The course covers the theory and applications of both classical and quantum learning models, analyzing their properties, advantages, and disadvantages. Knowledge and Understanding: The student will acquire a basic understanding of the theory and applications of models useful for describing the behavior of quantum information processing systems. Application of Knowledge: The student will be able to develop and test simple models from scratch, both classical and quantum machine learning models. Communication Skills: The student will acquire the ability to present the results of model applications and provide an explanation of the motivations behind such choices. Learning Ability: The student will be able to navigate the literature related to the course topics and will be able to compare and improve the chosen modeling strategy.

Knowledge of scientific Python. Knowledge of linear algebra, ordinary differential equations. Knowledge of quantum mechanics. No previous knowledge of machine learning is assumed.

1.Machine learning methods for quantum mechanics: we will recap on some notions and models of supervised and unsupervised learning and strategies to attack problems of interest in quantum mechanics 2.Quantum mechanics in information processing 3. Applications of Machine Learning to Quantum Control

"Quantum Computation and Quantum Information" by Michael A. Nielsen and Isaac L. Chuang. Schuld, M., & Petruccione, F. . Machine learning with quantum computers Cham: Springer (2021) Understanding Deep learning, J. Prince. (available online);Dong, Daoyi, and Ian R. Petersen. “Learning and robust control in quantum technology”, Springer, 2023 ;Claudio Conti, “Quantum Machine Learning”, Springer, 2024; De Kirk, “Optimal Control Theory: an introduction”, Dover, 1998.

Review or brief introduction of machine learning methods, supervised and unsupervised, useful for the course: Discriminative models (neural networks, transformers) Generative models (autoencoders, diffusion models, normalizing flows) Applications of the models to quantum mechanics problems related to quantum computing: Entanglement detection Tunneling Decoherence reduction Symmetry The basic concepts of Optimal Control (OC) and the Pontryagin approach. Computational difficulties and non intepretability of the solution of the state-costate system. Machine Learning applied to OC of Quantum Systems (QS). Methods based on automatic differentiation and gradient descent; neural optimal control of QS; methods based on gradient-free global stochastic optimization: simulated annealing, differential evolution, particle swarm optimization Sampling-based learning control of heterogenous ensembles of QS Open quantum systems as stochastically perturbed quantum systems: how to derive the Lindblad Equation from simple principles Machine Learning applied to the OC of Open Quantum Systems Machine learning applied to the stochastic OC of stochastically perturbed QS Time-optimal control of QS Robust control of QS Introduction to the statistical approach of Gardner and Derrida’ to continuous and discrete models of quantum perceptrons.

Frontal lectures and hands on sessions ( the latter both individual and in groups). The balance will be frontal lectures and practical sessions.

Bring your laptop

The exam will consist of two parts:

1. Each student will propose one final project for the exam typically analyzing a parameter dependent problem in quantum mechanics and will have to give a brief presentation
explaining the work done and provide commented code upon request.

2. an interview where few questions will be asked to assess the preparation on the topics of the course. The final mark is obtained by averaging the score for the project (max 12) and the oral part, max (18) to reach a maximum of 30. In the portal part we will ask 3 questions of increasing difficulty.

The course introduces the student to the modern techniques in machine learning and knowledge representation to tackle problems in quantum mechanics. It is a shared opinion that data science and artificial intelligence are one of the backbones for sustainable development, and all techniques learned in this course can be applied in this respect.