Prof Konstantinos Kardaras COL.6.07

This course is available on the MSc in Applicable Mathematics, MSc in Data Science, MSc in Financial Mathematics, MSc in Operations Research & Analytics, MSc in Quantitative Methods for Risk Management, MSc in Statistics, MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (Research) and MSc in Statistics (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.

Advanced knowledge of linear algebra, as well as basics of complex numbers, at the level of MA222, are essential. Familiarity with Python is also required.

Students who have no previous experience in Python are required to complete an online pre-sessional Python course from the Digital Skills Lab before the start of the course (https://moodle.lse.ac.uk/course/info.php?id=8709).

The course will start with reminders on linear algebra and complex numbers. Then, foundational principles of quantum mechanics necessary for understanding quantum computation will be established: postulates of quantum mechanics, quantum superposition, and the measurement problem. The concept of qubits and their representation will be studied, as well as basic quantum gates, such as the Pauli and Hadamard gates. Subsequently, the course will move to discussing quantum algorithms, focusing on foundational ones such as Deutsch-Jozsa, and Grover's search algorithm. In terms of quantum information theory, concepts such as quantum entanglement and quantum teleportation will be discussed, as well as the no-cloning theorem. If time permits, quantum error correction will be covered.

For all the previous, hands-on exercises and demonstrations using Python through the quantum programming package Qiskit will enable students to gain practical experience in implementing and simulating quantum algorithms.

30 hours of seminars in the WT.

There will be a mixture of theory and examples/applications/homework solutions (roughly split in half between theory and practice). The third of the three weekly hours will be mostly used for working out problems from the formative coursework, and illustrations through computer code. A mid-term summative assessment will be provided, to be worked out by students during the reading week.

Students will be expected to produce 9 problem sets in the WT.

Weekly problem sets will be provided, and will be discussed during the seminars.

The main material will come from the first two sources:

- Quantum Computation and Quantum Information. M. A. Nielsen and I. L. Chuang, Cambridge University Press; 2010

- Lecture Notes on Quantum Computation and Information. A. Jacquier and K. Kardaras; 2024

- Mathematics of Quantum Computing: An Introduction. W. Scherer, Springer; 2020. 

- Classical and Quantum Computation. A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi, American Mathematical Society; 2002

Exam (80%, duration: 2 hours, reading time: 15 minutes) in the spring exam period.
Coursework (20%) in the WT.

Coursework accounting for 20% of the grade will be given to be worked on during the reading week. This will consist of a number of exercises students will be required to solve throughout the term.