QUANTUM SCIENCE, FOUNDATIONS AND TECHNOLOGIES

The course treats the modern scenario of Quantum Physics (QP), from fundamental principles to emerging "Quantum Technologies" (QT). It rigorously covers key concepts—such as entanglement, decoherence, and quantum measurement—which, combined with the control of electron and photon dynamics, form the functional paradigm for applications in computing, communication, and sensing. The course is theoretical in nature, incorporating exercises and numerical applications. The learning objectives are:
Knowledge and understanding – Knowledge of the main theoretical and numerical concepts and techniques required to: (1) represent a quantum system and describe its dynamics; (2) understand the operating principles of physical systems used in QT, from coherent nanodevices to atomic and photonic architectures; (3) introduce algebraic and field-theoretic tools for analyzing bipartite systems (entanglement, decoherence, and measurement); (4) study key quantum algorithms.
Applying knowledge and understanding – Ability to solve problems by applying theoretical techniques and approximations to the analysis and simulation of quantum dynamics. Ability to become familiar with the opportunities offered by QT across various disciplines.
Making judgments – Ability to make choices regarding one's educational path, articulate interpretations of physical phenomena, and evaluate the potential of QT for post-graduate professional activities.
Communication skills – Proficiency in interdisciplinary communication within the field of QT, developed through the presentation part of the exam and informal interim assessments.
Learning skills – Acquisition of tools for continuous knowledge updating through access to laboratories and specialized literature, as well as through the presentation part of the exam.

The courses on quantum physics, advanced quantum mechanics, and linear algebra are essential prerequisites. Courses on condensed matter physics, solid-state physics, and elementary statistical mechanics serve as important prerequisites. Although the courses on "Superconductivity and Superfluidity," "Mesoscopic and Topological Materials," and "Many-Body Theory" are highly beneficial—and attendance is therefore recommended—they are not strictly required as prerequisites.

1. Representation of quantum systems (12+2 h)
   Quantum bits, composite systems; physical systems (photons, nuclear spin, confined atoms, artificial atoms based on semiconductors/superconductors, cavities); algebra in Hilbert spaces and applications to quantum networks; examples; classical and quantum computation (seminar)
2. Quantum dynamics (12+2 h)
   Time evolution operator; pulsed dynamics; Heisenberg and von Neumann equation and their phenomenological generalization to relaxation and dephasing; quantum systems in oscillatory fields; time-dependent unitary transformations (rotating frame, adiabatic frame, geometric phases)
3. Bipartite and multipartite systems (6+2 h)
   Density matrix; quantum measurement and von Neumann model; applications (superdense coding, no-cloning theorem, cryptography, quantum teleportation)  Entanglement; EPR paradox and Bell inequality (seminar).
4. Coherent nanosystems (4 h) (two or three of the following topics)
   NMR molecules in liquids; photons and atoms in cavities; artificial atoms and circuit QED; trapped ions and cold atoms; nanomechanical and nanoelectromechanical systems; topological excitations in condensed matter.
5. Selected topic (2 h) (seminar, one of the following topics)
   New quantum technologies for measurement and sensing; open quantum systems; introduction to quantum information; introduction to quantum thermodynamics; introduction to quantum control theory.

• L'esame orale standard comprende: (a) parte espositiva: un argomento a scelta del candidato, concordato in anticipo col docente; (b) una domanda scelta dal candidato tra tre proposti dal docente, di diversa difficoltà.
• A richiesta dello studente, e subordinatamente al consenso del docente, la prova (a) può essere sostituita da un elaborato che comprenda un calcolo analitico o numerico che lo studente dovrà sviluppare in maniera indipendente ma assistita, nel qual caso la parte (b) sarà a carattere espositivo.

• Il superamento dell'esame dipende dalla prova (a) mentre la (b) determina la valutazione. Quest’ultima è effettuata tenendo conto di: (1) pertinenza delle risposte rispetto alle domande formulate; (2) livello di comprensione dei contenuti esposti; (3) accuratezza nell'esposizione dei calcoli; (4) capacità di collegamento con altri temi dell'insegnamento (o di insegnamenti precedenti) e di riportare esempi; (5) proprietà di linguaggio e chiarezza espositiva.