Fault-tolerant conversion between stabilizer codes by Clifford operations

Abstract: We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying Clifford gates. The Clifford gates are chosen from the comparisons between both codes. The fault tolerance of the conversion is guaranteed by quantum error correction in every step during the entire conversion process. As examples, we show three conversions: the $[[5,1,3]]$ stabilizer code and Steane code, Steane code and $[[15,1,3]]$ Reed-Muller code, and Steane code and $(3,4)$-QPC code.