https://doi.org/10.1140/epjb/e2020-100429-1
Regular Article
Free fermion representation of the topological surface code
School of Physics and Astronomy, University of Leeds,
Leeds
LS2 9JT, UK
a e-mail: py12af@leeds.ac.uk
Received:
2
September
2019
Received in final form:
30
December
2019
Published online: 4 March 2020
The toric code is known to be equivalent to free fermions. This paper presents explicit local unitary transformations that map the ℤ2 toric and surface code – the open boundary equivalent of the toric code – to fermions. Through this construction it is shown that the surface code can be mapped to a set of free fermion modes, while the toric code requires additional fermionic symmetry operators. Finally, it is demonstrated how the anyonic statistics of these codes are encoded in the fermionic representations.
Key words: Solid State and Materials
© The Author(s) 2020. This article is published with open access at Springerlink.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
