Lecture Topics
1. Review of quantum mechanics:
- Notions of linear algebra of finite-dimensional Hilbert spaces including spectral decomposition of operators
- Introduction of density matrices as generalizations of quantum states. CPTP maps as generalizations of unitary evolution
2. What is quantum information?
- The qubit
- Measurements in quantum mechanics
- Projective measurements and POVMs
- Different types of POVMs
3. Entanglement
- Measures of entanglement
- The Bell states and the GHZ states
- Bell’s theorem
- Purification of density matrices and the Schmidt decomposition
- Entanglement entropy and the area law
4. The circuit model of quantum computation
- Introduction to quantum algorithms: Teleportation, the Deutsch-Josza algorithm, Grover’s algorithm, Shor’s algorithm.
5. The basics of quantum cryptography: quantum key distribution
- Open quantumsystems
- Quantum information and thermodynamics.
6. Experimental implementation of a quantum processor: the rotating frame andNMR
- Other modern implementations
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Dr. Shajid Haque: Lecture Topics
1. Quantum Circuit Complexity
- Background and Motivation for studying quantum complexity.
- What is Circuit Complexity?
- Operator and State circuit complexities
2. Squeezed States
- Examples: Displacement operator, Harmonic Oscillators, Free field Theory (I will apply both state and operator circuits)
- What is Squeezed States?
- Complexity of Purification
3. Cosmological Complexity
- Cosmological Perturbation Model
- Cosmological Squeezed states
- Operator Complexity for cosmological perturbation
- Sate Complexity for cosmological perturbation
- Open System: Complexity of Purification for Cosmological Perturbation
Contact Dr. Shajid Haque: shajid.haque@uct.ac.za
Dr. Garreth Kemp: Lecture Topics
Open Quantum Systems Applied to Quantum Brownian Motion - I
The Feynman-Vernon path integral formalism is a powerful tool for studying open quantum systems. As a concrete example, quantum Brownian motion may be studied using the theory of open quantum systems. The goal of the first lecture will be to outline the Caldeira-Leggett model for quantum Brownian motion. The goal of the second lecture will be to introduce the Feynman-Vernon path integral formalism for open quantum systems and then to apply it to the Caldeira-Leggett model for quantum Brownian motion.
Lecture I
- Caldeira-Leggett model for quantum Brownian motion.
- Derive the high temperature equation of motion.
- Obtain an approximate stationary solution.
- Derive the exact Heisenberg equations of motion.
Lecture II
- Basic formalism of the Feynman-Vernon path integral.
- Apply this formalism to the above model.
- Use this formalism to re-derive the exact equations of motions.
Dr. Khushboo Dixit: Lecture Topics
1. Introduction to Various Measures of Quantum Correlations
- Background/ Motivation
- Entanglement (short discussion)
- Spatial correlations
- Temporal correlations
2. Applications of Quantum Correlations in Particle Physics
- Spatial correlations in neutrino and neutral meson system
- Temporal correlations in neutrino system
