Quantum Machine Learning

Course objectives

The main purpose of the course is to present a compact but effective introduction to the basics of quantum machine learning (QML) starting from fundamental notions of quantum mechanics and quantum computing. The idea is to explain how the foundations of quantum mechanics enable new and efficient learning schemes to students with no background in quantum mechanics and quantum computing. Students will not merely learn how to translate classical machine learning techniques into the language of quantum computing, but rather a new approach to data representation and processing that is intrinsically different from that performed by standard computers. The course includes lectures and classroom exercises, useful to check students' personal preparation.

Channel 1
CARLO PRESILLA Lecturers' profile

Program - Frequency - Exams

Course program
Introduction to machine learning (ML). Machine learning with quantum computers (QML). Phenomenology of quantum mechanics. Mathematical structure. Quantum states and observables. Quantum dynamics. Composite quantum systems. Encoding of data in quantum states. Quantum circuits. Quantum oracles. Adiabatic quantum computing. Quantum annealing. Remarkable quantum algorithms in QML schemes Quantum Fourier transform. Grover search algorithm. Amplitude amplification. Evaluation of the quantum phase. Notions and technical tools for use in QML. Quantum random access memory. Simulation of Hamiltonian. Estimation of the difference between quantum states and their distances. Unsupervised learning. Dimensionality reduction of the space of variables. Quantum K-means and K-medians. Supervised learning, training. Quantum distance-based classification. Quantum nearest neighbors of order k. Quantum-inspired ML algorithms for classical computers. Quantum pattern recognition. Recognition algorithms. Quantum neural networks. Quantum perceptron. Quantum Boltzmann machine. Quantum convolutional neural networks.
Prerequisites
Students should essentially be familiar with basic concepts of statistics and probability theory, and fundamentals of linear algebra like: vector spaces and their bases, linear maps, matrix operations, eigenvalues and eigenvectors, diagonalizability, tensor products. Knowledge of quantum computing and machine learning is obviously an excellent starting point; nevertheless, I will present the foundations of QML in a self-contained manner.
Books
D. Pastorello, "Concise Guide to Quantum Machine Learning", Springer
Frequency
Recommended attendance of lectures and exercise sessions.
Exam mode
The exam includes a written test, aimed at assessing basic skills, and an oral test. The written test, lasting 120 minutes, consists of open-ended questions. The oral test consists of an interview of variable length that leads - together with the written test - to the definition of the overall grade.
Bibliography
A. Teta, "A Mathematical Primer on Quantum Mechanics", Springer C. Conti, "Quantum Machine Learning: Thinking and Exploration in Neural Network Models for Quantum Science and Quantum Computing", Springer Nature Simeone, "An Introduction to Quantum Machine Learning for Engineers", arXiv:2205.09510
Lesson mode
Lectures in class.
  • Lesson code10619690
  • Academic year2025/2026
  • CourseApplied Mathematics
  • CurriculumMatematica per Data Science - 10
  • Year1st year
  • Semester2nd semester
  • SSDMAT/07
  • CFU6