Quantum Information Workshop 2024

5 Feb 2024, 08:30 → 7 Feb 2024, 15:00 Africa/Johannesburg

Seminar Room (Physics Department, University of Johannesburg (APK Campus))

Virtual Attendance Now Available: Please note that you must register on Indico first before receiving an email with the login credentials to join the workshop virtually. 

The Quantum Information Workshop 2024 is scheduled to take place from February 5-7, 2024. The event will be hosted by the Centre for Astro-Particle Physics (CAPP) in the Physics Department at the University of Johannesburg (UJ).

This follows the Applications of Quantum Information in Astrophysics and Cosmology Workshop, which took place at the Mathematics & Applied Mathematics Department at the University of Cape Town (UCT) in Cape Town from April 24-26, 2023.

These lectures aim to introduce the fundamental concepts of quantum information and its applications to physical problems. The intended audience is advanced undergraduates or beginning graduate students interested in reading papers on quantum information. The lectures are planned to be self-contained. The minimum prerequisite assumed is a good undergraduate course on quantum mechanics. The lectures will be complemented by tutorial problems that are designed to solved collaboratively by the students.

Monday 5 February

08:45 Morning Coffee & Snack Break

Prof. Tibra Ali: 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

QI L1.pdf

10:15 Break

Prof. Tibra Ali: What is Quantum Information?

• The qubit
• Measurements in quantum mechanics
• Projective measurements and POVMs
• Different types of POVMs

QI L2.pdf

Dr. Shajid Haque: Quantum Circuit Complexity

• Background and Motivation for studying quantum complexity.
• What is Circuit Complexity?
• Operator and State circuit complexities

UJ Lectures 5.pdf

12:30 Lunch

Dr. Shajid Haque: 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

UJ Lectures 5.pdf

Dr. Khushboo Dixit: Introduction to Various Measures of Quantum Correlations

• Background/ Motivation
• Entanglement (short discussion)
• Spatial correlations
• Temporal correlations

Dixit_L1.pdf

Tuesday 6 February

08:45 Morning Coffee & Snack Break

Prof. Tibra Ali: 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

QI L3.pdf

10:15 Break

Prof. Tibra Ali: The Circuit Model of Quantum Computation

• Introduction to quantum algorithms: Teleportation, the Deutsch-Josza algorithm, Grover’s algorithm, Shor’s alg

QI L4.pdf

Dr. Shajid Haque: Basics of Cosmology

• What is Cosmology?
• The Big Bang Theory
• Our Observable Universe
• Cosmological Principle
• Geometry of Spacetime
• Geodesic in GR
• Dynamics of Spacetime
• Cosmological Solutions
• Inflation

UJ Lectures 5.pdf

12:30 Lunch

Dr. Garreth Kemp: 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.

• 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.

Dr. Khushboo Dixit: Applications of Quantum Correlations in Particle Physics

• Spatial correlations in neutrino and neutral meson system
• Temporal correlations in neutrino system

Talk (3).pdf

Wednesday 7 February

09:00 Morning Coffee & Snack Break

Prof. Tibra Ali: The Basics of Quantum Cryptography: Quantum Key Distribution

• Open quantumsystems
• Quantum information and thermodynamics.

QI L5.pdf

Break

Prof. Tibra Ali: Experimental Implementation of a Quantum Processor: The Rotating Frame and NMR

• Other modern implementations

QI L6.pdf

11:45 Lunch

Dr. Garreth Kemp: Open Quantum Systems Applied to Quantum Brownian Motion - II

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.

• 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. Shajid Haque: 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

UJ Lectures 5.pdf