Preface |
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v | |
About the Authors |
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vii | |
List of Figures |
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xix | |
List of Tables |
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xxi | |
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Chapter 1 Introduction to Quantum Neuroscience |
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1 | (26) |
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1.1 The Brain Is the "Killer Application" of Quantum Computing |
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1 | (3) |
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1.1.1 The complexity of the brain |
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3 | (1) |
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1.2 The Brain and Quantum Computing |
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4 | (2) |
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1.3 Status of Neuroscience |
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6 | (2) |
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1.3.1 Whole-brain simulation |
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7 | (1) |
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1.4 Status of Quantum Computing |
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8 | (10) |
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10 | (1) |
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1.4.2 Three-dimensional format |
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11 | (1) |
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1.4.3 Quantum advantage over classical computing |
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12 | (2) |
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1.4.4 Supercomputing versus quantum computing |
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14 | (1) |
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1.4.5 Quantum finance and AdS/Finance |
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14 | (4) |
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1.5 What This Book Does Not Cover |
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18 | (1) |
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1.6 Quantum Neuroscience and AdS/Brain |
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19 | (1) |
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20 | (7) |
Part 1 Foundations |
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27 | (96) |
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Chapter 2 Neural Signaling Basics |
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29 | (20) |
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2.1 Scale Levels in the Brain |
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29 | (4) |
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2.1.1 Relative size of neural entities |
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31 | (2) |
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2.2 Neural Signaling Overview |
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33 | (3) |
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2.2.1 Electrical-to-chemical interconnects |
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35 | (1) |
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2.2.2 Neural signaling energy budget |
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36 | (1) |
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2.3 Sending Neuron (Presynaptic Terminal) |
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36 | (2) |
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2.4 Receiving Neuron (Postsynaptic Density) |
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38 | (2) |
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2.5 Synaptic (Dendritic) Spike Integration |
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40 | (5) |
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2.5.1 Excitatory and inhibitory postsynaptic potentials |
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42 | (1) |
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2.5.2 Dendritic pathologies |
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43 | (1) |
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2.5.3 Dendritic integration filtering |
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43 | (1) |
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2.5.4 Computational neuroscience and biophysical modeling |
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44 | (1) |
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2.6 Neural Signaling and Quantum Computing |
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45 | (1) |
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46 | (3) |
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Chapter 3 The AdS/Brain Correspondence |
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49 | (28) |
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3.1 The AdS/CFT Correspondence |
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49 | (3) |
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3.1.1 Stating the AdS/CFT correspondence |
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50 | (2) |
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3.2 AdS/CFT Correspondence Studies |
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52 | (2) |
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3.2.1 AdS/CFT hybrid approaches |
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52 | (1) |
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52 | (2) |
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54 | (12) |
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3.3.1 AdS/QCD (quantum chromodynamics) |
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55 | (1) |
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3.3.2 AdS/CMT (condensed matter theory) |
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56 | (2) |
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3.3.3 AdS/SYK (SYK model) |
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58 | (1) |
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3.3.4 AdS/Chaos (thermal systems) |
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59 | (2) |
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3.3.5 AdS/QIT (quantum information theory) |
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61 | (1) |
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3.3.6 AdS/TN (tensor networks) |
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62 | (2) |
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3.3.7 AdS/ML (machine learning) |
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64 | (2) |
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66 | (6) |
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3.4.1 The AdS/CFT equations |
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67 | (5) |
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72 | (5) |
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Chapter 4 Tabletop Experiments |
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77 | (30) |
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4.1 Black Holes and Quantum Gravity in the Lab |
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77 | (1) |
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4.2 Particle Accelerator on a Chip |
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78 | (2) |
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4.3 Quantum Gravity in the Lab |
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80 | (9) |
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80 | (2) |
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4.3.2 Wormholes and holographic teleportation |
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82 | (1) |
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4.3.3 Preparing the thermofield double state |
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83 | (4) |
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4.3.4 Rydberg atoms and trapped ions |
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87 | (2) |
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89 | (3) |
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91 | (1) |
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4.5 QSims: The SYK Model and Beyond |
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92 | (11) |
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92 | (2) |
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4.5.2 Tabletop platforms for quantum simulation |
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94 | (2) |
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4.5.3 Simulation with ultracold gases |
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96 | (3) |
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4.5.4 Simulation with quantum computing |
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99 | (4) |
