Introduction to Quantum Information Science

Code School Level Credits Semesters
MATH4049 Mathematical Sciences 4 20 Autumn UK
Code
MATH4049
School
Mathematical Sciences
Level
4
Credits
20
Semesters
Autumn UK

Summary

The paradigm of Quantum Information Science (QIS) is that quantum devices made of systems such as atoms and photons, can out perform the present day technology in key applications ranging from computing power and communication security to precision measurements. Quantum information processing and the measurement and control of individual quantum systems are central topics in QIS, lying at the intersection of quantum mechanics with "classical" disciplines such as information theory, probability and statistics, computer science and control engineering.

This course gives an introduction to QIS, emphasising the differences and similarities between the classical and the quantum theories. After a short review of the necessary probabilistic notions, the first part introduces the operational framework of quantum theory involving the fundamental concepts of states, measurements, quantum channels, instruments. This includes some of the influential results in the field such as entanglement and quantum teleportation, Bell's theorem and the quantum no-cloning theorem. The second part covers at least two topics from: quantum Markovian evolutions, quantum statistics, continuous variable systems.

Target Students

Single and Joint Honours students from the School of Mathematical Sciences. Mathematical Physics students. MSc students on the Gravity, Particles and Fields Programme. Natural Sciences students.

Classes

Assessment

Assessed by end of autumn semester

Educational Aims

This Quantum Theory Pathwaycourse gives a mathematical introduction to quantum information theory. Its content builds onMATH2013 with the aim of providing the student with a background in Quantum Information Science which will facilitate further independent learning and the access to current research topics.

Learning Outcomes

A student who completes this course successfully should be able to:

L1 - perform computations involving Hilbert spaces, tensor products, and operators on Hilbertspaces;
 

L2 - state the postulates and describe the mathematical formalism of quantum mechanics;
 

L3 - use the Bloch sphere notation to compute states and measurements on qubit systems;
 


L4 - define and compute the Schmidt decomposition of an entangled state;
 

L5 - explain the details of the BB84 quantum key distribution, and the teleportation protocols;
 

L6 - derive the Bell inequality and show how it is violated in quantum mechanics;
 

L7 - define the notion of quantum channel and work out the action of different qubit channels.

Conveners

View in Curriculum Catalogue
Last updated 07/01/2025.