This course will provide the theoretical tools for the analysis and the optimisation of quantum information processing tasks (e.g. cloning, estimation, discrimination) and for the study and the simulation of quantum many body systems.
Prerequisiti
Linear algebra, quantum physics, fundamental notions of quantum computing and quantum information.
Metodi didattici
The course is organised with blackboard lectures, where all the details and tools necessary to the understanding of the topics will be properly addressed, with the aim of stimulating an interactive atmosphere with the students.
Verifica Apprendimento
The exam consists of an oral test aimed at verifying the ability of the student to present rigorously and with an appropriate technical language all concepts learned.
Testi
M. Nielsen and I. Chuang “Quantum Computation and Quantum Information” Cambridge University Press (2000).
G.M. D’Ariano, G. Chiribella, P. Perinotti “Quantum Theory from First Principles” Cambridge University Press (2017).
Lecture notes and bibliographic references provided by the teacher
Contenuti
- The church of the larger Hilbert space: Stinespring dilation theorem and Choi-Jamiolkowsky isomorphism. - Quantum information processing: estimation, discrimination, tomography, cloning and teleportation. - Multi-round protocols and quantum strategies: network of quantum operations and quantum combs, optimisation problems and semidefinite programming, fully quantum machine learning. - Quantum Cellular Automata and quantum walks: fundamental definitions, structure theorems, applications, experimental implementations. - Tensor networks: fundamental definitions, application to quantum simulation of many body systems (Matrix Product States and Density Matrix Renormalisation Group).
