Generalized performance of concatenated quantum codes - A dynamical systems approach

Jesse Fern, Julia Kempe, Slobodan N. Simić, Shankar Sastry

Research output: Contribution to journalArticlepeer-review


We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing on particular types of noise channels, we study the geometry of the coding map as a discrete-time dynamical system on the entire space of noise channels. In the case of diagonal channels, we show that any code with distance at least three corrects (in the infinite concatenation limit) an open set of errors. For Calderbank-Shor-Steane (CSS) codes, we give a more precise characterization of that set. We show how to incorporate noise in the gates, thus completing the framework. We derive some general bounds for noise channels, which allows us to analyze several codes in detail.

Original languageEnglish (US)
Pages (from-to)448-459
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Mar 2006


  • Quantum channels
  • Quantum error corrections
  • Quantum fault tolerance

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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