Minimal memory requirements for pearl-necklace encoders of quantum convolutional codes

Understand

One of the major goals in quantum information processing is to reduce the overhead associated with the practical implementation of quantum protocols, and often, routines for quantum error correction account for most of this overhead.

• A particular technique for quantum error correction that may be useful for protecting a stream of quantum information is quantum convolutional coding.
• The encoder for a quantum convolutional code has a representation as a convolutional encoder or as a "pearl-necklace" encoder.
• In the pearl-necklace representation, it has not been particularly clear in the research literature how much quantum memory such an encoder would require for implementation.