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Codigos convolucionais quanticos concatenados

Antonio Carlos Aido de Almeida

Published Oct 14, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.47749/t/unicamp.2004.322954

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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.
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.
Quantum error correction codes were introduced as a means to protect quantum information from decoherance and operational errors. Based on their approach to error control, error correcting codes can be divided into two different classes: block codes and convolutional codes. There has been significant development towards finding quantum block codes, since they were first discovered in 1995. In contrast, quantum convolutional codes remained mainly uninvestigated. In this thesis, we develop the stabilizer formalism for quantum convolutional codes. We define distance properties of these codes and give a general method for constructing encoding circuits, given a set of generators of the stabilizer of a quantum convolutional stabilizer code, is shown. The resulting encoding circuit enables online encoding of the qubits, i.e., the encoder does not have to wait for the input transmission to end before starting the encoding process. We develop the quantum analogue of the Viterbi algorithm. The quantum Viterbi algorithm (QVA) is a maximum likehood error estimation algorithm, the complexity of which grows linearly with the number of encoded qubits. A variation of the quantum Viterbi algorithm, the Windowed QVA, is also discussed. Using Windowed QVA, we can estimate the most likely error without waiting for the entire received sequence.
One of the most challenges to prove the feasibility of quantum computers is to protect the quantum nature of information. Quantum convolutional codes are aimed at protecting a stream of quantum information in a long distance communication, which are the correct generalization to the quantum domain of their classical analogs. In this paper, we construct some classes of quantum convolutional codes by employing classical constacyclic codes. These codes are optimal in the sense that they attain the Singleton bound for pure convolutional stabilizer codes.