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Quantum error correction via convex optimization

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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.

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Authors and Affiliations

  1. SC Solutions, Sunnyvale, CA, 94085, USA

    Robert L. Kosut

  2. Departments of Chemistry, Electrical Engineering, and Physics, Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, CA, 90089, USA

    Daniel A. Lidar

Authors
  1. Robert L. Kosut
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  2. Daniel A. Lidar
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Correspondence to Robert L. Kosut.

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Kosut, R.L., Lidar, D.A. Quantum error correction via convex optimization. Quantum Inf Process 8, 443–459 (2009). https://doi.org/10.1007/s11128-009-0120-2

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  • DOI: https://doi.org/10.1007/s11128-009-0120-2

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