Quantum Neural Computation

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 QNNs1.7 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 Memory2.5.3 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