QuantumComputationandQuantumInformation

Quantum Computation and Quantum InformationAuthor: Michael A. Nielsen, Isaac L. Chuang完整可搜索PDF版Quantum Computation and Quantum InformationThis text is a comprehensive introduction to the main ideas and techniquesof the field of quantum computation and quantum information. Until nowthe rapid rate of progress and its cross-disciplinary nature have made itdifficult for newcomers to the field to obtain a broad overview of the mostimportant techniques and resultsMichael Nielsen and Isaac Chuang ask the question: what are the ultimatephysical limits to computation and communication? They describe in detailsuch remarkable effects as fast quantum algorithms, quantum teleportationquantum cryptography and quantum error-correction. A wealth ofaccompanying figures and exercises illustrate and develop the material inmore depth. a special feature is the tutorial introductions to quantummechanics and computer science included in Part I of the book, ensuring thatthe subject is accessible even without a background in physics or computerscience. In Part Il, the authors present quantum computation, and describewhat a quantum computer is, how it can be used to solve problems fasteran familiar classical'computers, and the real-world implementation ofquantum computers. Part III concludes the book with an in-depth treatmentof quantum information, explaining how quantum states can be used toperform remarkable feats of communication, together with a discussion ofhow it is possible to protect quantum states against the effects of noiseThis exciting text will be of interest to beginning graduate students andresearchers in physICS, computer science, mathematics, and electricalengineering with an interest in quantum computation and quantuminformation, and may be used as a text in courses on the subjectMichael Nielsen is a Postdoctoral Research Fellow at the University ofQueensland. He was born in Brisbane, Australia, and received his educationat the University of Queensland, obtaining postgraduate degrees inMathematics and physics before receiving his Ph D. in Physics as aFulbright Scholar at the University of New Mexico. He has held a visitingposition at the los alamos National Laboratory, and was the tolmanPostdoctoral Fellow at the California Institute of TechnologyIsaac Chuang is with IBM Research, and also serves as a consulting professorat Stanford University. He received his doctorate in Electrical Engineeringfrom Stanford university, where he was a Hertz Foundation Fellow andalso holds degrees in Physics and in Electrical Engineering from MIT. DrChuang is a native of louisville, Kentucky and enjoys reading hiking, andplaying his violin.Quantum Computation and Quantum InformationMichael A. nielsen isaac l. ChuanCAMBRIDGEUNIVERSITY PRESSPUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGEThe Pitt Building, Trumpington Street, Cambridge, United KingdomCAMBRIDGE UNIVERSITY PRESSThe Edinburgh Building, Cambridge CB2 2RU, UK40 West 20th Street, New York, NY 00114421lUSA10 Stamford Road, Oakleigh, VIC 3166, AustraliaRuiz de alarcon 13, 28014 Madrid, spainDock House, The Waterfront, Cape Town 8001, South Africahttp://www.cambridge.orgrsityThis book is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,oductnay take place withethe written permission of Cambridge University Pressablished 2000printed 2001(twice)Printed in the United Kingdom at the university Press, cambridgeTypeset in Monotype Ehrhardt 10)/13pt, in IATEX LE [EPC]A catalogue record of this book is available from the British LibraryLibrary of congress Cataloguing in Publication dataNielsen Michel A. and Chuang, Isaac IQuantum Computation and Quantum Information Michael A Nielsen and Isaac L chuangIncludes bibliographical references and indexⅠSBN0-521-63503-9Ⅰ. TitleQA401.G47200051l.8dc219822029CIPISBN 0 521 63235 8 hardbackISBn 0 521 635039 paperbackTo our parentsand our teachersContentsPrefacepage xvAcknowledgementsXXINomenclature and notationXX111Part I Fundamental concepts1 Introduction and overview1. I Global perspectives1. 1. 1 History of quantum computation and quantum information21. 1.2 Future directions121.2 Quantum bits1.2. 1 Multiple qubits161.3 Quantum comput13. 1 Single qubit gates171.3.2 Multiple qubit gates201.3.3 Measurements in bases other than the computational basis221.3.4 Quantum circuits221.3.5 Qubit copying circuit1.3.6 Example: Bell states251.3.7 Example: quantum teleportation261.4 Quantum algorithms281.4.1 Classical computations on a quantum computer291. 4.2 Quantum parallelism301.4.3 Deutsch's algorithm321.4.4 The Deutsch Jozsa algorithm1.4.5 Quantum algorithms summarized361.5 Experimental quantum information processing1.5.1 The Stern-Gerlach experiment1.5.2 Prospects for practical quantum information processing461.6 Quantum information501.6.1 Quantum information theory: example problems1.6.2 Quantum information in a wide2 Introduction to quantum mechanics2. 1 Linear algebra2.1. 1 Bases and linear independence622.1.2 Linear operators and matricesVlllContents2.1.3 The pauli matrices652. 1.4 Inner products2. 1.5 Eigenvectors and eigenvalues2. 1.6 Adjoints and hermitian operators692.1.7 Tensor products712.1.8 Operator functions2. 1.9 The commutator and anti-commutator762. 1. 10 The polar and singular value decompositions782. 2 The postulates of quantum mechanics802. 2. 1 State space2.2.2 Evolution2.2.3 Quantum measurement2.2.4 Distinguishing quantum states862.2.5 Projective measurements2.2.6 POVM measurements2.2.7 Phase932.2.8 Composite systems932.2.9 Quantum mechanics: a global view2.3 Application: superdense coding2. 4 The density operator982. 4. 1 Ensembles of quantum states992.4.2 General properties of the density operator2.4.3 The reduced density operator1052.5 The schmidt decomposition and purifications1092.6 EPR and the Bell inequality1113 Introduction to computer science1203. 1 Models for computation1223.1.1 Turing machines1223.1.2 Circuits1293.2 The analysis of computational problems1353.2.1 How to quantify computational resources1363.2.2 Computational complexity1383.2.3 Decision problems and the complexity classes P and NP1413.2.4 a plethora of complexity classes1503.2.5 Energy and computation1533.3 Perspectives on computer science161Part II Quantum computation1714 Quantum circuits174. 1 Quantum algorithms1724.2 Single qubit operations1744.3 Controlled operations1774.4 Measurement1854.5 Universal quantum gates188