BSc Computer Science and Mathematics

Quantum computing is one of the most intriguing of modern developments at the interface of computing, mathematics and physics, whose long term impact is far from clear as yet.

Pre-requisites

You have to be happy to do plenty of mathematics, linear algebra in particular. The material is covered in the course itself (and includes topics in linear algebra not covered elsewhere), but it's a great help if you've seen (at least some) linear algebra before. By all means contact me if you're unsure.

The perspective that quantum phenomena bring to the questions of information and algorithm is quite unlike the conventional one. In particular, selected problems which classically have only slow algorithms, have in the quantum domain, algorithms which are exponentially faster. Most important among these is the factoring of large numbers, whose difficulty underpins the security of the RSA encryption protocol, used for example in the secure socket layer of the internet. If serious quantum computers could ever be built, RSA would become instantly insecure. This course aims to give the student an introduction to this unusual new field.

• Use a subset of linear algebra to express quantum concepts.

• Define concepts in quantum theory and be able to elicit the consequences of different quantum scenarios.

• Interpret and analyse simple quantum circuits.

State Transition Systems. Nondeterministic Transition Systems, Stochastic Transition Systems, and Quantum Transition Systems. The key issues: Exponentiality, Destructive Interference, Measurement. (1)

Review of Linear Algebra. Complex Inner Product Spaces. Eigenvalues and Eigenvectors, Diagonalisation. Tensor Products. (3)

Pure Quantum Mechanics. Quantum states. Unitary Evolution. Observables, Operators and Commutativity. Measurement. Simple Systems. The No-Cloning theorem. The Qubit. (3)

Entanglement. Schrodinger's cat. EPR states. Bell and CHSH Inequalities. The GHZ Argument. Basis copying versus cloning. (1)

Basic quantum gates. Simple quantum algorithms. Quantum Teleportation. (3)

Quantum Search (Grover's Algorithm). Quantum Fourier Transform. Phase estimation. Quantum Counting. (5)

Quantum Order Finding. Continued Fractions. Quantum Factoring (Shor's Algorithm). (3)

Lectures

20

Interactive sessions

Interactive sessions will be arranged as required 
 

Feedback is provided face to face or via email, in response to student queries regarding both the course exercises (5 formative exercise sheets with subsequently published answers) and the course material more generally.

The main items on the COMP39112 reading list can be found on the Department of Computer Science website for current students.

A more extensive reading list can be found on the course's Blackboard site, or at COMP39112 Supplementary Information