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E-grāmata: Quantum Computing For The Brain

(Univ College London, Uk), (Univ College London, Uk), (Lutheran Univ Of Brazil, Brazil), (National Research Univ Higher School Of Economics, Russia)
  • Formāts: 552 pages
  • Sērija : Between Science And Economics 3
  • Izdošanas datums: 30-May-2022
  • Izdevniecība: World Scientific Europe Ltd
  • Valoda: eng
  • ISBN-13: 9781800610637
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  • Formāts: 552 pages
  • Sērija : Between Science And Economics 3
  • Izdošanas datums: 30-May-2022
  • Izdevniecība: World Scientific Europe Ltd
  • Valoda: eng
  • ISBN-13: 9781800610637
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"Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain. Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in neuroscience applications such as neural signaling and synaptic integration. State-of-the-art methods are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, spiking neural networks, quantum teleportation, and quantum walks. Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing"--

Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain. Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in brain applications. State-of-the-art methods and models are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, and spiking neural networks, quantum teleportation, and quantum walks. Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing.

Preface v
About the Authors vii
List of Figures xix
List of Tables xxi
Chapter 1 Introduction to Quantum Neuroscience
1(26)
1.1 The Brain Is the "Killer Application" of Quantum Computing
1(3)
1.1.1 The complexity of the brain
3(1)
1.2 The Brain and Quantum Computing
4(2)
1.3 Status of Neuroscience
6(2)
1.3.1 Whole-brain simulation
7(1)
1.4 Status of Quantum Computing
8(10)
1.4.1 2n scalability
10(1)
1.4.2 Three-dimensional format
11(1)
1.4.3 Quantum advantage over classical computing
12(2)
1.4.4 Supercomputing versus quantum computing
14(1)
1.4.5 Quantum finance and AdS/Finance
14(4)
1.5 What This Book Does Not Cover
18(1)
1.6 Quantum Neuroscience and AdS/Brain
19(1)
References
20(7)
Part 1 Foundations 27(96)
Chapter 2 Neural Signaling Basics
29(20)
2.1 Scale Levels in the Brain
29(4)
2.1.1 Relative size of neural entities
31(2)
2.2 Neural Signaling Overview
33(3)
2.2.1 Electrical-to-chemical interconnects
35(1)
2.2.2 Neural signaling energy budget
36(1)
2.3 Sending Neuron (Presynaptic Terminal)
36(2)
2.4 Receiving Neuron (Postsynaptic Density)
38(2)
2.5 Synaptic (Dendritic) Spike Integration
40(5)
2.5.1 Excitatory and inhibitory postsynaptic potentials
42(1)
2.5.2 Dendritic pathologies
43(1)
2.5.3 Dendritic integration filtering
43(1)
2.5.4 Computational neuroscience and biophysical modeling
44(1)
2.6 Neural Signaling and Quantum Computing
45(1)
References
46(3)
Chapter 3 The AdS/Brain Correspondence
49(28)
3.1 The AdS/CFT Correspondence
49(3)
3.1.1 Stating the AdS/CFT correspondence
50(2)
3.2 AdS/CFT Correspondence Studies
52(2)
3.2.1 AdS/CFT hybrid approaches
52(1)
3.2.2 Duality lens
52(2)
3.3 Applied AdS/CFT
54(12)
3.3.1 AdS/QCD (quantum chromodynamics)
55(1)
3.3.2 AdS/CMT (condensed matter theory)
56(2)
3.3.3 AdS/SYK (SYK model)
58(1)
3.3.4 AdS/Chaos (thermal systems)
59(2)
3.3.5 AdS/QIT (quantum information theory)
61(1)
3.3.6 AdS/TN (tensor networks)
62(2)
3.3.7 AdS/ML (machine learning)
64(2)
3.4 AdS/DIY
66(6)
3.4.1 The AdS/CFT equations
67(5)
References
72(5)
Chapter 4 Tabletop Experiments
77(30)
4.1 Black Holes and Quantum Gravity in the Lab
77(1)
4.2 Particle Accelerator on a Chip
78(2)
4.3 Quantum Gravity in the Lab
80(9)
4.3.1 Quantum gravity
80(2)
4.3.2 Wormholes and holographic teleportation
82(1)
4.3.3 Preparing the thermofield double state
83(4)
4.3.4 Rydberg atoms and trapped ions
87(2)
4.4 Black Hole on a Chip
89(3)
4.4.1 Fast scramblers
91(1)
4.5 QSims: The SYK Model and Beyond
92(11)
4.5.1 The SYK model
92(2)
4.5.2 Tabletop platforms for quantum simulation
94(2)
4.5.3 Simulation with ultracold gases
96(3)
4.5.4 Simulation with quantum computing
99(4)
References
103(4)
Chapter 5 Neuronal Gauge Theory
107(16)
5.1 Concept of the Neuronal Gauge Theory
107(7)
5.1.1 Gauge theory
109(5)
5.2 Details of the Neuronal Gauge Theory
114(6)
5.2.1 Rebalancing global symmetry
115(4)
5.2.2 Diffeomorphism invariance
119(1)
5.2.3 Symmetry and Yang-Mills theory
120(1)
References
120(3)
Part 2 Substrate 123(76)
Chapter 6 Quantum Information Theory
125(18)
6.1 Quantum Information
125(7)
6.1.1 Entropy and quantum information
126(3)
6.1.2 Superposition, entanglement, and interference
129(3)
6.2 Quantum Toolbox
132(8)
6.2.1 Quantum teleportation
132(1)
6.2.2 Quantum error correction
133(4)
6.2.3 Out-of-time-order correlators
137(1)
6.2.4 Quantum walks and Hadamard coins
138(2)
References
140(3)
Chapter 7 Quantum Computing 101
143(18)
7.1 Quantum Algorithms and Quantum Circuits
143(1)
7.2 Qubit Encoding
144(3)
7.2.1 Quantum circuit demonstrations
145(2)
