Quantum Computing Explained

A self-contained treatment of the fundamentals of quantum computing This clear, practical book takes quantum computing out of therealm of theoretical physics and teaches the fundamentals of thefield to students and professionals who have not had training inquantum computing or quantum information th...

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Bibliographic Details
Main Author: McMahon, David
Format: eBook Book
Language:English
Published: Hoboken, N.J Wiley 2007
Wiley-Interscience : IEEE Computer Society
IEEE Computer Society Press
Wiley-IEEE Press
Wiley-Blackwell
Edition:1
Subjects:
Computers
Computing and Processing
Quantum computers
ISBN:9780470096994, 0470096993, 9780470181362, 0470181362, 9780470181386, 0470181389
Online Access:Get full text
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Table of Contents:
  • Preface. Chapter 1: A Brief Introduction to Information Theory.Chapter 2: Qubits and Quantum States.Chapter 3: Matrices and Operators.Chapter 4: Tensor Products.Chapter 5: The Density Operator.Chapter 6: Quantum Measurement Theory.Chapter 7: Entanglement.Chapter 8: Quantum Gates and Circuits.Chapter 9: Quantum Algorithms.Chapter 10: Applications of Entanglement: Teleportation andSuperdense Coding.Chapter 11: Quantum Cryptography.Chapter 12: Quantum Noise and Error Correction.Chapter 13: Tools of Quantum Information Theory.Chapter 14. Adiabatic Quantum Computation.Chapter 15. Cluster State Quantum Computing.References.Index.Â&#160
  • Intro -- QUANTUM COMPUTING EXPLAINED -- CONTENTS -- Preface -- 1 A BRIEF INTRODUCTION TO INFORMATION THEORY -- Classical Information -- Information Content in a Signal -- Entropy and Shannon's Information Theory -- Probability Basics -- Example 1.1 -- Solution -- Exercises -- 2 QUBITS AND QUANTUM STATES -- The Qubit -- Example 2.1 -- Solution -- Vector Spaces -- Example 2.2 -- Solution -- Linear Combinations of Vectors -- Example 2.3 -- Solution -- Uniqueness of a Spanning Set -- Basis and Dimension -- Inner Products -- Example 2.4 -- Solution -- Example 2.5 -- Solution -- Orthonormality -- Gram-Schmidt Orthogonalization -- Example 2.6 -- Solution -- Bra-Ket Formalism -- Example 2.7 -- Solution -- The Cauchy-Schwartz and Triangle Inequalities -- Example 2.8 -- Solution -- Example 2.9 -- Solution -- Summary -- Exercises -- 3 MATRICES AND OPERATORS -- Observables -- The Pauli Operators -- Outer Products -- Example 3.1 -- Solution -- You Try It -- The Closure Relation -- Representations of Operators Using Matrices -- Outer Products and Matrix Representations -- You Try It -- Matrix Representation of Operators in Two-Dimensional Spaces -- Example 3.2 -- Solution -- You Try It -- Definition: The Pauli Matrices -- Example 3.3 -- Solution -- Hermitian, Unitary, and Normal Operators -- Example 3.4 -- Solution -- You Try It -- Definition: Hermitian Operator -- Definition: Unitary Operator -- Definition: Normal Operator -- Eigenvalues and Eigenvectors -- The Characteristic Equation -- Example 3.5 -- Solution -- You Try It -- Example 3.6 -- Solution -- Spectral Decomposition -- Example 3.7 -- Solution -- The Trace of an Operator -- Example 3.8 -- Solution -- Example 3.9 -- Solution -- Important Properties of the Trace -- Example 3.10 -- Solution -- Example 3.11 -- Solution -- The Expectation Value of an Operator -- Example 3.12 -- Solution -- Example 3.13
