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

TL;DR

This paper introduces a general method for constructing quantum convolutional encoders that use minimal memory, are non-catastrophic, and have polynomial depth, improving quantum data transmission reliability.

Contribution

It presents a universal technique for designing quantum convolutional encoders with desirable properties, extending previous specific cases to arbitrary codes.

Findings

The encoders are proven to be non-recursive.

The technique applies to many existing quantum convolutional codes.

Encoders achieve minimal memory and avoid catastrophic error propagation.

Abstract

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.