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Topological quantum memory

Dennis, Eric and Kitaev, Alexei and Landahl, Andrew and Preskill, John (2002) Topological quantum memory. Journal of Mathematical Physics, 43 (9). pp. 4452-4505. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:DENjmp02

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Abstract

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 Z(2) 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.


Item Type:Article
Additional Information:Copyright © 2002 American Institute of Physics. Received 25 October 2001; accepted 16 May 2002. We happily acknowledge helpful discussions with many colleagues, including Dorit Aharonov, Charlie Bennett, Daniel Gottesman, Randy Kamien, Greg Kuperberg, Paul McFadden, Michael Nielsen, Peter Shor, Andrew Steane, Chenyang Wang, and Nathan Wozny. We are especially grateful to Peter Hoyer for discussions of efficient perfect matching algorithms. This work originated in 1997, while E.D. received support from Caltech’s Summer Undergraduate Research Fellowship (SURF) program. This work has been supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, by DARPA through the Quantum Information and Computation (QUIC) project administered by the Army Research Office under Grant No. DAAH04-96-1-0386, by the National Science Foundation under Grant No. EIA-0086038, by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374, and by an IBM Faculty Partnership Award.
Subject Keywords:ERROR-CORRECTING CODES; ISING-MODEL; GROUND-STATES; 2 DIMENSIONS; COMPUTATION; GEOMETRY
Record Number:CaltechAUTHORS:DENjmp02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:DENjmp02
Alternative URL:http://dx.doi.org/10.1063/1.1499754
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1702
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Feb 2006
Last Modified:26 Dec 2012 08:45

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