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Computare Errare Est: Quantum Error Correction

  • Bernard Zygelman
Chapter

Abstract

We show how to diagnose and rehabilitate bit-flip errors in a classical error correcting model. We compare logical vs. physical bits, define codewords and introduce a classical error correcting model. Quantum codes must take into account the no-cloning theorem, the collapse hypothesis, and the possibility of continuous errors. We present encoding, syndrome measurement, and recovery circuits for single qubit bit-flip and phase shift errors. We review the Shor code and the role that stabilizers play in its implementation. We illustrate the use of the stabilizer formalism in the analysis of quantum error-correcting codes (QECC). We discuss the threshold theorem and its role in allowing for fault-tolerant quantum computing.

References

  1. 1.
    K. Fujii, Quantum Computation with Topological Codes, Springer Briefs in Mathematical Physics 2015Google Scholar
  2. 2.
    Daniel Gottsman, Stabilizer Codes and Quantum Error Correction, arxiv:quant-ph/9705052v1 1997Google Scholar
  3. 3.
    Michael E. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge U. Press, 2011zbMATHGoogle Scholar
  4. 4.
    A. Zee, Group Theory in a Nutshell for Physicists, Princeton University Press 2016Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Bernard Zygelman
    • 1
  1. 1.Department of Physics and AstronomyUniversity of NevadaLas VegasUSA

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