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arXiv · 1810.02590

Jordan-Wigner transformations for tree structures

Stefan Backens·Alexander Shnirman·Yuriy Makhlin
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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.

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Stefan Backens, Alexander Shnirman, Yuriy Makhlin. 2018-10-05. Jordan-Wigner transformations for tree structures. https://doi.org/10.1038/s41598-018-38128-8

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