Quantum Machine Learning

Peter Wittek created this course before quantum machine learning was a recognized field. His book and these lectures established the vocabulary and the mathematical framework that researchers still use today, and the course has been maintained and updated by the community following his death in 2019. It remains the most rigorous publicly available treatment of the subject and is the standard reference for anyone who wants to understand what quantum speedups in machine learning actually mean mathematically, as opposed to what they are claimed to mean in press releases.

The course covers quantum analogues of the core machine learning primitives. Quantum principal component analysis uses the HHL algorithm and quantum phase estimation to factor a density matrix, potentially achieving exponential speedup over classical PCA under specific data-access assumptions. Quantum support vector machines apply the same linear-systems subroutine to kernel matrix inversion. Quantum Boltzmann machines and quantum neural networks are treated carefully, with attention to the gap between theoretical models and what current hardware can actually implement. QBoost, the D-Wave-inspired approach to ensemble learning, is analyzed as a quadratic unconstrained binary optimization problem.

A major strength of the course is its intellectual honesty. Wittek was careful to distinguish genuine quantum advantages from heuristic improvements and from results that depend on quantum RAM assumptions that may never be physically realizable. The hybrid algorithm section reflects the more pragmatic post-NISQ turn in the field: variational quantum eigensolvers and quantum approximate optimization used as subroutines within classical pipelines. Students leave with both the mathematical tools to evaluate quantum ML claims and the practical context to decide when hybrid approaches are worth the engineering overhead.