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103 | (4) |
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Chapter 5 Neuronal Gauge Theory |
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107 | (16) |
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5.1 Concept of the Neuronal Gauge Theory |
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107 | (7) |
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109 | (5) |
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5.2 Details of the Neuronal Gauge Theory |
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114 | (6) |
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5.2.1 Rebalancing global symmetry |
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115 | (4) |
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5.2.2 Diffeomorphism invariance |
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119 | (1) |
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5.2.3 Symmetry and Yang-Mills theory |
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120 | (1) |
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120 | (3) |
Part 2 Substrate |
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123 | (76) |
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Chapter 6 Quantum Information Theory |
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125 | (18) |
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125 | (7) |
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6.1.1 Entropy and quantum information |
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126 | (3) |
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6.1.2 Superposition, entanglement, and interference |
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129 | (3) |
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132 | (8) |
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6.2.1 Quantum teleportation |
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132 | (1) |
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6.2.2 Quantum error correction |
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133 | (4) |
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6.2.3 Out-of-time-order correlators |
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137 | (1) |
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6.2.4 Quantum walks and Hadamard coins |
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138 | (2) |
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140 | (3) |
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Chapter 7 Quantum Computing 101 |
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143 | (18) |
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7.1 Quantum Algorithms and Quantum Circuits |
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143 | (1) |
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144 | (3) |
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7.2.1 Quantum circuit demonstrations |
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145 | (2) |
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7.3 How Does Quantum Computing Work? |
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147 | (8) |
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7.3.1 Input, processing, output, repeat |
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147 | (2) |
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7.3.2 Step 1: Data encoding (embedding) |
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149 | (3) |
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7.3.3 Step 2: Data processing |
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152 | (2) |
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7.3.4 Steps 3 and 4: Results and repetition |
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154 | (1) |
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7.4 Advances in Quantum Computing |
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155 | (2) |
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7.5 Unitary Transformation |
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157 | (1) |
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158 | (3) |
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Chapter 8 Glia Neurotransmitter Synaptome |
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161 | (24) |
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161 | (7) |
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8.1.1 Astrocyte calcium signaling |
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163 | (4) |
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8.1.2 Glia and neuropathology |
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167 | (1) |
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8.2 Neurotransmitters and Chemical Signaling |
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168 | (5) |
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8.2.1 Glutamate (excitatory) and GABA (inhibitory) |
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168 | (2) |
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8.2.2 Neurotransmitter transport |
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170 | (3) |
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173 | (7) |
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8.3.1 Genome, connectome, and synaptome |
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173 | (2) |
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8.3.2 Mouse synaptome: Aging pathologies |
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175 | (2) |
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8.3.3 Alzheimer's disease synaptome |
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177 | (3) |
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180 | (5) |
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Chapter 9 Black Hole Information Theory |
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185 | (14) |
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185 | (6) |
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9.1.1 Black holes as a model system |
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186 | (3) |
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9.1.2 Hologram decoding dictionaries |
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189 | (2) |
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9.2 Practical Quantum Communications Protocols |
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191 | (5) |
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9.2.1 UV-IR information compression |
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192 | (4) |
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196 | (3) |
Part 3 Connectivity |
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199 | (100) |
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Chapter 10 Quantum Photonics and High-Dimensional Entanglement |
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201 | (34) |
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201 | (3) |
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10.1.1 Technical benefits and qudits |
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201 | (3) |
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204 | (6) |
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10.2.1 Gaussian boson sampling |
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205 | (3) |
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10.2.2 Gaussian boson sampling/graph theory |
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208 | (2) |
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10.3 Space-Division Multiplexing Innovation |
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210 | (5) |
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10.3.1 Information multiplexing |
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211 | (3) |
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10.3.2 Personal brain networks |
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214 | (1) |
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10.4 Photonic Qubit Encoding |
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215 | (6) |
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10.4.1 Physics: Angular momentum |
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216 | (2) |
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10.4.2 Technology: Path and time-frequency bins |
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218 | (3) |
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10.5 High-dimensional Quantum Entanglement |
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221 | (8) |
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10.5.1 Theoretical development |
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221 | (3) |
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10.5.2 Experimental implementation |
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224 | (5) |
