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.

ILO 1: Define concepts in quantum theory and be able to elicit the consequences of different quantum scenarios.

ILO 2: Use a subset of linear algebra to express quantum concepts.

ILO 3: 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.

Review of Linear Algebra. Complex Inner Product Spaces. Eigenvalues and Eigenvectors. Diagonalisation. Tensor Products.

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

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

Basic quantum gates. Simple quantum algorithms. Quantum Teleportation.

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

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

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.

Quantum computing for computer scientists     Yanofsky, Noson S.,    Cambridge University Press    2008    ISBN: 9780511813887

Quantum computation and quantum information     Nielsen, Michael A.,    Cambridge University Press    2010    ISBN: 9781107002173

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £39,700 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our  undergraduate student finance pages .