Topological quantum computation

Topological Quantum Computation

* Copyright (C) 2010: Permission is granted to everyone to make verbatim copies of this document provided that the copyright notice and this permission notice are preserved. Synopsis • Introduction to anyons and topological models Anyons, their properties and their relation to topological quantum computation. • Quantum double models Quantum double models are stabilizer codes, that can be descri...

Topological Quantum Computation

Following a suggestion of A. Kitaev, we explore the connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions. A suitably designed spin system can support localized excitations (quasiparticles) that exhibit long-range nonabelian Aharonov-Bohm interactions. Quantum information encoded in the charges of the quasiparticles is highly resistant...

Topological quantum computation

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possibility...

Measurement-only topological quantum computation.

We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.

Topological phases and quantum computation