Quantum neural computation

목차 (Table of Contents)

• 자료제공 :
• 1 Introduction
• 1.1 Neurodynamics
• 1.2 Quantum Computation
• 1.3 Discrete Quantum Computers
• 1.4 Topological Quantum Computers
• 1.5 Computation at the Edge of Chaos and Quantum Neural Networks
• 1.6 Adaptive Path Integral: An 1-Dimensional QNN
• 1.6.1 Computational Partition Function
• 1.6.2 From Thermodynamics to Quantum Field Theory
• 1.6.3 1-Dimensional QNNs
• 1.7 Brain Topology vs. Small-World Topology
• 1.8 Quantum Brain and Mind
• 1.8.1 Connectionism, Control Theory and Brain Theory
• 1.8.2 Neocortical Biophysics
• 1.8.3 Quantum Neurodynamics
• 1.8.4 Bi-Stable Perception and Consciousness 1.9 Notational Conventions 2 Brain and Classical Neural Networks
• 2.1 Human Brain
• 2.1.1 Basics of Brain Physiology
• 2.1.2 Modern 3D Brain Imaging
• 2.2 Biological versus Artificial Neural Networks
• 2.2.1 Common Discrete ANNs
• 2.2.2 Common Continuous ANNs
• 2.3 Synchronization in Neurodynamics
• 2.3.1 Phase Synchronization in Coupled Chaotic Oscillators
• 2.3.2 Oscillatory Phase Neurodynamics
• 2.3.3 Kuramoto Synchronization Model
• 2.3.4 Lyapunov Chaotic Synchronization
• 2.4 Spike Neural Networks and Wavelet Resonance
• 2.4.1 Ensemble Neuron Model
• 2.4.2 Wavelet Neurodynamics
• 2.4.3 Wavelets of Epileptic Spikes
• 2.5 Human Motor Control and Learning
• 2.5.1 Motor Control
• 2.5.2 Human Memory
• 2.5.3 Human Learning
• 2.5.4 Spinal Musculo-Skeletal Control
• 2.5.5 Cerebellum and Muscular Synergy 3 Quantum Theory Basics
• 3.1 Basics of Non-Relativistic Quantum Mechanics
• 3.1.1 Soft Introduction to Quantum Mechanics
• 3.1.2 Quantum States and Operators
• 3.1.3 The Tree Standard Quantum Pictures
• 3.1.4 Dirac's Probability Amplitude and Perturbation
• 3.1.5 State-Space for n Non-Relativistic Quantum Particles
• 3.2 Introduction to Quantum Fields
• 3.2.1 Amplitude, Relativistic Invariance and Causality
• 3.2.2 Gauge Theories
• 3.2.3 Free andInteracting Field Theories
• 3.2.4 Dirac's Quantum Electrodynamics (QED)
• 3.2.5 Abelian Higgs Model
• 3.2.6 Topological Quantum Computation
• 3.3 The Feynman Path Integral
• 3.3.1 The Action-Amplitude Formalism
• 3.3.2 Correlation Functions and Generating Functional
• 3.3.3 Quantization of the Electromagnetic Field
• 3.3.4 Wavelet-Based QFT
• 3.4 The Path-Integral TQFT
• 3.4.1 Schwarz-Type and Witten-Type Theories
• 3.4.2 Hodge Decomposition Theorem
• 3.4.3 Hodge Decomposition and Chern-Simons Theory
• 3.5 Non-Abelian Gauge Theories
• 3.5.1 Introduction to Non-Abelian Theories
• 3.5.2 Yang-Mills Theory
• 3.5.3 Quantization of Yang-Mills theory
• 3.5.4 Basics of Conformal Field Theory (CFT) 4 Spatio-Temporal Chaos, Solitons and NLS
• 4.1 Reaction-Diffusion Processes and Ricci Flow
• 4.1.1 Bio-Reaction-Diffusion Systems
• 4.1.2 Reactive Neurodynamics
• 4.1.3 Dissipative Evolution Under the Ricci Flow
• 4.2 Turbulence and Chaos in PDEs
• 4.3 Quantum Chaos and Its Control
• 4.3.1 Quantum Chaos vs. Classical Chaos
• 4.3.2 Optimal Control of Quantum Chaos
• 4.4 Solitions
• 4.4.1 Short History of Solitons
• 4.4.2 Lie-Poisson Bracket
• 4.4.3 Solitons and Muscular Contraction
• 4.5 Dispersive Wave Equations and Stability of Solitons
• 4.5.1 KdV Solitons
• 4.5.2 The Inverse Scattering Approach
• 4.6 Nonlinear Schr odinger Equation (NLS)
• 4.6.1 Cubic NLS
• 4.6.2 Nonlinear Wave and Schr odinger Equations
• 4.6.3 Physical NLS-Derivation
• 4.6.4 A Compact Attractor for High-Dimensional NLS
• 4.6.5 Finite-Difference Scheme for NLS
• 4.6.6 Method of Lines for NLS 5 Quantum Brain and Cognition
• 5.1 Biochemistry of Microtubules
• 5.2 Kink Soliton Model of MT-Dynamics
• 5.3 Macro- and Microscopic Neurodynamical Self-Similarity
• 5.3.1 Open Liouville Equation
• 5.4 Dissipative Quantum Brain Model
• 5.5 QED Brain Model
• 5.6