Two-spectral Yang-Baxter operators in topological quantum computation

William F. Sanchez

doi:10.1117/12.884445

3 June 2011 Two-spectral Yang-Baxter operators in topological quantum computation

William F. Sanchez

Proceedings Volume 8057, Quantum Information and Computation IX; 80570W (2011) https://doi.org/10.1117/12.884445
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Citation Download Citation

William F. Sanchez "Two-spectral Yang-Baxter operators in topological quantum computation", Proc. SPIE 8057, Quantum Information and Computation IX, 80570W (3 June 2011); https://doi.org/10.1117/12.884445

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KEYWORDS

Quantum computing

Computing systems

Quantum communications

Computer simulations

Quantum efficiency

Algorithm development

Matrices

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