4. Quantum Machine Learning

This course "Quantum Machine Learning" was originally offered by Peter Wittek of Toronto University in 2019.  Professor Wittek, Unfortunately, died in an avalanche of northern India next year.  Here I posted an edited teaching material, pretty much my mental journey and experience when I took the course.

The pace of development in quantum computing mirrors the rapid advances made in machine learning and artificial intelligence. It is natural to ask whether quantum technologies could boost learning algorithms: this field of inquiry is called quantum-enhanced machine learning. The goal of this course is to show what benefits current and future quantum technologies can provide to machine learning, focusing on algorithms that are challenging with classical digital computers. We put a strong emphasis on implementing the protocols, using open source frameworks in Python. Prominent researchers in the field will give guest lectures to provide extra depth to each major topic. These guest lecturers include Alán Aspuru-Guzik, Seth Lloyd, Roger Melko, and Maria Schuld. (their videos are not available here.)

Course Modules:

Module 1: Quantum Systems

• Understand the basics of quantum states as a generalization of classical probability distributions;

• Their evolution in closed and open systems;

• Measurements as a form of sampling;

• Describe elementary classical and quantum many-body systems.

Module 2: Quantum Computation

• Contrast quantum computing paradigms and implementations;

• Recognize the limitations of current and near-future quantum technologies and the kind of the tasks where they outperform or are expected to outperform classical computers;

• Explain variational circuits.

Module 3: Classical-Quantum Hybrid Learning Algorithms

• Encode classical information in quantum systems;

• Describe and implement classical-quantum hybrid learning algorithms;

• Perform discrete optimization in ensembles and unsupervised machine learning with different quantum computing paradigms;

• Experiment with unusual kernel functions on quantum computers;

• Sample quantum states for probabilistic models.

Module 4: Coherent Learning Protocols

• Demonstrate coherent quantum machine learning protocols and estimate their resources requirements;

• Summarize quantum phase estimation and quantum matrix inversion;

• Overview quantum linear algebra routines that are useful in machine learning;

• Implement these algorithms for Gaussian processes. 

Note: In this Tutorial, whenever we mention "Rieffel’s textbook", we mean the book titled "Quantum Computing: a Gentle Introduction", authored by Elenor Rieffel and Wolfgan Polak, 2014.  MIT Press.  As for “Nielsen's textbook”, we mean the book titled "Quantum Computation and Quantum Information", authored by M.A. Nielsen and I.L. Chuang, 2010, Cambridge University Press.