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CSS code

From Wikipedia, the free encyclopedia

In quantum error correction, CSS codes, named after their inventors, Robert Calderbank, Peter Shor[1] and Andrew Steane,[2] are a special type of stabilizer code constructed from classical codes with some special properties. An example of a CSS code is the Steane code.

Construction

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Let and be two (classical) , codes such, that and both have minimal distance , where is the code dual to . Then define , the CSS code of over as an code, with as follows:

Define for , where is bitwise addition modulo 2. Then is defined as .

References

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  1. ^ Robert Calderbank and Peter Shor (1996). "Good quantum error-correcting codes exist". Physical Review A. 54 (2): 1098–1105. arXiv:quant-ph/9512032. Bibcode:1996PhRvA..54.1098C. doi:10.1103/PhysRevA.54.1098. PMID 9913578. S2CID 11524969.
  2. ^ Steane, Andrew (1996). "Multiple-Particle Interference and Quantum Error Correction". Proc. R. Soc. Lond. A. 452 (1954): 2551–2577. arXiv:quant-ph/9601029. Bibcode:1996RSPSA.452.2551S. doi:10.1098/rspa.1996.0136. S2CID 8246615.

Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-1-107-00217-3. OCLC 844974180.

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