  Quantum convolutional coding is a technique for encoding a stream of quantum
information before transmitting it over a noisy quantum channel. Two important
goals in the design of quantum convolutional encoders are to minimize the
memory required by them and to avoid the catastrophic propagation of errors. In
a previous paper, we determined minimal-memory, non-catastrophic,
polynomial-depth encoders for a few exemplary quantum convolutional codes. In
this paper, we elucidate a general technique for finding an encoder of an
arbitrary quantum convolutional code such that the encoder possesses these
desirable properties. We also provide an elementary proof that these encoders
are non-recursive. Finally, we apply our technique to many quantum
convolutional codes from the literature.
