Fault-tolerant quantum computation by anyons

Kitaev, A. Yu.

doi:10.1016/S0003-4916(02)00018-0

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Fault-tolerant quantum computation by anyons

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Author(s): A. Kitaev

Publication date: 2009-10-30

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Abstract

A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.

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Most cited references 6

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Fractional Statistics and the Quantum Hall Effect

Daniel Arovas, J. Schrieffer, Frank Wilczek (1984)

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Quantum Error Correction and Orthogonal Geometry

P W Shor, N. J. A. Sloane, A. R. Calderbank … (1996)

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.