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Quantum Information Processing

, Volume 8, Issue 5, pp 443–459 | Cite as

Quantum error correction via convex optimization

  • Robert L. Kosut
  • Daniel A. Lidar
Article

Abstract

We show that the problem of designing a quantum information processing error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to derive new codes that are locally optimal. We present examples of such codes that can handle errors which are too strong for codes derived by analogy to classical error correction techniques.

Keywords

Quantum error correction Convex optimization 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.SC SolutionsSunnyvaleUSA
  2. 2.Departments of Chemistry, Electrical Engineering, and Physics, Center for Quantum Information Science & TechnologyUniversity of Southern CaliforniaLos AngelesUSA

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