7.3 How Does Quantum Computing Work?
147(8)
7.3.1 Input, processing, output, repeat
147(2)
7.3.2 Step 1: Data encoding (embedding)
149(3)
7.3.3 Step 2: Data processing
152(2)
7.3.4 Steps 3 and 4: Results and repetition
154(1)
7.4 Advances in Quantum Computing
155(2)
7.5 Unitary Transformation
157(1)
References
158(3)
Chapter 8 Glia Neurotransmitter Synaptome
161(24)
8.1 Glial Cells
161(7)
8.1.1 Astrocyte calcium signaling
163(4)
8.1.2 Glia and neuropathology
167(1)
8.2 Neurotransmitters and Chemical Signaling
168(5)
8.2.1 Glutamate (excitatory) and GABA (inhibitory)
168(2)
8.2.2 Neurotransmitter transport
170(3)
8.3 Synaptome
173(7)
8.3.1 Genome, connectome, and synaptome
173(2)
8.3.2 Mouse synaptome: Aging pathologies
175(2)
8.3.3 Alzheimer's disease synaptome
177(3)
References
180(5)
Chapter 9 Black Hole Information Theory
185(14)
9.1 Black Holes
185(6)
9.1.1 Black holes as a model system
186(3)
9.1.2 Hologram decoding dictionaries
189(2)
9.2 Practical Quantum Communications Protocols
191(5)
9.2.1 UV-IR information compression
192(4)
References
196(3)
Part 3 Connectivity 199(100)
Chapter 10 Quantum Photonics and High-Dimensional Entanglement
201(34)
10.1 Quantum Photonics
201(3)
10.1.1 Technical benefits and qudits
201(3)
10.2 Boson Sampling
204(6)
10.2.1 Gaussian boson sampling
205(3)
10.2.2 Gaussian boson sampling/graph theory
208(2)
10.3 Space-Division Multiplexing Innovation
210(5)
10.3.1 Information multiplexing
211(3)
10.3.2 Personal brain networks
214(1)
10.4 Photonic Qubit Encoding
215(6)
10.4.1 Physics: Angular momentum
216(2)
10.4.2 Technology: Path and time-frequency bins
218(3)
10.5 High-dimensional Quantum Entanglement
221(8)
10.5.1 Theoretical development
221(3)
10.5.2 Experimental implementation
224(5)
References
229(6)
Chapter 11 Optical Machine Learning and Quantum Networks
235(24)
11.1 Quantum Optical Machine Learning
235(10)
11.1.1 Optical quantum computing
236(1)
11.1.2 Optical neural networks
237(3)
11.1.3 Quantum optical machine learning
240(5)
11.2 Global Quantum Networks
245(5)
11.2.1 End-to-end qubits
246(1)
11.2.2 Long-distance entanglement
247(3)
11.3 Global Quantum Clock Network
250(5)
11.3.1 GHZ state and optical oscillators
250(5)
11.3.2 Paper clocks
255(1)
References
255(4)
Chapter 12 Connectome and Brain Imaging
259(18)
12.1 Connectomics
259(2)
12.2 Brain Imaging
261(3)
12.2.1 Connectome parcellation
263(1)
12.3 High-Throughput Connectome Imaging
264(4)
12.3.1 Electron microscopy
264(1)
12.3.2 Light sheet microscopy
265(1)
12.3.3 Expansion light sheet microscopy
266(1)
12.3.4 X-ray microtomography
267(1)
12.4 High-Throughput Recording
268(5)
12.4.1 Light field microscopy
268(4)
12.4.2 Calcium imaging
272(1)
References
273(4)
Chapter 13 Brain Networks
277(22)
13.1 Brain Networks' Approach
277(4)
13.1.1 The brain as a communications network
278(3)
13.2 Wiring and Circuit Layout
281(2)
13.2.1 The brain is three-dimensional
281(2)
13.3 Connectivity
283(3)
13.3.1 Gray matter and white matter
283(3)
13.4 Energy Consumption
286(2)
13.4.1 Imputing traffic volume from energy consumption
287(1)
13.4.2 Bandwidth
288(1)
13.5 Signal Processing
288(3)
13.5.1 Signal conversion
288(3)
13.6 Signal-to-Noise Ratio
291(2)
13.6.1 Ion channels
291(2)
13.7 Network Rewiring: Synaptic Plasticity
293(2)
13.7.1 Neural signaling path integral
294(1)
References
295(4)
Part 4 System Evolution 299(52)
Chapter 14 Quantum Dynamics
301(16)
14.1 Dynamics of Quantum Systems
302(1)
14.2 Operator Size and Distribution Growth
303(1)
14.3 The Holographic SYK Model
304(8)
14.3.1 The Heisenberg uncertainty principle
304(3)
14.3.2 Out-of-time-order correlators
