Quantum $\mathcal{R}$-matrices as universal qubit gates

Abstract

We study the Chern-Simons approach to the topological quantum computing. We use quantum $\mathcal{R}$-matrices as universal quantum gates and study the approximations of some one-qubit operations. We make some modifications to the known Solovay-Kitaev algorithm suitable for our particular problem.

6 pages, 5 figures

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Cited by in corpus (10)

• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• Distinguishing Mutant Knots
• Quantization of Harer-Zagier formulas
• A new symmetry of the colored Alexander polynomial
• Solutions to the constant Yang-Baxter equation in all dimensions
• Polyadic braid operators and higher braiding gates
• Entangled states from arborescent knots
• Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism
• Entangling gates from cabling of knots
• Measuring Chern-Simons level $k$ by braiding $SU(2{)}_k$ anyons