Quantum Neural Computation

937 Pages·2010·11.476 MB·English

by  Vladimir G. Ivancevic, Tijana T. Ivancevic (auth.)

Quantum Neural Computation
International Series on
INTELLIGENT SYSTEMS, CONTROL, AND AUTOMATION:
SCIENCE AND ENGINEERING
VOLUME 40
Editor:
Professor S.G. Tzafestas, National Technical University of Athens, Greece
Editorial Advisory Board
Professor P. Antsaklis, University of Notre Dame, IN, USA
Professor P. Borne, Ecole Centrale de Lille, France
Professor D.G. Caldwell, University of Salford, UK
Professor C.S. Chen, University of Akron, Ohio, USA
Professor T. Fukuda, Nagoya University, Japan
Professor S. Monaco, University La Sapienza, Rome, Italy
Professor G. Schmidt, Technical University of Munich, Germany
Professor S.G. Tzafestas, National Technical University of Athens, Greece
Professor F. Harashima, University of Tokyo, Japan
Professor N.K. Sinha, McMaster University, Hamilton, Ontario, Canada
Professor D. Tabak, George Mason University, Fairfax, Virginia, USA
Professor K. Valavanis, University of Southern Louisiana, Lafayette, USA
For other titles published in this series, go to
www.springer.com/series/6259
Vladimir G. Ivancevic (cid:2) Tijana T. Ivancevic
Quantum Neural
Computation
Dr. Vladimir G. Ivancevic Dr. Tijana T. Ivancevic
Department of Defence School of Electrical &
Defence Science & Information Engineering
Technology Organisation University of South Australia
(DSTO) Mawson Lakes Campus
75 Labs. Adelaide SA 5095
Edinburgh SA 5111 Australia
Australia [e-mail]
[e-mail]
ISBN 978-90-481-3349-9 e-ISBN 978-90-481-3350-5
DOI 10.1007/978-90-481-3350-5
Springer Dordrecht Heidelberg London New York
LibraryofCongressControlNumber:2009939613
(cid:2)cSpringerScience+BusinessMediaB.V.2010
No part of this work may be reproduced, stored in a retrieval system, or transmitted in
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Printedonacid-freepaper
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Dedicated to Nick-Nitya, Atma and Kali
Preface
Quantum Neural Computation is a graduate-level monographic textbook. It
presentsacomprehensiveintroduction,bothnon-technicalandtechnical,into
modern quantum neural computation. Classical computing systems perform
classical computations (i.e., Boolean operations, such as AND, OR, NOT
gates)usingdevicesthatcanbedescribedclassically(e.g.,MOSFETs).Onthe
otherhand,quantumcomputingsystemsperformclassicalcomputationsusing
quantum devices (quantum dots), that is devices that can be described only
using quantum mechanics. Anyinformation transfer between such computing
systems involves a state measurement. This book describes this information
transfer at the edge of classical and quantum chaos and turbulence, where
mysteriousquantum-mechanicallinearitymeetsevenmoremysteriousbrain’s
nonlinear complexity, in order to perform a super-high-speed and error-free
computations. This monograph describes a crossroad between quantum field
theory, brain science and computational intelligence.
Quantum Neural Computation has six Chapters and Appendix. The In-
troduction gives a glimpse of what is to come later in the book, mostly vari-
ous forms of quantum computation, quantum neural networks and quantum
brain,togetherwithmodernadaptivepath-integralmethods.Chapter2gives
a modern review of classical neurodynamics, including brain physiology, bio-
logical and artificial neural networks, synchronization, spike neural nets and
wavelet resonance, motor control and learning. Chapter 3 presents a mod-
ern review of quantum physics, including quantum mechanics and quantum
fieldtheory(mostlyFeynmanpat-integral-based),aswellasbothAbelianand
non-Abeliangaugetheories(withtheirpat-integralquantizations).Chapter4
presents several fields from nonlinear dynamics that are related to quantum
neural computation, including classical and quantum chaos, turbulence and
solitons, with the special treatment to nonlinear Schr¨odinger equation (NLS,
the core model of quantum neural networks, in which quantum superposition
meets neural nonlinearity). Chapter 5 gives a personalized review (mostly
based on the authors’ own papers) of the current research in quantum-brain
and quantum-mind. Chapter 6 presents a review of quantum information,
viii Preface
quantumgametheory,quantumcomputationandclassicalelectronicforquan-
tumcomputing.TheAppendixgivesabriefreviewofsomemathematicaland
physiologicalconcepts(necessaryforcomprehensivereadingofthebook),fol-
lowed by classical computational tools used in quantum neural computation.
The objective of Quantum Neural Computation is to provide a serious
reader with a serious scientific tool that will enable them to actually perform
a competitive research in the rapidly-growing field of quantum neural com-
putation. The monograph includes a very comprehensive bibliography on the
subject and a detailed index.
TargetreadershipforQuantum Neural Computation includesallresearch-
ers and students of complex, classical+quantum nonlinear systems (in com-
puter science, physics, mathematics, engineering, medicine, chemistry, biol-
