Mathematics of topological quantum computing
نویسندگان
چکیده
منابع مشابه
Mathematics of Topological Quantum Computing
In topological quantum computing, information is encoded in “knotted” quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by experiments to an accuracy of 10−10 and harnessed to stabilize quantum memory. In this survey, we discuss the conceptual development of this interdisciplinary fi...
متن کاملTopological Quantum Computing
Quantum computers have the ability to solve certain problems exponentially faster than the best known algorithms for classical computers. Examples include database searching, simulation of quantum systems, and factoring large numbers.[1][2][3] However, the nature of most quantum systems makes the states too fragile for efficient calculations to be done. Topological quantum computing avoids thes...
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Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematicians perspective on some of the advantages and challenges of this model, highlighting some recent ad...
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Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with k>2, k not equal 4. This work exte...
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In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form e. This description is given with two objectives in mind. The first is to describe the algorithm in such a way as to make explicit the underlying and inherent control structure. The second is to make this alg...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2018
ISSN: 0273-0979,1088-9485
DOI: 10.1090/bull/1605