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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
, 2007
"... 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 know ..."
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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, which
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,
NonAbelian Anyons and Interferometry
 58 L. Zehnder, Ein neuer interferenzrefractor, Zeitschr. f. Instrkde
, 2007
"... To all my teachers, especially the three who have been with me from the very beginning: my parents, Mahrokh and Loren, and my sister, Roxana. iv Acknowledgments First and foremost, I would like to thank the members of my thesis defense committee: my advisor John Preskill for his guidance and support ..."
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To all my teachers, especially the three who have been with me from the very beginning: my parents, Mahrokh and Loren, and my sister, Roxana. iv Acknowledgments First and foremost, I would like to thank the members of my thesis defense committee: my advisor John Preskill for his guidance and support, and for giving me a chance and pointing me in the right direction when I was lost; Alexei Kitaev for providing inspiring and enlightening discussions; Kirill Shtengel for taking me under his wing and for all the help and advice he has given me; and NaiChang Yeh for her endless encouragement and enthusiasm. Also, I thank John Schwarz for his efforts and understanding during his time spent as my initial advisor at Caltech. I would like to recognize the hard work and affability of the Caltech staff, especially Donna Driscoll, Ann Harvey, and Carol Silberstein. I have had the pleasure and benefit of discussing physics, mathematics, and other interesting topics with Eddy Ardonne,
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.