This compendium brings together the fields of Quantum Computing, Machine Learning, and Neuromorphic Computing. It provides an elementary introduction for students and researchers interested in quantum or neuromorphic computing to the basics of machine learning and the possibilities for using quantum devices for pattern recognition and Bayesian decision tree problems. The volume also highlights some possibly new insights into the meaning of quantum mechanics, for example, why a description of Nature requires probabilistic rather than deterministic methods.
Contents:
Preface
About the Author
Acknowledgments
Introduction
Six Fundamental Discoveries:
Bayes's Probability Formula
The Wiener and KalmanBucy Filters
Bellman's Dynamic Programming Approach to Optimal Control
Feynman's Path Integral Approach to Quantum Mechanics
Quantum Solution of the Traveling Salesman Problem (TSP)
Ockham's Razor:
Bayesian Searches
A Tale of Two Costs
Hidden Factors and the Helmholtz Machine
Control Theory:
The HamiltonJacobiBellman Equation
Pontryagin Maximum Principle
LiePoisson Dynamics
H Control
Integrable Systems:
RH Solution of the Airy Equation
The KdV Equation
SegalWilson Construction
The NLS Equation
Galois Remembered
Quantum Tools:
Weyl Remembered
Helstrom's Theorem and Universal Hilbert Spaces
Measurement-based Quantum Computation
Quantum Self-organization:
Pontryagin Control and Quantum Criticality
Quantum Theory of Innovations
Quantum Helmholtz Machine
Ad Mammalian Intelligence
Holistic Computing:
Quantum Mechanics and 3D Geometry
Cognitive Science and Quantum Physics
Appendices:
Gaussian Processes
WienerHopf Methods
Riemann Surfaces
The Eightfold Way
Quantum Theory of Brownian Motion
References
Index
Readership: Researchers, academics, professionals and graduate students in pattern recognition/image analysis, machine learning, quantum mechanics and general applied maths.