Simulation on maple of the nine qubit Shor code using Feynman program

To simulate the evolution and behavior of an n-qubits system, a quantum simulator within the framework of the computer algebra system Maple called Feynman program has been built by S.Fritzsche and T.Radtke. In this work we use this program to implement the nine qubit Shor quantum error correcting code on a classical computer . We will present the encoding and decoding circuits and describe the error correction procedure using the Shor code gen-erators. We will verify that if any X, Y or Z error occur on any single qubit this correction procedure always allow to recover the usuful information. More-over, it permit at the end to put all the ancillas in the initial state and then too use them again. The simulation permit also the decoding without correction to measure all the output errors and know something about the canal transmitting the information.