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Topological quantum memory

J. Math. Phys. 43, 4452 (2002); doi:10.1063/1.1499754

Issue Date: September 2002

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Eric Dennis
Princeton University, Princeton, New Jersey 08544

Alexei Kitaev, Andrew Landahl, and John Preskill
Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z2 lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures. ©2002 American Institute of Physics.
History: Received 25 October 2001; accepted 16 May 2002
Permalink: http://link.aip.org/link/?JMAPAQ/43/4452/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.67.Lx
    Quantum mechanics, field theories, and special relativity Quantum information Quantum computation
  • 02.40.Pc
    Mathematical methods in physics Geometry, differential geometry, and topology General topology
  • YEAR: 2002

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0022-2488 (print)   1089-7658 (online)
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