Universal Quantum Gates Via Yang-Baxterization of Dihedral Quantum Double
The recently discovered Yang-Baxterization process for the quantum double of the dihedral group algebra, is presented keeping on mind the quantum computation. The products resultant from Yang-Baxterization process are interpreted as universal quantum gates using the Bryslinski’s theorem. Results are obtained for two-qubits and two-qutrits gates. Using the Zhang-Kauffman-Ge method (ZKGM), certain Hamiltonians responsible for the quantum evolution of the quantum gates are obtained. Possible physical systems such as anyons systems are mentioned as referents for practical implementation.
Unable to display preview. Download preview PDF.
- 2.Dancer, K., Isaac, P., Links, J.: Representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the yang-baxter equation (2006), Eprint: http://arXiv.org/abs/math.QA/0511072v2
- 3.Bigelow, S.: Braid groups and iwahori-hecke algebras (2005), Preprint: http://arXiv.org/abs/math.GT/0505064
- 4.Temperley, H., Lieb, E.: Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: Some exact results for the ‘percolation’ problem. Proceedings of the Royal Society of London A 32, 251–280 (1971)MathSciNetCrossRefGoogle Scholar
- 8.Kauffman, L.H., Lomonaco Jr., S.J.: Brading operators are universal quantum gates. New J. Phys. 6 (2004), Preprint: arXiv.org/abs/quant-ph/0401090