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Proceedings Paper

Applications of the Yang-Baxter-Rowell equation to topological quantum computation
Author(s): Aida Arnedo León
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Paper Abstract

The main goal of this paper is to apply the Yang-Baxter-Rowell equation in topological quantum computation, using the symbolic computational software Maple. Initially, using Maple, I reproduced the Dye classification of the 4x4 unitary solutions of the Yang-Baxter equation. Then, also using Maple, I reproduced the solutions given by Rebecca Chen to the Yang-Baxter-Rowell equation. Finally, the obtained solutions were applied to the problem of topological quantum categorification of the chromatic polynomial for graphs. It was claimed that the Yang-Baxter-Rowell operators, considered as quantum gates, can be incorporated in quantum circuit models and quantum games, such as the Grover algorithm and the game Battle of the Sexes. It is expected that a future investigation can provide a more complete classification of the solution to the Yang-Baxter-Rowell equation and its possible applications on topological quantum computation.

Paper Details

Date Published: 8 May 2012
PDF: 24 pages
Proc. SPIE 8400, Quantum Information and Computation X, 84000X (8 May 2012); doi: 10.1117/12.918413
Show Author Affiliations
Aida Arnedo León, Univ. EAFIT (Colombia)

Published in SPIE Proceedings Vol. 8400:
Quantum Information and Computation X
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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