  • Solution -- Example 8.4 -- Solution -- You Try It -- Exponentiation -- Example 8.5 -- Solution -- You Try It -- The Z-Y Decomposition -- Basic Quantum Circuit Diagrams -- Controlled Gates -- Example 8.6 -- Solution -- Example 8.7 -- Solution -- Example 8.8 -- Solution -- Example 8.9 -- Solution -- Gate Decomposition -- Exercises -- 9 QUANTUM ALGORITHMS -- Hadamard Gates -- Example 9.1 -- Solution -- The Phase Gate -- Matrix Representation of Serial and Parallel Operations -- Quantum Interference -- Quantum Parallelism and Function Evaluation -- Deutsch-Jozsa Algorithm -- Example 9.2 -- Solution -- Example 9.3 -- Solution -- Quantum Fourier Transform -- Phase Estimation -- Shor's Algorithm -- Quantum Searching and Grover's Algorithm -- Exercises -- 10 APPLICATIONS OF ENTANGLEMENT: TELEPORTATION AND SUPERDENSE CODING -- Teleportation -- Teleportation Step 1: Alice and Bob Share an Entangled Pair of Particles -- Teleportation Step 2: Alice Applies a CNOT Gate -- Teleportation Step 3: Alice Applies a Hadamard Gate -- Teleportation Step 4: Alice Measures Her Pair -- Teleportation Step 5: Alice Contacts Bob on a Classical Communications Channel and Tells Him Her Measurement Result -- The Peres Partial Transposition Condition -- Example 10.1 -- Solution -- Example 10.2 -- Solution -- Example 10.3 -- Solution -- Entanglement Swapping -- Superdense Coding -- Example 10.4 -- Solution -- Exercises -- 11 QUANTUM CRYPTOGRAPHY -- A Brief Overview of RSA Encryption -- Example 11.1 -- Solution -- Basic Quantum Cryptography -- Example 11.2 -- Solution -- An Example Attack: The Controlled NOT Attack -- The B92 Protocol -- The E91 Protocol (Ekert) -- Exercises -- 12 QUANTUM NOISE AND ERROR CORRECTION -- Single-Qubit Errors -- Quantum Operations and Krauss Operators -- Example 12.1 -- Solution -- Example 12.2 -- Solution -- Example 12.3 -- Solution
  • Characterizing Mixed States -- Example 5.5 -- Solution -- Example 5.6 -- Solution -- You Try It -- Example 5.7 -- Solution -- Example 5.8 -- Solution -- Example 5.9 -- Solution -- You Try It -- Probability of Finding an Element of the Ensemble in a Given State -- Example 5.10 -- Solution -- Completely Mixed States -- The Partial Trace and the Reduced Density Operator -- You Try It -- Example 5.11 -- Solution -- The Density Operator and the Bloch Vector -- Example 5.12 -- Solution -- Exercises -- 6 QUANTUM MEASUREMENT THEORY -- Distinguishing Quantum States and Measurement -- Projective Measurements -- Example 6.1 -- Solution -- Example 6.2 -- Solution -- You Try It -- Example 6.3 -- Solution -- Measurements on Composite Systems -- Example 6.4 -- Solution -- Example 6.5 -- Solution -- Example 6.6 -- Solution -- You Try It -- Example 6.7 -- Solution -- You Try It -- Example 6.8 -- Solution -- Generalized Measurements -- Example 6.9 -- Solution -- Example 6.10 -- Solution -- Positive Operator-Valued Measures -- Example 6.11 -- Solution -- Example 6.12 -- Solution -- Example 6.13 -- Solution -- Exercises -- 7 ENTANGLEMENT -- Bell's Theorem -- Bipartite Systems and the Bell Basis -- Example 7.1 -- Solution -- When Is a State Entangled? -- Example 7.2 -- Solution -- Example 7.3 -- Solution -- Example 7.4 -- Solution -- You Try It -- You Try It -- The Pauli Representation -- Example 7.5 -- Solution -- Example 7.6 -- Solution -- Entanglement Fidelity -- Using Bell States For Density Operator Representation -- Example 7.7 -- Solution -- Schmidt Decomposition -- Example 7.8 -- Solution -- Example 7.9 -- Solution -- Purification -- Exercises -- 8 QUANTUM GATES AND CIRCUITS -- Classical Logic Gates -- You Try It -- Single-Qubit Gates -- Example 8.1 -- Solution -- You Try It -- Example 8.2 -- Solution -- More Single-Qubit Gates -- You Try It -- Example 8.3
