Objectives:
The course will teach the subject of quantum information theory, with its application to quantum computation and quantum cryptography ( in the context of both quantum-secure primitives and quantum attack scenarios). Depending on time, there may also be a very brief discussion of the potential application of quantum computing in the context of machine learning. The course will cover the following basics (probability theory, vector spaces, and linear algebra will also be taught if necessary)
Content:
- Postulates of quantum mechanics (Hilbert, unitary and stochastic dynamics, density operators
- Quantum Entanglement and classifications, Nonlocality, Bell Inequalities, Tsirelson's bound
- Quantum Measurement Theory (POVMs ... etc)
- No-Cloning Theorem, Dense Coding, Teleportation
- Classical and quantum entropy and channel capacities, distance measures, fidelity
- Quantum Algorithms: Shor, Grover, MBQC .... etc
- Quantum Cryptography - Quantum Key Distribution (QKD), quantum protocols, min-entropy, privacy amplification, device-independent quantum cryptography, secure quantum channels, lattice-based cryptosystems
- Quantum Graph States, Topological Quantum Computation
- Various current Quantum Computer physical implementations
- Quantum machine learning