Mathematical aspects of Computer Science

MSC is dedicated to research in abstract and mathematical aspects of classical and quantum computing. The group comprises members from the departments of Computing and Technology, and Mathematics.

Areas of strength:

From the classical computing point, research is conducted in programming languages with specific interests in Functional Programming, Formal Semantics, Type Systems, Program Transformation, and the Design and Implementation of programming languages.

We are currently active participants in the PLanCompS project --- an international collaboration to develop a novel framework for Component-based Specification of programming languages.

Other recent work expected to return REF outputs include developing the theory of the Worker/wrapper Transformation, designing and implementing the strategic programming language KURE, implementing the HERMIT plugin for the Glasgow Haskell Compiler, and exploring the Remote Monad Design Pattern.

From the quantum computing point, research is conducted in Quantum Algorithms, Quantum Circuits, Quantum Cryptography, and Quantum Error-correction – all of which drives new work in the area of quantum technologies. Quantum technologies will be profound and far-reaching: secure communication networks for consumers, corporations and government; precision sensors for biomedical technology; quantum simulators for the design of new materials; and ultra-powerful quantum computers for addressing otherwise impossibly large datasets for machine learning and artificial intelligence applications. However, engineering quantum systems and controlling them is an immense technological challenge: they are inherently fragile; and information extracted from a quantum system necessarily disturbs the system itself. Of the various approaches to quantum technologies, photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level. We here at Nottingham Trent have developed a novel approach to photonic quantum circuits for high performance, miniaturisation and scalability, which makes great use of mathematical aspects from combinatorics and number theory. Our investigations are based on innovative, award-winning research into the implications of weak random processes on quantum cryptography pioneered by Wilmott, and the research project is supported by Swiss-based quantum technologies specialist ID-Quantique.

Areas of growing activity:

• Continued development of the CBS specification language, and application of CBS to further case studies.
• Application of genetic algorithms for the constructing quantum circuitry
• Investigations of genetic and Monte-Carlo algorithms for quantum data-mining
• Possible application of statistical and graph-theoretic approaches to classical and quantum computing

• WILMOTT, C.M., 2014. Establishing the number of distinct stabilizer bases for a quantum qudit error-correcting code. Journal of Physics: Conference Series. ISSN 1742-6596
• WILMOTT, C.M., 2014. From Fibonacci to the mathematics of cows and quantum circuitry. Journal of Physics: Conference Series. ISSN 1742-6596
• CHALAL, M.L., MEDJDOUB, B., WHITE, M., SHAHTAHMASSEBI, G., CUMBERBATCH, M. and SHRAHILY, R., 2017. The impact of the UK household life-cycle transitions on the electricity and gas usage patterns. Renewable & Sustainable Energy Reviews, 80, pp. 505-518. ISSN 1364-0321
• AMR, B., MILES, G., SHAHTAHMASSEBI, G., ROOBOTTOM, C. and STELL, D.A., 2017. Systematic evaluation of radiological findings in the assessment of resectability of peri-ampullary cancer by CT using different contrast phase protocols. Clinical Radiology. ISSN 0009-9260
• HAYMAN, G.D., ABBOTT, J., DAVIES, T.J., THOMSON, C.L., JENKIN, M.E., THETFORD, R. and FITZGERALD, P.L., 2010. The ozone source-receptor model - a tool for UK ozone policy. Atmospheric Environment, 44 (34), pp. 4283-4297. ISSN 1352-2310
• FITZGERALD, P.L., 2005. The superfield quantisation of a superparticle action with an extended line element. International Journal of Modern Physics A, 20 (12), pp. 2639-2655. ISSN 0217-751X