Algorithms in Quantum Theory

Module Number: EI71077

Duration: one Semester

Ocurrence: Winter Semester

Language: English

Number of ECTS: 6

Staff

Professor in charge: Gerhard Kramer

Amount of work

Contact hours: 90

Self-study hours: 90

Total: 180

Description of Achievement and Assessment Methods

By answering questions during an oral exam (30 min) the students prove their ability to explain the algorithms described in the course showing understanding of the quantum features behind the algorithms and mastering of the introductory material. Furthermore, the student should be able to compare the quantum algorithms to their classical counterpart. The students are allowed to bring one sheet of A4 paper with aiding notes.

Prerequisites (recommended)

- Basics of Complex Linear Algebra
- Basics of Probability Theory
- Basics of Computation theory
- Basics of Forward Error Correction

Intended Learning Outcomes

At the end of the course the student is expected to acquire an understanding of the principles of finite dimensional quantum systems and how they change the foundations of information processing, together with an overview of the main applications.
After the course the student should be able to explain and disseminate the principles as well as to start reading the literature in quantum information processing. However, the information-theoretic part, although crucial, will not be covered in the course.

Content

Introduction to quantum states, channels and measurements
Algorithms in Quantum communication, including:
Teleportation
Dense coding
Bell testing
Algorithms in Quantum computation, including:
Quantum Fourier Transform
Period finding
Phase estimation
Breaking RSA
Grover's search
Algorithms in Quantum error correction, including:
Shor's code
CSS codes
Topological codes
Toric code
Color codes

The course will not include:
Quantum Information

Teaching and Learning Methods

In addition to the individual methods of the students, consolidated knowledge is aspired by repeated lessons in exercises and tutorials. The teaching method in the lectures is teacher-centred instruction and in the exercises work instruction.

Reading List

Lecture notes are provided together with a list of alternative reading material