Quantum Techniques for Stochastic Mechanics - Course Introduction

Jacob D. Biamonte of the Institute for Scientific Interchange in Torino, taught a course titled "Quantum Techniques for Stochastic Mechanics" at the Institute for Quantum Computing, University of Waterloo in August 2012.

Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of chemical reaction networks, which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: stochastic Petri nets. But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas—but in a context where probabilities replace amplitudes.

In this course we will explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We will study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. These Hamiltonians are called Dirichlet forms, and they arise naturally from electrical circuits made only of resistors. The area is ripe to be further connected with modern topics in quantum computation and quantum information theory.

This lecture series is part of QIC 890/891 held at the University of Waterloo, Spring 2011 and organized by Michele Mosca. The content is primarily based on joint work with John Baez.

Course Introduction: http://youtu.be/ZiaD8WpYu4A
Lecture 1: http://youtu.be/vGHj5dJLOJs
Lecture 2: http://youtu.be/-C_sWIUwNg0
Lecture 3: http://youtu.be/YIeVQpiIsR0
Lecture 4: http://youtu.be/z1gPOYgZKOM

Course Book: http://arxiv.org/pdf/1209.3632.pdf