Simple Quantum Error Correcting Codes

1996/05/15 by Andrew Steane · 3 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.54.4741

published as Phys.Rev.A54:4741,1996 · Submitted to Phys. Rev. A. in May 1996. 21 pages, no figures. Further information at http://eve.physics.ox.ac.uk/ASGhome.html

arxiv created 1996/05/15 · arxiv updated 2009/12/01

Abstract

Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C₂^⊥ ⊆ C₁, where C₁ and C₂ are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing C₁ to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error correcting codes for 3, 4 and 5 information qubits with block lengths of 8, 10 and 11 qubits respectively.

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