Description

A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing.

This book covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing.

Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes.

Key Features

Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes.

Covers both classical and quantum information theory and error correcting codes.

The last chapter of the book covers physical implementation of quantum information processing devices.

Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information.

Readership

Graduate students, advanced undergraduate students and professionals (postdocs, faculty, industry research staff) in computer science, electrical engineering, physics, applied physics, mathematics, and maybe chemistry.

Table of Contents

DEDICATION

PREFACE

CHAPTER 1. Preliminaries

1.1 ELEMENTS OF LINEAR ALGEBRA

1.2 HILBERT SPACES AND DIRAC NOTATIONS

1.3 HERMITIAN AND UNITARY OPERATORS: PROJECTORS

1.4 POSTULATES OF QUANTUM MECHANICS

1.5 QUANTUM STATE POSTULATE

1.6 DYNAMICS POSTULATE

1.7 MEASUREMENT POSTULATE

1.8 LINEAR ALGEBRA AND SYSTEMS DYNAMICS

1.9 SYMMETRY AND DYNAMIC EVOLUTION

1.10 UNCERTAINTY PRINCIPLE AND MINIMUM UNCERTAINTY STATES

1.11 PURE AND MIXED QUANTUM STATES

1.12 ENTANGLEMENT AND BELL STATES

1.13 QUANTUM INFORMATION

1.14 PHYSICAL REALIZATION OF QUANTUM INFORMATION PROCESSING SYSTEMS

1.15 UNIVERSAL COMPUTERS: THE CIRCUIT MODEL OF COMPUTATION

1.16 QUANTUM GATES, CIRCUITS, AND QUANTUM COMPUTERS

1.17 UNIVERSALITY OF QUANTUM GATES: THE SOLOVAY-KITAEV THEOREM

1.18 QUANTUM COMPUTATIONAL MODELS AND QUANTUM ALGORITHMS

1.19 DEUTSCH, DEUTSCH-JOZSA, BERNSTEIN-VAZIRANI, AND SIMON ORACLES

1.20 QUANTUM PHASE ESTIMATION

1.21 WALSH-HADAMARD AND QUANTUM FOURIER TRANSFORMS

1.22 QUANTUM PARALLELISM AND REVERSIBLE COMPUTING

1.23 GROVER SEARCH ALGORITHM

1.24 AMPLITUDE AMPLIFICATION AND FIXED-POINT QUANTUM SEARCH

1.25 ERROR MODELS AND QUANTUM ALGORITHMS

1.26 HISTORY NOTES

1.27 SUMMARY

1.28 EXERCISES AND PROBLEMS

CHAPTER 2. Measurements and Quantum Information

2.1 MEASUREMENTS AND PHYSICAL REALITY

2.2 COPENHAGEN INTERPRETATION OF QUANTUM MECHANICS

2.3 MIXED STATES AND THE DENSITY OPERATOR

2.4 PURIFICATION OF MIXED STATES

2.5 BORN RULE

2.6 MEASUREMENT OPERATORS

2.7 PROJECTIVE MEASUREMENTS

2.8 POSITIVE OPERATOR-VALUED MEASURES (POVMs)

2.9 NEUMARK THEOREM

2.10 GLEASON THEOREM

2.11 MIXED ENSEMBLES AND THEIR TIME EVOLUTION

2.12 BIPARTITE SYSTEMS: SCHMIDT DECOMPOSITION

Details

No. of pages:
744
Language:
English
Copyright:
© 2011
Published:
Imprint:
Academic Press
eBook ISBN:
9780123838759
Print ISBN:
9780123838742

About the author

Dan Marinescu

Dan C. Marinescu was a Professor of Computer Science at Purdue University in West Lafayette, Indiana from 1984 till 2001 when he joined the Computer Science Department at the University of Central Florida. He has held visiting faculty positions at IBM T. J. Watson Research Center, Yorktown Heights, New York; Institute of Information Sciences, Beijing ; Scalable Systems Division of Intel Corporation; Deutsche Telecom; and INRIA Rocquancourt in France. In 2012 he was a Fulbright Professor at UTFSM (Universidad Tecnica Federico Santa Maria) in Valparaiso, Chile. His research interests cover parallel and distributed systems, cloud computing, scientific computing, and quantum computing and quantum information theory. He has published more than 220 papers in refereed journals and conference proceedings in these areas and authored three books. In 2007 he delivered the Boole Lecture at University College Cork, the school where George Boole taught from 1849 till his death in 1864. Dan Marinescu was the principal investigator of several grants from the National Science Foundation. In 2008 he was awarded a Earnest T.S. Walton fellowship from the Science Foundation of Ireland.

Affiliations and Expertise

Professor, Computer Science, University of Central Florida

Reviews

"At the intersection of physics, mathematics, and computer science, explain the authors in the preface, the discipline of quantum information science has emerged during the last two decades. The discipline has developed as a response to the limitations and challenges of information processing, which include "[h]eat dissipation, leakage, and other physical phenomena [that] limit our ability to build increasingly faster and, implicitly, increasingly smaller solid-state devices...." They continue: "Quantum information is information encoded to some property of quantum particles and obeys the laws of quantum mechanics." With this book, graduate students and researchers are presented with coverage of three areas: quantum computing, quantum information theory, and quantum error correction. Dan C. Marinescu (computer science, U. of Central Florida) and Gabriela M. Marinescu (affiliation not stated) have co-written many books and articles on the subject."--Book News, Reference & Research