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Quantum Computation and Quantum Information (Tenth Anniversary Edition) by Michael A. Nielsen and Isaac L. Chuang



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Quantum Computation and Quantum Information (Tenth Edition) written by Michael A. Nielsen and Isaac L. Chuang .
MICHAEL NIELSEN was educated at the University of Queensland, and as a Fulbright Scholar at the University of New Mexico. He worked at Los Alamos National Laboratory, as the Richard Chace Tolman Fellow at Caltech, was Foundation Professor of Quantum Information Science and a Federation Fellow at the University of Queensland, and a Senior Faculty Member at the Perimeter Institute for Theoretical Physics. He left Perimeter Institute to write a book about open science and now lives in Toronto.
ISAAC CHUANG is a Professor at the Massachusetts Institute of Technology, jointly appointed in Electrical Engineering & Computer Science, and in Physics. He leads the quanta research group at the Center for Ultracold Atoms, in the MIT Research Laboratory of Electronics, which seeks to understand and create information technology and intelligence from the fundamental building blocks of physical systems, atoms, and molecules.
One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.


Quantum Computation and Quantum Information (Tenth Edition) written by Michael A. Nielsen and Isaac L. Chuang cover the following topics.



  • Introduction to the Tenth Anniversary Edition page xvii
    Afterword to the Tenth Anniversary Edition xix
    Preface xxi
    Acknowledgements xxvii
    Nomenclature and notation xxix

  • 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 Quantum 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 plethora of complexity classes
    3.2.5 Energy and computation
    3.3 Perspectives on computer science

  • Part II 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
    4.5.5 Quantum 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 444
    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
    11.3.4 Subadditivity
    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. Quantum information theory
    12.1 Distinguishing quantum states and the accessible information
    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
    1: Notes on basic probability theory
    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
    4: 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
    5: Public key cryptography and the RSA cryptosystem
    6: Proof of Lieb’s theorem
    Bibliography
    Index

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