Intro: what is learning? What is learning theory?
Simple learning problems
Hardness of learning (query complexity/time complexity)
Connection (and disconnect) between theoretical learning and practical ML
General learning problem definition
Let there be quantum!
Statistical queries (classical/quantum)
Expressibility of PQCs.
Trainability of VQAs.
Generalisation for quantum process learning.
Classical simulability considerations.
Quantum advantage and the practical constraints to achieving it.
The simplest algorithms with a provable advantage: Hamiltonian simulation.
Mapping physical Hamiltonians onto Pauli operators, practical circuits, time evolution.
Quantum Fourier Models and Dequantization
Variational Quantum Circuits (VQCs), Quantum Fourier Models induced by VQCs.
Fourier models and design of classical surrogates.
Separation between the expressivity of quantum and classical Fourier models.
Introduction to Quantum Information and Algorithms
Fundamental concepts of quantum computing and quantum information.
Quantum states and operations, qubits and quantum gates
Quantum measurements, basic algorithms.