Charles Derby

Abstract Mappings between fermions and qubits are valuable constructions in physics. To date only a handful exist. In addition to revealing dualities between fermionic and spin systems, such mappings are indispensable in any simulation of fermionic physics on quantum computers. The number of qubits required per fermionic mode, and the locality of mapped fermionic operators strongly impact the cost of such simulations. Local fermionic encodings are a class of fermion to qubit mappings that map local fermionic operators to local qubit operators. We present a novel local fermionic encoding -- called the compact encoding -- which outperforms all previous local fermionic encodings in both the qubit to mode ratio, and the locality of mapped operators. We demonstrate how this encoding may be applied to any uniform tiling of degree 4 or less, for example square and hexagonal lattices, and to a 3d cubic lattice. In order to characterize the encoding on various lattices we clarify the group theoretic structure underlying the design of such encodings. We also illuminate an elegant relationship between the compact encoding and the toric code, and show how the compact encoding may be understood as condensing the fermionic excitations of the toric code into its code space.