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229 | (6) |
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Chapter 11 Optical Machine Learning and Quantum Networks |
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235 | (24) |
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11.1 Quantum Optical Machine Learning |
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235 | (10) |
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11.1.1 Optical quantum computing |
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236 | (1) |
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11.1.2 Optical neural networks |
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237 | (3) |
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11.1.3 Quantum optical machine learning |
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240 | (5) |
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11.2 Global Quantum Networks |
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245 | (5) |
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246 | (1) |
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11.2.2 Long-distance entanglement |
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247 | (3) |
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11.3 Global Quantum Clock Network |
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250 | (5) |
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11.3.1 GHZ state and optical oscillators |
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250 | (5) |
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255 | (1) |
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255 | (4) |
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Chapter 12 Connectome and Brain Imaging |
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259 | (18) |
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259 | (2) |
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261 | (3) |
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12.2.1 Connectome parcellation |
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263 | (1) |
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12.3 High-Throughput Connectome Imaging |
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264 | (4) |
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12.3.1 Electron microscopy |
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264 | (1) |
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12.3.2 Light sheet microscopy |
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265 | (1) |
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12.3.3 Expansion light sheet microscopy |
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266 | (1) |
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12.3.4 X-ray microtomography |
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267 | (1) |
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12.4 High-Throughput Recording |
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268 | (5) |
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12.4.1 Light field microscopy |
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268 | (4) |
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272 | (1) |
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273 | (4) |
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Chapter 13 Brain Networks |
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277 | (22) |
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13.1 Brain Networks' Approach |
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277 | (4) |
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13.1.1 The brain as a communications network |
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278 | (3) |
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13.2 Wiring and Circuit Layout |
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281 | (2) |
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13.2.1 The brain is three-dimensional |
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281 | (2) |
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283 | (3) |
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13.3.1 Gray matter and white matter |
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283 | (3) |
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286 | (2) |
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13.4.1 Imputing traffic volume from energy consumption |
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287 | (1) |
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288 | (1) |
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288 | (3) |
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288 | (3) |
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13.6 Signal-to-Noise Ratio |
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291 | (2) |
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291 | (2) |
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13.7 Network Rewiring: Synaptic Plasticity |
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293 | (2) |
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13.7.1 Neural signaling path integral |
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294 | (1) |
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295 | (4) |
Part 4 System Evolution |
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299 | (52) |
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Chapter 14 Quantum Dynamics |
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301 | (16) |
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14.1 Dynamics of Quantum Systems |
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302 | (1) |
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14.2 Operator Size and Distribution Growth |
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303 | (1) |
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14.3 The Holographic SYK Model |
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304 | (8) |
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14.3.1 The Heisenberg uncertainty principle |
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304 | (3) |
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14.3.2 Out-of-time-order correlators |
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307 | (3) |
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14.3.3 Thermofield double state |
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310 | (2) |
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14.4 Superconductivity and Spacetime Superfluids |
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312 | (3) |
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312 | (3) |
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315 | (2) |
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Chapter 15 Neural Dynamics |
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317 | (34) |
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317 | (4) |
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15.1.1 Centrality of wavefunction modeling |
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318 | (3) |
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15.2 Approaches to Collective Neural Behavior |
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321 | (2) |
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15.2.1 Nonlinear dynamical systems |
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321 | (1) |
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15.2.2 Neural dynamics in large-scale models |
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322 | (1) |
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15.3 Neural Ensemble Models |
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323 | (7) |
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15.3.1 Fokker-Planck dynamics for normal distributions |
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324 | (2) |
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15.3.2 Beyond linear Fokker-Planck equations |
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326 | (3) |
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15.3.3 Neural signaling: Orbits and bifurcation |
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329 | (1) |
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330 | (4) |
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15.4.1 Brain networks approach |
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330 | (1) |
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15.4.2 Technical aspects of neural mass methods |
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331 | (3) |
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334 | (11) |
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15.5.1 Statistical theory of neuron dynamics |
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335 | (2) |
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15.5.2 Neural field theory in practice |
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337 | (4) |
