Advanced Quantum Mechanics

This course aims at introducing the basic concepts of quantum information and computation, with the objective of applying them to the investigation of material systems.

Information and quantum states

• classical information: Shannon entropy
• quantum principles: density matrix, observables and measurement
• quantum information: qubit and von Neumann entropy, definition of entanglement, Bell and EPR
• open systems: generalized quantum dynamics and measurement
• entanglement measures: entropy, fidelity, concurrence…

Entanglement and algorithms

• quantum circuits: gates, universality, dense coding, teleportation and Deutsch algorithm
• algorithms: Fourier transform and phase detection; Shor factorization and Grover search
• error correction: Quantum codes and error correction theory

Applications

• Kitaev toric code
• cluster state and area law of entanglement
• cavity electrodynamics
• physical realization of qubits