QUANTUM INFORMATION

The course introduces key concepts of advanced quantum mechanics (superpositions, entangled states, bipartite systems, open systems), and the theoretical background of their dynamics. Electrons and photons, manipulated in coherent physical systems/architectures are nowadays studied to deepen the understanding of the foundations of quantum mechanics and extending it to gravitation and complex systems, and for "Quantum Technologies" (quantum computation and communication, quantum control, sensing and metrology) using mysterious aspects of the quantum nature as functional paradigms for radically new "quantum machines".

• Knowledge and understanding – Knowledge of ideas and theoretical/numerical techniques for the representation (kinematics) of complex quantum system and for the study of their dynamics. Understanding the conceptual connections between quantum mechanics and information/communication. Knowledge of the working principles of physical systems for quantum information (solid-state nanosystems, atomic/photonic architectures, topological systems) and examples of quantum protocols.
• Applying knowledge and understanding – Ability in the application of basic theoretical techniques and approximate schemes for the analysis and the simulation of dynamical processes in quantum systems. Ability to explore quantum mechanics in multidisciplinary physical contexts. Know a bit about what’s going on in current fundamental and applied research.
• Making judgements - Ability in developing personal interpretations of physical phenomena. Developing the ability to making choices for the education process and for the thesis. Capability in evaluating potentialities offered by Quantum Technologies for both academic and industrial job opportunities.
• Communication skills – Ability in communication in the field of Quantum Technologies, both at a specialized and at an interdisciplinary level.
• Learning skills – Acquiring skills allowing the continuous upgrade of the knowledge in the field, by accessing a research environment and specialized literature.

• The course is structured in three main parts: (1) representation of quantum systems (kinematics) and elementary dynamics; (2) bipartite systems (entanglement, measurement, open systems and decoherence); (3) application to quantum processing with physical systems. The end of the course will be devoted to seminars on selected topics.
• Introductory material can be found on the web page of the theory group on Condensed Matter & Quantum Technologies (www.dfa.unict.it/it/cmqt e www.dfa.unict.it/en/cmqt).
• Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.
• Exams may take place online, depending on circumstances.

1. Quantum Foundations to Technologies -- Quantum coherence. Representation of quantum nodes. von Neumann postulates and algebra of Hilbert spaces: states, transformations and associated Lie groups, projective measurement. Density matrix and Wigner function. Computer algebra in the Hilbert space.
2. Q-Technologies -- Elements of quantum computation; prototype hardware: photons, atoms and spins. Quantum gates and circuits: examples with computer algebra.
3. Q-dynamics & control -- Main analytical methods; Heisenberg & von Neumann equation and phenomenological generalization to open systems; time-dependent unitary transformations and applications (rotating frames, interaction picture, adiabatic and superadiabatic dynamics, geometric phases); numerical examples.
4. Bipartite quantum systems -- Entanglement: Schmidt decomposition, EPR/Bell correlations. Decoherence and the emergence of classical: the quantum operation approach. Measurement: operatorial formulation, von Neumann model. Applications (superdense coding, no-cloning theorem, cryptography, quantum teleportation).
5. Coherent nanosystems for q-information -- Atoms, cavity-QED. Artificial atoms with Super(semi)conductors, circuit QED. Topological q-computation.
6. Selected topic (seminar on one of the following topics) theory of open q-systems, theory of measurement, q-communication, q-thermodynamics, q-error correction. introduction to quantum control theory.

[1] S. Haroche and J.M. Raimond, Exploring the Quantum: Atoms, Cavities and Photons, Oxford, 2006.
[2] M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2010.
[3] G. Falci, Lecture notes on Quantum Information, 2020.
[4] G. Chen, D. A. Church, B.-G. Englert, C. Henkel, B. Rohwedder, M. O. Scully, and M. S. Zubairy. Quantum Computing Devices: Principles, Designs and Analysis. Chapman and Hall/CRC, 2007.
[5] G. Benenti, G. Casati, D. Rossini, G. Strini, Principles of Quantum Computation and Information: A Comprehensive Textbook, World Scientific, 2019.
[6] C. P. Williams, Explorations in Quantum Computing, Springer-Nature New York, 2010.
[7] Stephen Wolfram, An Elementary Introduction to the Wolfram Language, Cambridge University Press, 2015.
[8] G. Baumann, Mathematica for Theoretical Physics, Springer, 2005.