Abstract

The Jordan–Wigner transformation provides an efficient mapping between
spin chains and fermionic systems in one dimension. We extend the
transformation to tree structures, which allows us to map between
fermionic and spin systems with nearest-neighbour coupling. The mapping
is achieved with the help of additional spins at the junctions between
one-dimensional chains. This extension permits a straightforward
simulation of Majorana braiding in spin or qubit systems.