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量子计算与量子信息（影印版）

作者：
(美)Michael A. Nielsen, Isaac
定价：
59.00元
ISBN：
978-7-04-013502-2
版面字数：
840.000千字
开本：
16开
全书页数：
676页
装帧形式：
平装
重点项目：
暂无
出版时间：
2003-08-20
物料号：
13502-00
读者对象：
高等教育
一级分类：
计算机/教育技术类
二级分类：
计算机科学与技术专业课程
暂无
  • Preface
  • Acknowledgements
  • Nomenclature and notation
  • Part Ⅰ Fundamental concepts
    • 1 Introduction and overview
      • 1.1 Global perspectives
        • 1.1.1 History of quantum computation and quantum information
        • 1.1.2 Future directions
      • 1.2 Quantum bits
        • 1.2.1 Multiple qubits
      • 1.3 Quantum computation
        • 1.3.1 Single qubit gates
        • 1.3.2 Multiple qubit gates
        • 1.3.3 Measurements in bases other than the computational basis
        • 1.3.4 Quantum circuits
        • 1.3.5 Qubit copying circuit?
        • 1.3.6 Example: Bell states
        • 1.3.7 Example: quantum teleportation
      • 1.4 Quantum algorithms
        • 1.4.1 Classical computations on a quantum computer
        • 1.4.2 Quantum parallelism
        • 1.4.3 Deutsch's algorithm
        • 1.4.4 The Deutsch-jozsa algorithm
        • 1.4.5 Quantum algorithms summarized
      • 1.5 Experimental quantum information processing
        • 1.5.1 The Stern-Gerlach experiment
        • 1.5.2 Prospects for practical quantum information processing
      • 1.6 Quantum information
        • 1.6.1 Quantum information theory: example problems
        • 1.6.2 Quantum information in a wider context
    • 2 Introduction to quantum mechanics
      • 2.1 Linear algebra
        • 2.1.1 Bases and linear independence
        • 2.1.2 Linear operators and matrices
        • 2.1.3 The Pauli matrices
        • 2.1.4 Inner products
        • 2.1.5 Eigenvectors and eigenvalues
        • 2.1.6 Adjoints and Hermitian operators
        • 2.1.7 Tensor products
        • 2.1.8 Operator functions
        • 2.1.9 The commutator and anti-commutator
        • 2.1.10 The polar and singular value decompositions
      • 2.2 The postulates of quantum mechanics
        • 2.2.1 State space
        • 2.2.2 Evolution
        • 2.2.3 Quantum measurement
        • 2.2.4 Distinguishing quantum states
        • 2.2.5 Projective measurements
        • 2.2.6 POVM measurements
        • 2.2.7 Phase
        • 2.2.8 Composite systems
        • 2.2.9 Qntum mechanics: a global view
      • 2.3 Application: superdense coding
      • 2.4 The density operator
        • 2.4.1 Ensembles of quantum states
        • 2.4.2 General properties of the density operator
        • 2.4.3 The reduced density operator
      • 2.5 The Schmidt decomposition and purifications
      • 2.6 EPR and the Bell inequality
    • 3 Introduction to computer science
      • 3.1 Models for computation
        • 3.1.1 Turing machines
        • 3.1.2 Circuits
      • 3.2 The analysis of computational problems
        • 3.2.1 How to quantify computational resources
        • 3.2.2 Computational complexity
        • 3.2.3 Decision problems and the complexity classes P and NP
        • 3.2.4 A ptetnora of complexity classes
        • 3.2.5 Energy and computation
      • 3.3 Perspectives on computer science
  • PartⅡ Quantum computation
    • 4 Quantum circuits
      • 4.1 Quantum algorithms
      • 4.2 Single qubit operations
      • 4.3 Controlled operations
      • 4.4 Measurement
      • 4.5 Universal quantum gates
        • 4.5.1 Two-level unitary gates are universal
        • 4.5.2 Single qubit and CNOT gates are universal
        • 4.5.3 A discrete set of universal operations
        • 4.5.4 Approximating arbitrary unitary gates is generically hard
        • 4.5.5Quantum computational complexity
      • 4.6 Summary of the quantum circuit model of computation
      • 4.7 Simulation of quantum systems
        • 4.7.1 Simulation in action
        • 4.7.2 The quantum simulation algorithm
        • 4.7.3 An illustrative example
        • 4.7.4 Perspectives on quantum simulation
    • 5 The quantum Fourier transform and its applications
      • 5.1 The quantum Fourier transform
      • 5.2 Phase estimation
        • 5.2.1 Performance and requirements
      • 5.3 Applications: order-finding and factoring
        • 5.3.1 Application: order-finding
        • 5.3.2 Application: factoring
      • 5.4 General applications of the quantum Fourier transform
        • 5.4.1 Period-finding
        • 5.4.2 Discrete logarithms
        • 5.4.3 The hidden subgroup problem
        • 5.4.4 Other quantum algorithms?
