Quantum Mathematics and Computation

Lead Research Organisation: University of Oxford
Department Name: Computer Science


The Centre for Quantum Mathematics and Computation will integrate expertise in the Oxford Computer Science and Mathematics departments to tackle the fundamental problem of understanding the mathematical and computational nature of quantum phenomena. Through a distributed research agenda, we will develop a new geometrical language unifying diagrammatic methods in algebraic topology and quantum representation theory with graphical techniques from quantum computation, computational linguistics, and software and hardware design. This language will natively encode the fundamentally continuous, topological nature of the structures arising in these areas, enabling unprecedented advances of both a theoretical and practical kind.

This research effort will be organised into four cross-disciplinary strands, and the research projects of the Centre will address such fundamental problems as the flow of information in quantum protocols, the design of natural language processing platforms, the automated analysis of large unstructured data sets, and the classification of quantum field theories. The resulting integration of knowledge and methods has the potential to transform the practice of computer science and mathematics.

This ambitious, integrated research agenda will be achieved by uniting a robust group of researchers spanning the disciplines of the Centre, and by enabling its members to actively engage with the broader scientific community.

Planned Impact

The proposed Centre will foster excellent research in a range of emergent disciplines that are set to have a transformative effect on the practice of computer science and mathematics in the 21st century. International recognition of the Centre will put it at the heart of global efforts to understand and apply these new ideas, attracting international talent to the UK and sustaining a cross-disciplinary research culture of the highest quality. This Centre will have remarkable benefits for UK science more broadly, through cross-fertilization of other disciplines and by training the next generation of research leaders.

The Centre will have a broad range of interactions with and impact on the academic community. The research team will be supported by the existing research strengths at Oxford, particularly in the computer science, mathematics, and physics faculties. The Centre will host visiting faculty members of the highest reputation, from the UK and around the world, in order to incorporate outside expertise into Centre activities, and also as a means of disseminating the research objectives, ideas, and results into the broader community. Integration of the Centre with the strong, multidisciplinary Masters in the Foundations of Mathematics and Computer Science at Oxford, already in operation, will ensure a new generation of students from both disciplines is educated in the basis of work at the Centre, through courses given by the investigators of this proposal. This will ensure a ready stream of highly-qualified candidates for entry into D.Phil. programmes in the area of Quantum Mathematics and Computation. Altogether, the Centre will play a crucial role in the international community in supporting and developing research in these compelling new areas.

There is real potential for the techniques developed at the Centre to shift research paradigms in computer science, by changing the basic tools for encoding problems and the techniques available for their solution. This shift can lead to technologies that will matter to wider society in the relatively near future, such as novel natural language processing and search tools, automated reasoning systems, and new computational software and hardware platforms.


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Abramsky S (2013) Robust Constraint Satisfaction and Local Hidden Variables in Quantum Mechanics in IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013

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Abramsky S (2015) Games for Dependent Types in CoRR

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Abramsky S (2016) Possibilities determine the combinatorial structure of probability polytopes in Journal of Mathematical Psychology

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Abramsky S (2015) Contextuality, Cohomology and Paradox in 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, September 7-10, 2015, Berlin, Germany

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Arthur Bartles; Christopher L Douglas; Andre Henriques Conformal nets II: conformal blocks in arXiv

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Arthur Bartles; Christopher L Douglas; Andre Henriques Conformal nets III: fusion of defects in arXiv

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Arthur Bartles; Christopher L Douglas; Andre Henriques (2014) Dualizability and Index of Subfactors in Quantum Topology

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B Bartlett; C L Douglas; C Schommer-Pries; J Vicary Modular categories as representations of the 3-dimensional bordism 2-category in arXiv

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B Bartlett; C L Douglas; C Schommer-Pries; J Vicary Extended 3-dimensional bordism as the theory of modular objects in arXiv

Description We have developed new methods for representing and reasoning with higher-dimensional categories. These offer great possibilities for modelling a wide range of phenomena in computer science, physics, biology and other sciences. The concepts are supported by a software tool which is being developed. We have also developed methods for reasoning about contextuality in the use of quantum resources, and applications to quantum advantage in a range of information processing tasks.
Exploitation Route People interested in exploiting quantum advantage, or in high level modelling of processes, can take advantage of the tools we have developed.
Sectors Digital/Communication/Information Technologies (including Software)

Description Some work done by Vicary has led to a technical consultancy agreement with a networking startup. Coecke has obtained an award from Cambridge Quantum computing to develop the ZX calculus as a quantum circuit design tool. He is also involved in a start-up aimed at tool development related to the ZX calculus.
First Year Of Impact 2018
Sector Digital/Communication/Information Technologies (including Software)