  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.