ogy, psychology, sociology, economics, etc.), working in industry, clinics and
academia.
Adelaide V. Ivancevic
May 2009 T. Ivancevic
Acknowledgments
The authors wish to thank Land Operations Division, Defence Science &
TechnologyOrganisation,Australia,forthesupportindevelopingtheHuman
Biodynamics Engine (HBE)andcrowdmodellingsimulator.Inparticular,we
thank Dr. Darryn Reid, LOD–LRR Task Leader, for his support.
Wealso express our gratitude to Springer book series Intelligent Systems,
Control and Automation: Science and Engineering and especially to the Edi-
tor, Professor Spyros Tzafestas.
Contents
1 Introduction............................................... 1
1.1 Neurodynamics ......................................... 2
1.2 Quantum Computation .................................. 3
1.3 Discrete Quantum Computers............................. 4
1.4 Topological Quantum Computers.......................... 14
1.5 Computation at the Edge of Chaos and Quantum Neural
Networks............................................... 18
1.6 Adaptive Path Integral: An ∞-Dimensional QNN............ 22
1.6.1 Computational Partition Function ................... 22
1.6.2 From Thermodynamics to Quantum Field Theory ..... 24
1.6.3 ∞-Dimensional QNNs ............................. 24
1.7 Brain Topology vs. Small-World Topology .................. 26
1.8 Quantum Brain and Mind ................................ 30
1.8.1 Connectionism, Control Theory and Brain Theory..... 30
1.8.2 Neocortical Biophysics ............................. 31
1.8.3 Quantum Neurodynamics .......................... 35
1.8.4 Bi-Stable Perception and Consciousness .............. 37
1.9 Notational Conventions .................................. 40
2 Brain and Classical Neural Networks ...................... 43
2.1 Human Brain ........................................... 43
2.1.1 Basics of Brain Physiology.......................... 50
2.1.2 Modern 3D Brain Imaging.......................... 70
2.2 Biological versus Artificial Neural Networks................. 78
2.2.1 Common Discrete ANNs ........................... 80
2.2.2 Common Continuous ANNs ........................ 98
2.3 Synchronization in Neurodynamics ........................106
2.3.1 Phase Synchronization in Coupled Chaotic Oscillators .106
2.3.2 Oscillatory Phase Neurodynamics ...................109
2.3.3 Kuramoto Synchronization Model ...................112
xii Contents
2.3.4 Lyapunov Chaotic Synchronization ..................113
2.4 Spike Neural Networks and Wavelet Resonance..............114
2.4.1 Ensemble Neuron Model ...........................117
2.4.2 Wavelet Neurodynamics............................119
2.4.3 Wavelets of Epileptic Spikes ........................129
2.5 Human Motor Control and Learning .......................133
2.5.1 Motor Control ....................................134
2.5.2 Human Memory...................................138
2.5.3 Human Learning ..................................140
2.5.4 Spinal Musculo-Skeletal Control.....................142
2.5.5 Cerebellum and Muscular Synergy...................145
3 Quantum Theory Basics ...................................151
3.1 Basics of Non-Relativistic Quantum Mechanics..............151
3.1.1 Soft Introduction to Quantum Mechanics.............152
3.1.2 Quantum States and Operators .....................157
3.1.3 The Tree Standard Quantum Pictures................163
3.1.4 Dirac’s Probability Amplitude and Perturbation.......165
3.1.5 State-Space for n Non-Relativistic Quantum Particles..168
3.1.6 Quantum Fourier Transform ........................170
3.2 Introduction to Quantum Fields...........................171
3.2.1 Amplitude, Relativistic Invariance and Causality ......171
3.2.2 Gauge Theories ...................................173
3.2.3 Free and Interacting Field Theories..................176
3.2.4 Dirac’s Quantum Electrodynamics (QED) ............177
3.2.5 Abelian Higgs Model ..............................179
3.2.6 Topological Quantum Computation..................181
3.3 The Feynman Path Integral...............................188
3.3.1 The Action-Amplitude Formalism ...................188
3.3.2 Correlation Functions and Generating Functional......191
3.3.3 Quantization of the Electromagnetic Field ............193
3.3.4 Wavelet-Based QFT ...............................194
3.4 The Path-Integral TQFT.................................199
3.4.1 Schwarz-Type and Witten-Type Theories.............199
3.4.2 Hodge Decomposition Theorem .....................201
3.4.3 Hodge Decomposition and Chern–Simons Theory......204
3.5 Non-Abelian Gauge Theories..............................207
3.5.1 Introduction to Non-Abelian Theories................207
3.5.2 Yang–Mills Theory ................................207
3.5.3 Quantization of Yang–Mills Theory ..................212
3.5.4 Basics of Conformal Field Theory (CFT) .............214
4 Spatio-Temporal Chaos, Solitons and NLS .................219
4.1 Reaction–Diffusion Processes and Ricci Flow................219
4.1.1 Bio-Reaction–Diffusion Systems .....................223