QUANTUM MECHANICS AND BAYESIAN MACHINES

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 Kalman–Bucy 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 Hamilton–Jacobi–Bellman Equation
  • Pontryagin Maximum Principle
  • Lie–Poisson Dynamics
  • H_∞ Control
• Integrable Systems:
  • RH Solution of the Airy Equation
  • The KdV Equation
  • Segal–Wilson 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
  • Wiener–Hopf 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.