Approximate quantum error correction can lead to better codes

  • Leung D
  • Nielsen M
  • Chuang I
 et al. 
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We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process, and does not fit into the GF(4) classification.

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  • Debbie W. Leung

  • M. A. Nielsen

  • Isaac L. Chuang

  • Yoshihisa Yamamoto

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