Encoding Subsystem Codes with and without Noisy Gauge Qubits

In this paper, we investigate a rather neglected aspect of subsystem codes viz. that of encoding. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use the known results on encoding of stabilizer codes. Along the way we also show how Clifford codes can be encoded. These encoding schemes can tolerate initialization errors on the gauge qubits. This tolerance can be traded for reduced encoding complexity.