Applications of the Yang-Baxter-Rowell equation to topological quantum computation

Aida Arnedo León

doi:10.1117/12.918413

8 May 2012 Applications of the Yang-Baxter-Rowell equation to topological quantum computation

Aida Arnedo León

Proceedings Volume 8400, Quantum Information and Computation X; 84000X (2012) https://doi.org/10.1117/12.918413
Event: SPIE Defense, Security, and Sensing, 2012, Baltimore, Maryland, United States

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.

Citation Download Citation

Aida Arnedo León "Applications of the Yang-Baxter-Rowell equation to topological quantum computation", Proc. SPIE 8400, Quantum Information and Computation X, 84000X (8 May 2012); https://doi.org/10.1117/12.918413

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