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 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 with 1.25 for the best-known locality-preserving mapping by Chen and Xu []. Our family of mappings (parameterized by integer n) establishes a direct trade-off between the number of auxiliary qubits (1/n2) and the circuit length [O(logn)]. Furthermore, we present a nonlocal 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 seemingly incompatible mappings at different scales, making it possible for their respective strengths to complement each other. Published by the American Physical Society 2024