  • The Depolarization Channel -- The Bit Flip and Phase Flip Channels -- Amplitude Damping -- Example 12.4 -- Solution -- Phase Damping -- Example 12.5 -- Solution -- Quantum Error Correction -- Exercises -- 13 TOOLS OF QUANTUM INFORMATION THEORY -- The No-Cloning Theorem -- Trace Distance -- Example 13.1 -- Solution -- You Try It -- Example 13.2 -- Solution -- Example 13.3 -- Solution -- Fidelity -- Example 13.4 -- Solution -- Example 13.5 -- Solution -- Example 13.6 -- Solution -- Example 13.7 -- Solution -- Entanglement of Formation and Concurrence -- Example 13.8 -- Solution -- Example 13.9 -- Solution -- Example 13.10 -- Solution -- Example 13.11 -- Solution -- You Try It -- Information Content and Entropy -- Example 13.12 -- Solution -- Example 13.13 -- Solution -- Example 13.14 -- Solution -- Example 13.15 -- Solution -- Example 13.16 -- Solution -- Example 13.17 -- Solution -- Exercises -- 14 ADIABATIC QUANTUM COMPUTATION -- Example 14.1 -- Solution -- Adiabatic Processes -- Example 14.2 -- Solution -- Adiabatic Quantum Computing -- Example 14.3 -- Solution -- Exercises -- 15 CLUSTER STATE QUANTUM COMPUTING -- Cluster States -- Cluster State Preparation -- Example 15.1 -- Solution -- Adjacency Matrices -- Stabilizer States -- Aside: Entanglement Witness -- Cluster State Processing -- Example 15.2 -- Exercises -- References -- Index
  • Solution -- Functions of Operators -- Unitary Transformations -- Example 3.14 -- Solution -- Projection Operators -- Example 3.15 -- Solution -- You Try It -- Example 3.16 -- Solution -- Positive Operators -- Commutator Algebra -- Example 3.17 -- Solution -- The Heisenberg Uncertainty Principle -- Polar Decomposition and Singular Values -- Example 3.18 -- Solution -- The Postulates of Quantum Mechanics -- Postulate 1: The State of a System -- Postulate 2: Observable Quantities Represented by Operators -- Postulate 3: Measurements -- Postulate 4: Time Evolution of the System -- Exercises -- 4 TENSOR PRODUCTS -- Representing Composite States in Quantum Mechanics -- Example 4.1 -- Solution -- Example 4.2 -- Solution -- Computing Inner Products -- Example 4.3 -- Solution -- You Try It -- Example 4.4 -- Solution -- You Try It -- Example 4.5 -- Solution -- You Try It -- Tensor Products of Column Vectors -- Example 4.6 -- Solution -- You Try It -- Operators and Tensor Products -- Example 4.7 -- Solution -- You Try It -- Example 4.8 -- Solution -- Example 4.9 -- Solution -- Example 4.10 -- Solution -- You Try It -- Example 4.11 -- Solution -- You Try It -- Tensor Products of Matrices -- Example 4.12 -- Solution -- You Try It -- Exercises -- 5 THE DENSITY OPERATOR -- The Density Operator for a Pure State -- Definition: Density Operator for a Pure State -- Definition: Using the Density Operator to Find the Expectation Value -- Example 5.1 -- Solution -- You Try It -- Time Evolution of the Density Operator -- Definition: Time Evolution of the Density Operator -- The Density Operator for a Mixed State -- Key Properties of a Density Operator -- Example 5.2 -- Solution -- Expectation Values -- Probability of Obtaining a Given Measurement Result -- Example 5.3 -- Solution -- You Try It -- Example 5.4 -- Solution -- You Try It -- You Try It -- You Try It