Numerical techniques for finding the distances of quantum codes

  title={Numerical techniques for finding the distances of quantum codes},
  author={Ilya Dumer and Alexey A. Kovalev and Leonid P. Pryadko},
  journal={2014 IEEE International Symposium on Information Theory},
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces complexity exponent of all existing deterministic techniques designed for codes with small relative distances (which include all known families of quantum LDPC codes), and also surpasses the probabilistic technique for sufficiently high code rates. 
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In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product.
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Homological product codes
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Improved quantum hypergraph-product LDPC codes
  • A. Kovalev, L. Pryadko
  • Computer Science
    2012 IEEE International Symposium on Information Theory Proceedings
  • 2012
The rotated lattices specified by two integer-valued periodicity vectors are introduced for the usual toric codes and several related algebraic constructions are suggested which increase the rate of the existing hypergraph-product codes by up to four times.
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