    • 6 Quantum search algorithms
      • 6.1 The quantum search algorithm
        • 6.1.1 The oracle
        • 6.1.2 The procedure
        • 6.1.3 Geometric visualization
        • 6.1.4 Performance
      • 6.2 Quantum search as a quantum simulation
      • 6.3 Quantum counting
      • 6.4 Speeding up the solution of NP-complete problems
      • 6.5 Quantum search of an unstructured database
      • 6.6 Optimality of the search algorithm
      • 6.7 Black box algorithm limits
    • 7 Quantum computers: physical realization
      • 7.1 Guiding principles
      • 7.2 Conditions for quantum computation
        • 7.2.1 Representation of quantum information
        • 7.2.2 Performance of unitary transformations
        • 7.2.3 Preparation of fiducial initial states
        • 7.2.4 Measurement of output result
      • 7.3 Harmonic oscillator quantum computer
        • 7.3.1 Physical apparatus
        • 7.3.2 The Hamiltonian
        • 7.3.3 Quantum computation
        • 7.3.4 Drawbacks
      • 7.4 Optical photon quantum computer
        • 7.4.1 Physical apparatus
        • 7.4.2 Quantum computation
        • 7.4.3 Drawbacks
      • 7.5 Optical cavity quantum electrodynamics
        • 7.5.1 Physical apparatus
        • 7.5.2 The Hamiltonian
        • 7.5.3 Single-photon single-atom absorption and refraction
        • 7.5.4 Quantum computation
      • 7.6 Ion traps
        • 7.6.1 Physical apparatus
        • 7.6.2 The Hamiltonian
        • 7.6.3 Quantum computation
        • 7.6.4 Experiment
      • 7.7 Nuclear magnetic resonance
        • 7.7.1 Physical apparatus
        • 7.7.2 The Hamiltonian
        • 7.7.3 Quantum computation
        • 7.7.4 Experiment
      • 7.8 Other implementation schemes
  • Part Ⅲ Quantum information
    • 8 Quantum noise and quantum operations
      • 8.1 Classical noise and Markov processes
      • 8.2 Quantum operations
        • 8.2.1 Overview
        • 8.2.2 Environments and quantum operations
        • 8.2.3 Operator-sum representation
        • 8.2.4 Axiomatic approach to quantum operations
      • 8.3 Examples of quantum noise and quantum operations
        • 8.3.1 Trace and partial trace
        • 8.3.2 Geometric picture of single qubit quantum operations
        • 8.3.3 Bit flip and phase flip channels
        • 8.3.4 Depolarizing channel
        • 8.3.5 Amplitude damping
        • 8.3.6 Phase damping
      • 8.4 Applications of quantum operations
        • 8.4.1 Master equations
        • 8.4.2 Quantum process tomography
      • 8.5 Limitations of the quantum operations formalism
    • 9 Distance measures for quantum information
      • 9.1 Distance measures for classical information
      • 9.2 How close are two quantum states?
        • 9.2.1 Trace distance
        • 9.2.2 Fidelity
        • 9.2.3 Relationships between distance measures
      • 9.3 How well does a quantum channel preserve information?
