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Quantum technologies
Quantum mechanics is now driving a technological revolution, enabling new paradigms for computing, communication, and sensing. This course provides a comprehensive introduction to the principles of quantum information science, from the fundamentals of qubits and entanglement to the implementation of quantum algorithms, quantum communication protocols, and strategies for protecting fragile quantum states.
Programme
1. Foundations
1.1 Historical Perspective
1.2 Postulates of Quantum Mechanics
1.3 Birth of Quantum Technologies
1.4 Qubits
1.5 Experimental Control of Qubits
1.6 Measuring Qubits: The Rules of Quantum Mechanics
1.7 Density Matrix and Mixed States: The Bloch Ball
1.8 Bloch Equations
1.9 Multipartite Systems
1.10 Von Neumann Entropy
1.11 Separability
1.12 Entanglement or Not?
1.13 Quantum Correlations
2. Quantum Computing
2.1 Turing Machines
2.2 Quantum Computing: From Sequential to Parallel Computation
2.3 Hadamard Gates and the Clifford Group
2.4 Quantum Gates with Trapped Ions
2.5 Important Quantum Algorithms
2.6 Quantum Fourier Transform
2.7 Quantum Advantage
2.8 Quantum Simulation
2.9 Digital and Analog Quantum Simulation
2.10 Experimental Implementations
3. Measurement, Decoherence, and Protection of Quantum States
3.1 Orthogonal Measurements
3.2 Measuring the Spin States of Atoms
3.3 Which-Path Experiments
3.4 Decoherence Scaling
3.5 Distance Measures
3.6 Dynamical Decoupling
3.7 Quantum Error Correction
3.8 Stabilizer Codes
4. Quantum Communication
4.1 Introduction
4.2 Single-Photon Sources
4.3 Fidelity Measures for Quantum Communication
4.4 Quantum Teleportation
4.5 Quantum Key Distribution
4.6 State Purification
4.7 Entanglement Distribution: Probabilistic Communication
4.8 Entanglement Swapping
4.9 Quantum Memories
4.10 Quantum Repeaters
Bibliography
1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010).
2. J. Preskill, Lecture Notes on Quantum Computation, Caltech. Available at:
http://theory.caltech.edu/~preskill/ph219/
Evaluation
Written exam
