Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Quantum Error Correction and Fault Tolerant Quantum Computing

  • Markus Grassl
  • Martin Rötteler
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_435

Definition of the Subject

Quantum error correction offers a solution to the problem of protecting quantum systems against noise induced by interactions with theenvironment or caused by imperfect control of the system. The need for error correction arises not only in communication, when quantum information is sentover some distance, but also in locally, when storing and processing quantum information. Fault-tolerant quantum computing builds on quantum errorcorrection and denotes techniques that allow computations to be performed on a quantum system with faulty gates as well as storage errors. Withoutmechanisms for quantum error correction and fault-tolerance, quantum computing would be impossible even for moderate error rates.

The idea of quantum error correction was first conceived in a paper [64] by Shor in 1995in which a particular quantum code was given that encodes one quantum bit (qubit) into nine quantum bits, while being able to correct against onearbitrary error on one of...

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Markus Grassl
    • 1
  • Martin Rötteler
    • 2
  1. 1.Institute for Quantum Optics and Quantum InformationAustrian Academy of SciencesInnsbruckAustria
  2. 2.NEC Laboratories America, Inc.PrincetonUSA