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Error correction and decoding for quantum stabilizer codes

Xiao Fang-Ying Chen Han-Wu

Error correction and decoding for quantum stabilizer codes

Xiao Fang-Ying, Chen Han-Wu
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Publishing process
  • Received Date:  10 September 2010
  • Accepted Date:  17 December 2010
  • Published Online:  05 April 2011

Error correction and decoding for quantum stabilizer codes

  • 1. School of Computer Science and Engineering, Southeast University, Nanjing 211189, China; Key Laboratory of Computer Network and Information Integration of Ministry of Education, Southeast University, Nanjing 211189, China

Abstract: Mapping the error syndromes to error operators is the core of quantum decoding network and the key step to realize quantum error correction. The definitions of the bit flip error syndrome matrix and the phase flip error syndrome matrix are presented, and then the error syndromes of Pauli errors are expressed in terms of the columns of the bit flip error syndrome matrix and the phase flip error syndrome matrix. It is also shown that the error syndrome matrix of a stabilizer code is determined by its check matrix, which is similar to the relationship between the classical error and the parity check matrix of classical codes. So, the techniques of error detection and error correction for classical linear codes can be applied to quantum stabilizer codes after some modifications. The error correction circuits are constructed based on the relationship between the error operator and error syndrom. The decoding circuit is constructed by reversing the encoding circuit because the encoding operators are unitary.

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