fermions
Mapping
Online Access:Get full text
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Summary:Fermion-to-qubit mappings play a crucial role in representing fermionic interactions on a quantum computer. Efficient mappings translate fermionic modes of a system to qubit interactions with a high degree of locality while using few auxiliary resources. We present a family of locality-preserving fermion-to-qubit mappings that require fewer auxiliary qubits than all existing schemes known to date. One instance requires only 1.016 qubits-per-fermion compared to 1.25 for the best-known locality-preserving mapping by Y.-A. Chen and Y. Xu [PRX Quantum 4, 010326 (2023)]. Our family of mappings (parameterised by integer \(n\)) establishes a direct trade-off between the number of auxiliary qubits (\(\frac{1}{n^2}\)) and the circuit length (\(O(\log n)\)). Furthermore, we present a non-local variant that combines the strengths of the Jordan-Wigner and Bravyi-Kitaev mappings to give 98\% shorter circuits than the Jordan-Wigner mapping. This is achieved by applying seemly incompatible mappings at different scales, making it possible for their respective strengths to complement each other.
ISSN:2331-8422
DOI:10.48550/arxiv.2211.16389