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Nonabelian anyons and topological quantum computation
 Reviews of Modern Physics
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
NonAbelian Anyons and Topological Quantum Computation. arxiv: condmat.strel/0707.1889
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
Anyons and the quantum Hall effect – a pedagogical review
 Ann. Phys
"... The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to superfluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the inte ..."
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The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to superfluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined ”anyons”, may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to nonabelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation. Key words: Anyons, Quantum Hall Effect There are two basic principles on which the entire formidable world of nonrelativistic quantum mechanics resides. First, the world is described in terms of wave functions that satisfy Schroedinger’s wave equation. And second, these wave functions should satisfy certain symmetry properties with respect to the exchange of identical particles. For fermions the wave function should be antisymmetric, for bosons it should be symmetric. It is impossible to overrate the importance of these symmetries in determining the properties of quantum systems made of many identical particles. Bosons form superfluids, fermions form Fermi liquids. The former may carry current without dissipating energy,
MeasurementOnly Topological Quantum Computation via Anyonic Interferometry
, 808
"... We describe measurementonly topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using “forced measurement ” protocols for both types of measurement. Using this, it is shown how topolo ..."
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We describe measurementonly topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using “forced measurement ” protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurementonly approach) in fractional quantum Hall systems.