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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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