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A concatenated [(4, 1, 3)] quantum convolutional code

Antonio Carlos Aido de Almeida, Reginaldo Palazzo

Published Apr 6, 2005• 25 citations
Publisher

Abstract

We construct a concatenated [(4, 1, 3)] quantum convolutional code from a (2, 1, 2) classical convolutional code. This quantum convolutional code can correct one general error.
DOI
10.1109/itw.2004.1405269

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I report two general methods to construct quantum convolutional codes for quantum registers with internal NNN states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general quantum error for every eight consecutive quantum registers.
I report two general methods to construct quantum convolutional codes for NNN-state quantum systems. Using these general methods, I construct a quantum convolutional code of rate 1/4, which can correct one quantum error for every eight consecutive quantum registers.
Using the idea of code concatenation in classical coding theory, we make the suggestion of constructing general concatenated quantum codes by choosing certain quantum codes as outer code and inner code. Then by concatenating quantum RS outer codes with a set of special quantum inner codes, one can construct a family of concatenated quantum codes, which is asymptotically good. In the field of quantum error-correcting codes, this is the first time that a family of asymptotically good quantum code is constructed using bad classical codes.
Decoherence is one of the major challenges facing the field of quantum computation.The field of quantum error correction has developed to meet this challenge.A group-theoretical structure and associated class of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specified codes and classes of codes.All stabilizer codes discovered so far are block codes.In this thesis, we will construct a class of concatenated quantum convolutional codes.We will introduce the concept of quantum convolutional memory and some simple techniques to produce good quantum convolutional codes from classes of classical convolutional codes.