Quantum Convolutional Codes: Encoders and Structural Properties

Quantum convolutional codes can be used to protect streams of quantum bits against errors when sending them along a quantum channel. We review the underlying error model, conditions for quantum convolutional codes, and present a product code construction that yields families of quantum convolutional codes. Concerning the structure of encoding circuits for general quantum convolutional codes, we review the notion of catastrophic errors and show that each quantum convolutional code has encoders which are non-catastrophic, i.e., which have good error propagation properties. We present an algorithm to compute a quantum circuit which can be used to perform non-catastrophic encoding and inverse encoding in constant depth and give several examples for illustration.