Foundational Structures and Methods for Quantum Informatics

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

Abstract

Quantum Mechanics offers radically new possibilities for information processing, with phenomena such as entanglement --- the possibility of strong instantaneous correlations between spatially separated particles, leading to highly counter-intuitive non-local effects --- playing a central role.Current methods for dealing with these ideas, and with the subtle interplays and information flows between a quantum system and its classical observer, are cumbersome, and somewhat like the early days of programming computers in machine code.In this proposal, building on our previous work, we aim to use ideas and methods which have already proved useful in Computer Science to develop an elegant, conceptual approach, both to the foundations of Quantum Mechanics itself, and to the description, design and analysis of quantum information processing systems. The effect is something like having a high-level programming language --- in which the `computer' is the physical world!While the underlying mathematics we use (category theory) is quite abstract, it is accompanied by a very intuitive diagrammatic formalism, which is useful both as a practical tool for calculations, and for bringing the ideas to life in a very vivid and visual fashion.This formalism also leads to fascinating and unexpected links with logic --- our diagrams can be seen as graphical representations of formal proofs --- and with geometric ideas such as knots and braids.

Publications

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Abramsky S (2012) The Cohomology of Non-Locality and Contextuality in Electronic Proceedings in Theoretical Computer Science

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Abramsky S (2011) The sheaf-theoretic structure of non-locality and contextuality in New Journal of Physics

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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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Abramsky S (2012) Logical Bell Inequalities in CoRR

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Abramsky S (2012) Relational Databases and Bell's Theorem in CoRR

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Abramsky S (2012) Logical Bell inequalities in Physical Review A

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Abramsky S (2013) Relational Hidden Variables and Non-Locality in Studia Logica

 
Description We developed high-level methods for quantum information, laying the basis for categorical quantum mechanics, now widely studied and used as the basis of several courses.
We also made important advances in the general understanding of contextuality and non-locality, the key non-classical ingredients of quantum mechanics, important both at a fundamental level, and as a resource which can be used in information processing tasks.
Exploitation Route The work in this project has been influential and led to new insights and advances in diagrammatic formalism for quantum information, and in powerful new ways of understanding contextuality. These are now being applied in the qauntum technologies program.
Sectors Digital/Communication/Information Technologies (including Software)