Quantum information processing and quantum error correction pdf

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quantum information processing and quantum error correction pdf

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The need for error correction arises not only in communication, when quantum information is sentover some distance, but also in locally, when storing and processing quantum information.

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Quantum Error Correction and Fault Tolerant Quantum Computing

Quantum error correction QEC is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum information, but also with faulty quantum gates, faulty quantum preparation, and faulty measurements. Classical error correction employs redundancy. The simplest way is to store the information multiple times, and—if these copies are later found to disagree—just take a majority vote; e. Suppose further that a noisy error corrupts the three-bit state so that one bit is equal to zero but the other two are equal to one. If we assume that noisy errors are independent and occur with some probability p , it is most likely that the error is a single-bit error and the transmitted message is three ones. It is possible that a double-bit error occurs and the transmitted message is equal to three zeros, but this outcome is less likely than the above outcome.

Quantum error correction

To implement fault-tolerant quantum computation with continuous variables, the Gottesman—Kitaev—Preskill GKP qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large-scale quantum computation with the GKP qubit [ Phys. X 8 , ], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large-scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit-level quantum error correction is partially substituted by the single-qubit-level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit-level quantum error correction almost identical to those of the logical-qubit-level quantum error correction in a practical noise level. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to expoloit the advantages of the GKP qubits in practical quantum computation.

The first 6 chapters were originally prepared in , Chapter 7 was added in , and Chapter 9 was added in A typeset version of Chapter 8 on fault-tolerant quantum computation is not yet available; nor are the figures for Chapter 7. Additional material is available in the form of handwritten notes. Chapters 2 and 3 were updated in July What is now Chapter 5 also updated July is a new version of what was previously the first half of Chapter 6. Chapter 10, updated April , is a revised and expanded version still not quite complete of what was previously Chapter 5.

CMSC 858K: Introduction to quantum information processing (Fall 2016)

The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include:.

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Supplemental: Michael A. Nielsen and Isaac L.