  It is important to protect quantum information against decoherence and
operational errors, and quantum error-correcting (QEC) codes are the keys to
solving this problem. Of course, just the existence of codes is not efficient.
It is necessary to perform operations fault-tolerantly on encoded states
because error-correction process (i.e., encoding, decoding, syndrome
measurement and recovery) itself induces an error. By using simulation, this
paper investigates the effects of some important QEC codes (the five qubit
code, the seven qubit code and the nine qubit code) and their fault-tolerant
operations when the error-correction process itself induces an error. The
corresponding results, statistics and analyses are presented in this paper.
