Acknowledgments |
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ix | (2) |
Preface |
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xi | (8) |
CD-ROM Contents |
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xix | |
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Chapter 1. Computer Technology Meets Quantum Reality |
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1 | (16) |
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1.1 Computers as Physical Systems |
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2 | (5) |
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7 | (4) |
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1.3 Economic and Environmental Issues |
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11 | (3) |
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1.4 Social and Political Pressures |
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14 | (1) |
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14 | (3) |
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Chapter 2. The Capabilities of Computing Machinery |
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17 | (28) |
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2.1 How the Turing Machine Came About |
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18 | (3) |
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2.2 Deterministic Turing Machines |
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21 | (1) |
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2.3 Probabilistic Turing Machines |
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22 | (2) |
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2.4 Quantum Turing Machines |
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24 | (2) |
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26 | (1) |
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27 | (4) |
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2.7 Proving Versus Providing Proof |
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31 | (2) |
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33 | (12) |
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Chapter 3. Quantum Mechanics and Computers |
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45 | (30) |
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3.1 Physics and Computers |
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45 | (4) |
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3.2 Taking the Quantum Leap |
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49 | (1) |
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3.3 Quantization: From Bits to Qubits |
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50 | (1) |
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3.4 State Vectors and Dirac Notation |
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50 | (2) |
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52 | (2) |
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3.6 Probability Interpretation |
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54 | (1) |
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55 | (1) |
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55 | (2) |
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3.9 State of a Quantum Memory Register |
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57 | (2) |
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59 | (2) |
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3.11 Schrodinger's Equation |
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61 | (1) |
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3.12 What Does the Hamiltonian Mean Physically and Computationally? |
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62 | (1) |
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63 | (1) |
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63 | (6) |
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3.15 Observables as Hermitian Operators |
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69 | (1) |
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3.16 Measurement: Extracting Answers From Quantum Computers |
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70 | (1) |
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3.17 Benioff's Quantum Computer |
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71 | (1) |
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3.18 Feynman's Quantum Computer |
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72 | (1) |
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3.19 Deutsch's Quantum Computer |
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73 | (2) |
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Chapter 4. Simulating a Simple Quantum Computer |
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75 | (30) |
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4.1 What Computation Are We Going to Simulate? |
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76 | (1) |
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4.2 Representing a Computation as a Circuit |
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77 | (4) |
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4.3 Determining the Size of the Memory Register |
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81 | (3) |
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4.4 Computing the Hamiltonian Operator |
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84 | (3) |
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4.5 Computing the Unitary Evolution Operator |
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87 | (1) |
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4.6 Running the Quantum Computer for a Fixed Length of Time |
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88 | (5) |
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4.7 Running the Quantum Computer Until the Computation Is Done |
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93 | (2) |
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4.8 Extracting the Answer |
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95 | (1) |
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4.9 Putting It All Together |
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96 | (9) |
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Chapter 5. The Effects of Imperfections |
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105 | (8) |
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5.1 Imperfections in Preparation |
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106 | (2) |
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5.2 Imperfections in Evolution |
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108 | (3) |
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5.3 Imperfections in Measurement |
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111 | (2) |
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Chapter 6. Breaking Unbreakable Codes |
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113 | (34) |
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6.1 Codes and Code-Breakers |
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114 | (1) |
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115 | (3) |
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118 | (1) |
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119 | (3) |
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6.5 The RSA Public Key Cryptography Scheme |
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122 | (5) |
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6.6 Code-Breaking on a Classical Computer |
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127 | (3) |
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6.7 Code-Breaking on a Quantum Computer |
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130 | (1) |
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6.8 A Trick From Number Theory |
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131 | (2) |
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6.9 Shor's Algorithm for Factoring on a Quantum Computer |
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133 | (4) |
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6.10 Simulation of Shor's Algorithm |
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137 | (5) |
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6.11 Shor's Algorithm Can Sometimes Fail |
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142 | (5) |
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Chapter 7. True Randomness |
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147 | (16) |
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7.1 The Concept of Randomness |
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148 | (1) |
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7.2 Does Randomness Exist in Nature? |
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149 | (2) |
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7.3 Uses of Random Numbers |
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151 | (4) |
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7.4 Randomness and Classical Computers |
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155 | (3) |
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7.5 The Plague of Correlations |
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158 | (1) |
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7.6 Randomness and Quantum Computers |
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159 | (1) |
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7.7 Simulation of a Quantum Computer Generating a True Random Number |
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160 | (3) |
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Chapter 8. Quantum Cryptography |
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163 | (20) |
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8.1 Heisenberg's Uncertainty Principle |
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164 | (3) |
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167 | (2) |
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8.3 Using Polarized Photons to Encode a Message |
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169 | (1) |
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8.4 Measuring the Polarization of a Photon |
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169 | (1) |
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8.5 Uncertainty Principle for Polarized Photons |
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170 | (2) |
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8.6 Quantum Cryptography Using Polarized Photons |
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172 | (1) |
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8.7 Simulation of Quantum Cryptography in the Absence of Eavesdropping |
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172 | (3) |
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8.8 Simulation of Quantum Cryptography in the Presence of Eavesdropping |
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175 | (2) |
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8.9 The Working Prototype |
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177 | (1) |
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8.10 Other Approaches to Quantum Cryptography |
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178 | (5) |
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Chapter 9. Quantum Teleportation |
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183 | (30) |
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9.1 What Is Teleportation? |
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183 | (3) |
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9.2 Physics Behind Teleportation |
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186 | (1) |
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9.3 Local Versus Nonlocal Interactions |
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186 | (2) |
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188 | (2) |
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9.5 Spooky Action at a Distance |
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190 | (1) |
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191 | (5) |
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9.7 How to Teleport One Qubit |
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196 | (4) |
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9.8 Teleportation Circuit for a Quantum Computer |
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200 | (5) |
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9.9 Simulation of Quantum Teleportation |
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205 | (2) |
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9.10 Experimental Status of Quantum Teleportation |
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207 | (1) |
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9.11 Other Uses of Entangled Qubits |
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208 | (5) |
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Chapter 10. Quantum Error Correction |
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213 | (28) |
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10.1 Decoherence and Dissipation |
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214 | (4) |
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218 | (3) |
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10.3 Classical Versus Quantum Error Correction |
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221 | (1) |
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10.4 Elementary Error Correction Using Redundancy |
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222 | (2) |
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10.5 The Problem With a Quantum Version of Majority Voting |
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224 | (1) |
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10.6 Error Correction via Symmetrization |
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225 | (3) |
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10.7 Quantum Error-Correcting Codes |
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228 | (1) |
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10.8 Quantum Circuit for Correcting a Phase Shift and/or Bit Flip Error |
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229 | (7) |
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10.9 How Many Errors Can Be Tolerated? |
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236 | (2) |
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10.10 Computing Forever Without Error |
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238 | (3) |
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Chapter 11. How to Make a Quantum Computer |
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241 | (26) |
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11.1 Heteropolymer-Based Quantum Computers |
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241 | (10) |
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11.2 Ion Trap-Based Quantum Computers |
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251 | (5) |
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11.3 Cavity QED-Based Quantum Computers |
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256 | (2) |
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11.4 NMR-Based Quantum Computers |
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258 | (9) |
Appendix. Using the Code Supplements |
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267 | (22) |
Bibliography |
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289 | (14) |
Index |
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303 | |