    • 10 Quantum error-correction
      • 10.1 Introduction
        • 10.1.1 The three qubit bit flip code
        • 10.1.2 Three qubit phase flip code
      • 10.2 The Shor code
      • 10.3 Theory of quantum error-correction
        • 10.3.1 Discretization of the errors
        • 10.3.2 Independent error models
        • 10.3.3 Degenerate codes
        • 10.3.4 The quantum Hamming bound
      • 10.4 Constructing quantum codes
        • 10.4.1 Classical linear codes
        • 10.4.2 Calderbank-Shor-Steane codes
      • 10.5 Stabilizer codes
        • 10.5.1 The stabilizer formalism
        • 10.5.2 Unitary gates and the stabilizer formalism
        • 10.5.3 Measurement in the stabilizer formalism
        • 10.5.4 The Gottesman-Knill theorem
        • 10.5.5 Stabilizer code constructions
        • 10.5.6 Examples
        • 10.5.7 Standard form for a stabilizer code
        • 10.5.8 Quantum circuits for encoding, decoding, and correction
      • 10.6 Fault-tolerant quantum computation
        • 10.6.1 Fault-tolerance: the big picture
        • 10.6.2 Fault-tolerant quantum logic
        • 10.6.3 Fault-tolerant measurement
        • 10.6.4 Elements of resilient quantum computation
    • 11 Entropy and information
      • 11.1 Shannon entropy
      • 11.2 Basic properties of entropy
        • 11.2.1 The binary entropy
        • 11.2.2 The relative entropy
        • 11.2.3 Conditional entropy and mutual information
        • 11.2.4 The data processing inequality
      • 11.3 Von Neumann entropy
        • 11.3.1 Quantum relative entropy
        • 11.3.2 Basic properties of entropy
        • 11.3.3 Measurements and entropy
        • 11.3.5 Concavity of the entropy
        • 11.3.6 The entropy of a mixture of quantum states
      • 11.4 Strong subadditivity
        • 11.4.1 Proof of strong subadditivity
        • 11.4.2 Strong subadditivity: elementary applications
    • 12 Ouantum information theory
      • 12.1 Distinguishing quantum states and the accessible tntormanon
        • 12.1.1 The Holevo bound
        • 12.1.2 Example applications of the Holevo bound
      • 12.2 Data compression
        • 12.2.1 Shannon’s noiseless channel coding theorem
        • 12.2.2 Schumacher’s quantum noiseless channel coding theorem
      • 12.3 Classical information over noisy quantum channels
        • 12.3.1 Communication over noisy classical channels
        • 12.3.2 Communication over noisy quantum channels
      • 12.4 Quantum information over noisy quantum channels
        • 12.4.1 Entropy exchange and the quantum Fano inequality
        • 12.4.2 The quantum data processing inequality
        • 12.4.3 Quantum Singleton bound
        • 12.4.4 Quantum error-correction, refrigeration and Maxwell’s demon
      • 12.5 Entanglement as a physical resource
        • 12.5.1 Transforming bi-partite pure state entanglement
        • 12.5.2 Entanglement distillation and dilution
        • 12.5.3 Entanglement distillation and quantum error-correction
      • 12.6 Quantum cryptography
        • 12.6.1 Private key cryptography
        • 12.6.2 Privacy amplification and information reconciliation
        • 12.6.3 Quantum key distribution
        • 12.6.4 Privacy and coherent information
        • 12.6.5 The security of quantum key distribution
  • Appendices
    • Appendix 1: Notes on basic probability theory
    • Appendix 2: Group theory
      • A2.1 Basic definitions
        • A2.1.1 Generators
        • A2.1.2 Cyclic groups
        • A2.1.3 Cosets
      • A2.2 Representations
        • A2.2.1 Equivalence and reducibility
        • A2.2.2 Orthogonality
        • A2.2.3 The regular representation
      • A2.3 Fourier transforms
    • Appendix 3:The Solovay-Kitaev theorem
    • Appendix4:Number theory
      • A4.1 Fundamentals
      • A4.2 Modular arithmetic and Euclid’s algorithm
      • A4.3 Reduction of factoring to order-finding
      • A4.4 Continued fractions
  • Appendix 5:Public key cryptography and the RSA cryptosystem
  • Appendix 6:Proof of Lieb’s theorem
  • Bibliography
  • Index

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