Jordan-Wigner transformations for tree structures

TL;DR

This paper extends the Jordan-Wigner transformation to arbitrary tree structures, enabling efficient mapping between spin and fermionic systems with applications in simulating Majorana braiding.

Contribution

It introduces a novel mapping technique for tree-structured systems, broadening the applicability of spin-fermion transformations beyond linear chains.

Findings

Extended Jordan-Wigner transformation to tree structures.

Facilitates simulation of Majorana braiding in spin systems.

Enables mapping with nearest-neighbor coupling in complex networks.

Abstract

The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.