Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate

Details Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate

2010-01-22

arxiv.org/abs/1001.4085v2

Phys. Rev. A 84, 012332 (2011)

Physics

Quantum Physics

4.5 pages, 3 figures, published in PRA

Scientific paper

10.1103/PhysRevA.84.012332

Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation by braiding ($k\geq 3,\ k \neq 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k\geq 3,\ k \neq 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory.

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