Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders

Understand

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.