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Topological Quantum Computing

The Kitaev honeycomb model on surfaces of genus g geq 2

arXiv
Authors: John Brennan, Jiří Vala

Year

2022

Paper ID

58318

Status

Preprint

Abstract Read

~2 min

Abstract Words

113

Citations

N/A

Abstract

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan-Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled mathbb{Z}2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.

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  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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  • We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface.

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