We describe in this work a five-qubit quantum convolutional error correcting code and its implementation on a classical computer.  The encoding and decoding circuits and an error correction procedure are presented.  We will verify that if any  X, Y, Z error or any product of them occurs on one or two qubit, this correction always  allows  to  recover the useful information or  to  obtain a list of possible errors. The originality in  this correction is the winning time obtained by looking at only the required syndromes for each error,   thus avoiding the decoherence phenomenon.   Also,  we give the  average fidelity  for double errors recovered  as single  errors  having same syndrome.  This work is described in more detail in  convo2012.pdf , included with this application.  

NOTE: 
a)  This application requires the use of the Feynman package, by T.Radtke and S.Fritzsche. This Maple package is available from the CPC Program Library from Queen’s University in Belfast, as
http://cpc.cs.qub.ac.uk/summaries/ADWE_v4_0.html.  You must install that package first before running this application.  
b) The running time is very short for the coding circuit but can be much more higher for the orthers parts of the application.

Acknowledgement

  We would like to thank very much Mrs S.Fritzsch and T.Radtke for providing us with the version 4 (2008) of Feynman Program.

This circuit is schematized in figure 11 , page 22 of the ref[4] (see the included file convo2012.pdf).