Preface |
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v | |
Preface |
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vii | |
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1 | (6) |
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2 Mathematical Realization of Quantum Mechanics |
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7 | (12) |
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7 | (4) |
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11 | (2) |
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2.3 Time evolution of wave function |
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13 | (1) |
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2.4 Eigenvalue and eigenstate of Hamiltonian |
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14 | (3) |
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17 | (2) |
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3 Basic Concepts of Quantum Mechanics |
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19 | (18) |
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3.1 Wave function and probability interpretation |
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19 | (1) |
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3.2 Commutation relation and uncertainty relation |
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20 | (3) |
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3.3 Quantum states of spin 1/2 particles |
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23 | (5) |
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28 | (1) |
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3.5 Angular momentum, spin and rotation |
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29 | (6) |
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35 | (2) |
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4 EPR Pair and Measurement |
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37 | (28) |
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37 | (2) |
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4.2 Transmission of quantum states |
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39 | (2) |
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4.3 Einstein's locality principle in quantum mechanics |
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41 | (5) |
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4.4 Measurement of two correlated particles and hidden variable theorem |
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46 | (8) |
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46 | (5) |
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4.4.2 Classical correlation vs. quantal correlation: a case of nuclear fission |
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51 | (3) |
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4.5 EPR experiment by photon pairs |
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54 | (5) |
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4.6 Four-photon GHZ states |
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59 | (4) |
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63 | (2) |
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65 | (24) |
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65 | (5) |
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70 | (1) |
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5.3 Possibility and complexity of computation |
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71 | (7) |
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5.3.1 Arithmetic operations |
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72 | (1) |
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5.3.2 Factorization and decision of prime numbers |
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73 | (1) |
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5.3.3 Combination problem |
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74 | (4) |
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5.3.4 Computational complexity and amount of computation |
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78 | (1) |
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78 | (2) |
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80 | (3) |
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5.6 Sequential circuit and memory |
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83 | (5) |
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88 | (1) |
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89 | (18) |
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90 | (5) |
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6.2 Controlled-operation gates |
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95 | (6) |
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6.3 Quantum Turing machine |
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101 | (1) |
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6.4 Quantum Fourier transformation (3 bit case) |
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102 | (3) |
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105 | (2) |
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7 Theory of Information and Communication |
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107 | (14) |
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107 | (6) |
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7.1.1 Amount of information |
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107 | (1) |
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108 | (2) |
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110 | (3) |
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7.1.4 Von Neumann entropy |
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113 | (1) |
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7.2 Transmission error in communication |
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113 | (6) |
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7.2.1 Errors and channel capacity |
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113 | (3) |
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116 | (3) |
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119 | (2) |
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121 | (24) |
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8.1 Quantum bit and quantum register |
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122 | (3) |
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8.2 Deutsch-Jozsa algorithm |
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125 | (2) |
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8.3 Shor's factorization algorithm |
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127 | (3) |
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8.4 Quantum Fourier transformation with n bits |
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130 | (3) |
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8.5 Quantum phase estimation and order finding algorithm |
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133 | (8) |
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8.6 Calculation of modular exponentials |
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141 | (2) |
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143 | (2) |
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145 | (24) |
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9.1 Secret key cryptography |
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145 | (2) |
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9.2 "One-time pad" cryptography |
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147 | (1) |
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9.3 Public key cryptography |
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148 | (5) |
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9.4 Quantum key distribution |
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153 | (14) |
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9.4.1 Non-cloning theorem |
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154 | (1) |
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155 | (6) |
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161 | (2) |
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163 | (4) |
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167 | (2) |
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10 Quantum Search Algorithm |
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169 | (12) |
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170 | (1) |
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170 | (10) |
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180 | (1) |
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11 Physical Devices of Quantum Computers |
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181 | (36) |
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11.1 Nuclear magnetic resonance (NMR) computers |
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182 | (14) |
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11.1.1 Principles of NMR computers |
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182 | (2) |
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11.1.2 NMR and spin rotations |
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184 | (4) |
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11.1.3 Statistical treatment |
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188 | (3) |
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11.1.4 Experiment of quantum factorization |
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191 | (5) |
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196 | (11) |
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196 | (1) |
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196 | (7) |
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203 | (1) |
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11.2.4 Preparation of the initial states |
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204 | (1) |
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205 | (1) |
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11.2.6 Example of quantum gate |
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206 | (1) |
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11.3 Quantum dot computer |
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207 | (8) |
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208 | (7) |
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215 | (2) |
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217 | (32) |
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12.1 What is the quantum annealing? |
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217 | (5) |
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12.2 Formulation of quantum annealing |
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222 | (8) |
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12.2.1 A case in which the Hamiltonians H0 and H1 do not depend on the time |
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222 | (3) |
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12.2.2 The wave function of the time-dependent Hamiltonian |
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225 | (2) |
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12.2.3 Adiabatic approximation |
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227 | (3) |
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12.3 Quantum search problems |
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230 | (2) |
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232 | (10) |
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12.4.1 What is the Ising model? |
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232 | (2) |
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12.4.2 Application to quantum computers |
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234 | (1) |
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12.4.3 Optimization by the quantum annealing |
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235 | (1) |
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12.4.4 Application to the traveling salesman problem (TSP) |
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236 | (6) |
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12.5 Construction of the quantum annealing computer |
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242 | (5) |
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12.5.1 Parameter control in the quantum annealing |
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243 | (1) |
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12.5.2 Hardware structure |
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244 | (3) |
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247 | (2) |
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Appendix A Basic Theory of Numbers |
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249 | (18) |
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249 | (4) |
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A.2 Euler's theorem (Fermat's little theorem) |
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253 | (3) |
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256 | (1) |
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A.4 Diophantus equation (Indeterminate equation) |
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257 | (2) |
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A.5 Chinese remainder theorem |
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259 | (3) |
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262 | (5) |
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Appendix B Solutions of Problems |
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267 | (24) |
Bibliography |
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291 | (2) |
Index |
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293 | |