307(3)
14.3.3 Thermofield double state
310(2)
14.4 Superconductivity and Spacetime Superfluids
312(3)
14.4.1 Time crystals
312(3)
References
315(2)
Chapter 15 Neural Dynamics
317(34)
15.1 Multiscale Modeling
317(4)
15.1.1 Centrality of wavefunction modeling
318(3)
15.2 Approaches to Collective Neural Behavior
321(2)
15.2.1 Nonlinear dynamical systems
321(1)
15.2.2 Neural dynamics in large-scale models
322(1)
15.3 Neural Ensemble Models
323(7)
15.3.1 Fokker-Planck dynamics for normal distributions
324(2)
15.3.2 Beyond linear Fokker-Planck equations
326(3)
15.3.3 Neural signaling: Orbits and bifurcation
329(1)
15.4 Neural Mass Models
330(4)
15.4.1 Brain networks approach
330(1)
15.4.2 Technical aspects of neural mass methods
331(3)
15.5 Neural Field Models
334(11)
15.5.1 Statistical theory of neuron dynamics
335(2)
15.5.2 Neural field theory in practice
337(4)
15.5.3 Statistical neural field theory
341(3)
15.5.4 Quantum neural field theory
344(1)
References
345(6)
Part 5 Modeling Toolkit 351(136)
Chapter 16 Quantum Machine Learning
353(26)
16.1 Machine Learning-Physics Collaboration
353(8)
16.1.1 Quantum machine learning overview
355(3)
16.1.2 Structural similarities
358(1)
16.1.3 Problems in quantum mechanics
359(2)
16.2 Wavefunction Approximation
361(10)
16.2.1 Quantum state neural networks
361(10)
16.3 Quantum Transformer Neural Networks
371(5)
16.3.1 Transformer attention mechanism
372(4)
References
376(3)
Chapter 17 Born Machine and Pixel = Qubit
379(32)
17.1 The Born Machine
379(10)
17.1.1 Boltzmann machine versus born machine
382(1)
17.1.2 Supervised versus unsupervised learning
383(2)
17.1.3 Unsupervised generative learning
385(4)
17.2 Probabilistic Methods: Reduced Density Matrix
389(6)
17.2.1 Modeling classical data with quantum states
390(3)
17.2.2 Density matrices and density operators
393(2)
17.3 Tensor Networks: Pixel = Spin (Qubit)
395(6)
17.3.1 Decomposition of high-dimensional vectors
395(6)
17.4 Tensor Networks: Wavelet = Spin (Qubit)
401(7)
17.4.1 Wavelet transform
403(5)
References
408(3)
Chapter 18 Quantum Kernel Learning and Entanglement Design
411(22)
18.1 Quantum Kernel Methods
412(12)
18.1.1 Machine learning approaches
412(1)
18.1.2 Kernel methods
412(4)
18.1.3 Quantum kernel methods
416(2)
18.1.4 Embedded data Hilbert spaces
418(1)
18.1.5 Quantum finance
419(2)
18.1.6 Squeezed states of light
421(2)
18.1.7 RHKS and machine learning
423(1)
18.2 Entanglement as a Design Principle
424(7)
18.2.1 Entanglement and tensor networks
425(3)
18.2.2 Classical data and quantum states
428(2)
18.2.3 Entanglement entropy
430(1)
References
431(2)
Chapter 19 Brain Modeling and Machine Learning
433(36)
19.1 Brain Modeling
433(11)
19.1.1 Compartmental neuroscience models
435(6)
19.1.2 Theoretical neuroscience
441(3)
19.2 Classical Machine Learning and Neuroscience
444(8)
19.2.1 Machine learning and biomedicine
444(1)
19.2.2 Machine learning and neuroscience
445(2)
19.2.3 Machine learning and connectomics
447(3)
19.2.4 Rapprochement
450(2)
19.3 Neuromorphics and Spiking Neural Networks
452(9)
19.3.1 Neuromorphic computing
452(2)
19.3.2 Spiking neural networks
454(7)
19.4 Optical Spiking Neural Networks
461(1)
References
462(7)
Chapter 20 Conclusion: AdS/Brain Theory and Quantum Neuroscience
469(18)
20.1 Quantum Computing for the Brain
469(1)
20.2 AdS/Brain Theory
470(6)
20.2.1 Quantum neural signaling
470(5)
20.2.2 Risks and limitations
475(1)
20.3 Millennium Prize-Type Challenges
476(4)
20.3.1 NISQ device neuroscience applications
476(4)
20.4 The Future of Quantum Neuroscience
480(3)
References
483(4)
Glossary 487(28)
Index 515