  In this paper we demonstrate how data encoded in a five-qubit quantum error
correction code can be converted, fault-tolerantly, into a seven-qubit Steane
code. This is achieved by progressing through a series of codes, each of which
fault-tolerantly corrects at least one error. Throughout the conversion the
encoded qubit remains protected. We found, through computational search, that
the method used to convert between codes given in this paper is optimal.