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15.5.3 Statistical neural field theory |
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341 | (3) |
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15.5.4 Quantum neural field theory |
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344 | (1) |
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345 | (6) |
Part 5 Modeling Toolkit |
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351 | (136) |
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Chapter 16 Quantum Machine Learning |
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353 | (26) |
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16.1 Machine Learning-Physics Collaboration |
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353 | (8) |
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16.1.1 Quantum machine learning overview |
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355 | (3) |
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16.1.2 Structural similarities |
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358 | (1) |
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16.1.3 Problems in quantum mechanics |
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359 | (2) |
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16.2 Wavefunction Approximation |
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361 | (10) |
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16.2.1 Quantum state neural networks |
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361 | (10) |
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16.3 Quantum Transformer Neural Networks |
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371 | (5) |
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16.3.1 Transformer attention mechanism |
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372 | (4) |
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376 | (3) |
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Chapter 17 Born Machine and Pixel = Qubit |
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379 | (32) |
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379 | (10) |
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17.1.1 Boltzmann machine versus born machine |
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382 | (1) |
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17.1.2 Supervised versus unsupervised learning |
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383 | (2) |
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17.1.3 Unsupervised generative learning |
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385 | (4) |
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17.2 Probabilistic Methods: Reduced Density Matrix |
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389 | (6) |
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17.2.1 Modeling classical data with quantum states |
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390 | (3) |
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17.2.2 Density matrices and density operators |
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393 | (2) |
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17.3 Tensor Networks: Pixel = Spin (Qubit) |
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395 | (6) |
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17.3.1 Decomposition of high-dimensional vectors |
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395 | (6) |
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17.4 Tensor Networks: Wavelet = Spin (Qubit) |
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401 | (7) |
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403 | (5) |
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408 | (3) |
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Chapter 18 Quantum Kernel Learning and Entanglement Design |
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411 | (22) |
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18.1 Quantum Kernel Methods |
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412 | (12) |
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18.1.1 Machine learning approaches |
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412 | (1) |
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412 | (4) |
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18.1.3 Quantum kernel methods |
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416 | (2) |
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18.1.4 Embedded data Hilbert spaces |
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418 | (1) |
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419 | (2) |
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18.1.6 Squeezed states of light |
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421 | (2) |
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18.1.7 RHKS and machine learning |
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423 | (1) |
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18.2 Entanglement as a Design Principle |
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424 | (7) |
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18.2.1 Entanglement and tensor networks |
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425 | (3) |
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18.2.2 Classical data and quantum states |
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428 | (2) |
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18.2.3 Entanglement entropy |
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430 | (1) |
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431 | (2) |
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Chapter 19 Brain Modeling and Machine Learning |
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433 | (36) |
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433 | (11) |
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19.1.1 Compartmental neuroscience models |
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435 | (6) |
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19.1.2 Theoretical neuroscience |
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441 | (3) |
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19.2 Classical Machine Learning and Neuroscience |
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444 | (8) |
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19.2.1 Machine learning and biomedicine |
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444 | (1) |
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19.2.2 Machine learning and neuroscience |
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445 | (2) |
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19.2.3 Machine learning and connectomics |
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447 | (3) |
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450 | (2) |
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19.3 Neuromorphics and Spiking Neural Networks |
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452 | (9) |
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19.3.1 Neuromorphic computing |
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452 | (2) |
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19.3.2 Spiking neural networks |
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454 | (7) |
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19.4 Optical Spiking Neural Networks |
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461 | (1) |
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462 | (7) |
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Chapter 20 Conclusion: AdS/Brain Theory and Quantum Neuroscience |
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469 | (18) |
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20.1 Quantum Computing for the Brain |
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469 | (1) |
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470 | (6) |
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20.2.1 Quantum neural signaling |
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470 | (5) |
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20.2.2 Risks and limitations |
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475 | (1) |
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20.3 Millennium Prize-Type Challenges |
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476 | (4) |
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20.3.1 NISQ device neuroscience applications |
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476 | (4) |
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20.4 The Future of Quantum Neuroscience |
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480 | (3) |
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483 | (4) |
Glossary |
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487 | (28) |
Index |
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515 | |