| Acknowledgments | p. xi |
| Introduction | p. 1 |
| What is Quantum Computing? | p. 1 |
| Why Another Quantum Computing Tutorial? | p. 1 |
| Quantum Computation and Quantum Information | p. 2 |
| Computer Science | p. 3 |
| Introduction | p. 3 |
| History | p. 3 |
| Turing Machines | p. 5 |
| Binary Numbers and Formal Languages | p. 7 |
| Turing Machines in Action | p. 9 |
| The Universal Turing Machine | p. 10 |
| The Halting Problem | p. 11 |
| Circuits | p. 13 |
| Common Gates | p. 13 |
| Combinations of Gates | p. 15 |
| Relevant Properties | p. 16 |
| Universality | p. 16 |
| Computational Resources and Efficiency | p. 17 |
| Quantifying Computational Resources | p. 19 |
| Standard Complexity Classes | p. 20 |
| The Strong Church-Turing Thesis | p. 22 |
| Quantum Turing-Machines | p. 23 |
| Energy and Computation | p. 24 |
| Reversibility | p. 24 |
| Irreversibility | p. 24 |
| Landauer's Principle | p. 24 |
| Maxwell's Demon | p. 25 |
| Reversible Computation | p. 26 |
| Reversible Gates | p. 26 |
| Reversible Circuits | p. 29 |
| Mathematics for Quantum Computing | p. 31 |
| Introduction | p. 31 |
| Polynomials | p. 32 |
| Logical Symbols | p. 32 |
| Trigonometry Review | p. 33 |
| Right Angled Triangles | p. 33 |
| Converting Between Degrees and Radians | p. 33 |
| Inverses | p. 34 |
| Angles in Other Quadrants | p. 34 |
| Visualisations and Identities | p. 35 |
| Logs | p. 37 |
| Complex Numbers | p. 37 |
| Polar Coordinates and Complex Conjugates | p. 39 |
| Rationalising and Dividing | p. 43 |
| Exponential Form | p. 43 |
| Matrices | p. 45 |
| Matrix Operations | p. 46 |
| Vectors and Vector Spaces | p. 50 |
| Introduction | p. 50 |
| Column Notation | p. 53 |
| The Zero Vector | p. 54 |
| Properties of Vectors in Cn | p. 54 |
| The Dual Vector | p. 55 |
| Linear Combinations | p. 56 |
| Linear Independence | p. 57 |
| Spanning Set | p. 57 |
| Basis | p. 57 |
| Probability Theory | p. 58 |
| Probability Amplitudes | p. 59 |
| The Inner Product | p. 60 |
| Orthogonality | p. 63 |
| The Unit Vector | p. 64 |
| Bases for Cn | p. 65 |
| The Gram Schmidt Method | p. 67 |
| Linear Operators | p. 67 |
| Outer Products and Projectors | p. 68 |
| The Adjoint | p. 72 |
| Eigenvalues and Eigenvectors | p. 74 |
| Trace | p. 75 |
| Normal Operators | p. 77 |
| Unitary Operators | p. 78 |
| Hermitian and Positive Operators | p. 80 |
| Diagonalisable Matrix | p. 80 |
| The Commutator and Anti-Commutator | p. 81 |
| Polar Decomposition | p. 82 |
| Spectral Decomposition | p. 82 |
| Tensor Products | p. 83 |
| Fourier Transforms | p. 85 |
| The Fourier Series | p. 86 |
| The Discrete Fourier Transform | p. 89 |
| Quantum Mechanics | p. 93 |
| History | p. 94 |
| Classical Physics | p. 94 |
| Important Concepts | p. 95 |
| Statistical Mechanics | p. 97 |
| Important Experiments | p. 98 |
| The Photoelectric Effect | p. 100 |
| Bright Line Spectra | p. 101 |
| Proto Quantum Mechanics | p. 102 |
| The New Theory of Quantum Mechanics | p. 105 |
| Important Principles for Quantum Computing | p. 109 |
| Linear Algebra | p. 110 |
| Superposition | p. 110 |
| Dirac Notation | p. 111 |
| Representing Information | p. 112 |
| Uncertainty | p. 113 |
| Entanglement | p. 113 |
| Quantum Computing | p. 115 |
| Elements of Quantum Computing | p. 115 |
| Introduction | p. 115 |
| History | p. 115 |
| Bits and Qubits | p. 116 |
| Entangled States | p. 131 |
| Quantum Circuits | p. 133 |
| Important Properties of Quantum Circuits | p. 147 |
| Common Circuits | p. 148 |
| The Reality of Building Circuits | p. 154 |
| Building a Programmable Quantum Computer | p. 154 |
| The Four Postulates of Quantum Mechanics | p. 155 |
| Postulate One | p. 155 |
| Postulate Two | p. 156 |
| Postulate Three | p. 157 |
| Postulate Four | p. 160 |
| Information Theory | p. 163 |
| Introduction | p. 163 |
| History | p. 164 |
| Shannon's Communication Model | p. 164 |
| Channel Capacity | p. 165 |
| Classical Information Sources | p. 166 |
| Independent Information Sources | p. 166 |
| Classical Redundancy and Compression | p. 168 |
| Shannon's Noiseless Coding Theorem | p. 169 |
| Quantum Information Sources | p. 171 |
| Pure and Mixed States | p. 171 |
| Schumacher's Quantum Noiseless Coding Theorem | p. 172 |
| Noise and Error Correction | p. 179 |
| Quantum Noise | p. 181 |
| Quantum Error Correction | p. 181 |
| Bell States | p. 188 |
| Same Measurement Direction | p. 189 |
| Different Measurement Directions | p. 190 |
| Bell's Inequality | p. 191 |
| Cryptology | p. 195 |
| Classical Cryptography | p. 195 |
| Quantum Cryptography | p. 196 |
| Alternative Models of Computation | p. 200 |
| Quantum Algorithms | p. 201 |
| Introduction | p. 201 |
| Deutsch's Algorithm | p. 202 |
| The Problem Defined | p. 202 |
| The Classical Solution | p. 202 |
| The Quantum Solution | p. 203 |
| Physical Implementations | p. 207 |
| The Deutsch-Josza Algorithm | p. 207 |
| The Problem Defined | p. 207 |
| The Quantum Solution | p. 208 |
| Shor's Algorithm | p. 210 |
| The Quantum Fourier Transform | p. 210 |
| Fast Factorisation | p. 214 |
| Order Finding | p. 215 |
| Grover's Algorithm | p. 220 |
| The Travelling Salesman Problem | p. 221 |
| Quantum Searching | p. 221 |
| Using Quantum Mechanical Devices and Recent Developments | p. 225 |
| Introduction | p. 225 |
| Physical Realisation | p. 225 |
| Implementation Technologies | p. 227 |
| Quantum Computer Languages | p. 228 |
| Encryption Devices | p. 230 |
| Recent Developments | p. 230 |
| Hardware and Architecture | p. 230 |
| Cryptography | p. 231 |
| Algorithms | p. 231 |
| Bibliography | p. 233 |
| Index | p. 239 |
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