Computation and dynamics: quantum and classical
The present level of technology of computational devices approaches the atomic level. Thus the theory of quantum computations is in the spot of attention worldwide. Despite of important advances towards this target our understanding is still fundamentaly incomplete. For example, in classical theory of computation there is a visible borderline between data and algorithms. In quantum world they may be inseparable, similarly to deep interaction between a system and an observer. New vision is provided by the concept of computation as a dynamics in the phase space, which has a duality between coordinates/data and momenta/algorithms. Such a model would provide an opportunity for effectively estimating the overall cost of quantum computing during the entire cycle: preparation-computation-reading. Theoretical models for the first and the last stages within the theory of quantum computing are presently missing. For classical computing the ``computation time'' of the initial and final steps is often negligible and is not considered. For a quantum computer, preparation (input/programming) and reading (output) may be as costly (or even more so) as the computation itself. Therefore a more realistic comparison of the advantages of classical and quantum computation can be performed.
Analysis group at Leeds
The Analysis group at Leeds is one of the strongest in the UK in abstract analysis. The group comprises 5 members of staff (Jonathan Partington, Matthew Daws and Charles Read are also interested in supervising PhD students) together with a research Professor and a number of visiting Fellows. The group currently has six Graduate Students. Researchers at Leeds have interests ranging from the interplay between analysis and algebra (Daws and Read) to links with complex analysis and control theory (Partington) through to applications to Mathematical Physics (Kisil). Leeds hosts a weekly seminar series (which has close links with York University) and is currently the organising node for the North British Functional Analysis Seminar series.
This project is eligible for School of Mathematics EPSRC Doctoral Training Grant funding - please contact us for more information.