Minor Quantum Computing and Networking

The course will start with a basic introduction of some experimental observations which justify quantum mechanics principles and in particular the probabilistic description of a physical system. We will then introduce the concepts of quantum bits and describe how to manipulate them through quantum circuits. The advantages of quantum computing will be illustrated through some specific examples and algorithms including quantum search, quantum teleportation, and quantum random walks. Two lectures will be devoted to quantum communications and one will provide additional information about the physics of quantum systems and the devices used for technological applications.

Contents of lectures:

• First lesson refresher on linear algebras and complex numbers, an illustrative example (spin component measurements) to introduce some quantum mechanics findings (quantization, probabilistic description, measurements interact with the system), qubits, computation basis, bra-ket/Dirac notation, orthogonal kets, deriving a computational basis for spin component measurements, principles of quantum mechanics.
• Second lesson: derive the operators for the 3 spin components, multi qubit systems (product states and Bell states, entanglement), unitary property of quantum gates, qubit gates, quantum circuits, how to recover all classic logic circuits, a quantum computer to simulate quantum systems or to speed-up algorithms.
• Third lesson: BB84, E91, dense coding, and teleportation. and teleportation.
• Fourth lesson: review of background material on discrete-time and continuous-time random walks on graphs, discrete-time quantum walks, in particular, the coined model, Szegedy's model and the staggered model, continuous-time random walks, application of complex diffusion models and quantum walks to the distributed estimation of graph spectrum.
• Fifth lesson: no-cloning algorithm, reversible circuits and Landauer's principle, ancilla bits and uncomputation, Grover's search algorithm (geometric description, number of Grover iterates and success probability, how to perform rotations). Decoherence, density matrix, fidelity.
• Sixth lesson: Purification, quantum repeaters, entanglement swapping, quantum error.
• Seventh lesson: Quantum state decoherence, Superconducting Qubit, Non-linear optics as source of quantum entanglement for quantum communications.

• Konstantin Avrachenkov, Directeur de recherche, Inria
• Virginia D'Auria, Maître de conférences, Université Côte d'Azur
• Giovanni Neglia, Chargé de recherche, Inria

• Written mini-tests at the beginning of most lectures (40% of the final grade)
• Final written test (60% of the final grade) - 08/12/2022, 9h00-12h00 - Campus SophiaTech, Templiers 1, room O+108