Cohomology and the Algebraic Structure of Contextuality in Measurement Based Quantum Computation

Sivert Aasnæss
(Department of Computer Science, University of Oxford)

Okay, Roberts, Bartlett and Raussendorf recently introduced a new cohomological approach to contextuality in measurement based quantum computation. We give an abstract description of their obstruction and the algebraic structure it exploits, using the sheaf theoretic framework of Abramsky and Brandenburger. At this level of generality we contrast their approach to the Cech cohomology obstruction of Abramsky, Mansfield and Barbosa and give a direct proof that Cech cohomology is at least as powerful.

In Bob Coecke and Matthew Leifer: Proceedings 16th International Conference on Quantum Physics and Logic (QPL 2019), Chapman University, Orange, CA, USA., 10-14 June 2019, Electronic Proceedings in Theoretical Computer Science 318, pp. 242–253.
Published: 1st May 2020.

ArXived at: http://dx.doi.org/10.4204/EPTCS.318.15 bibtex PDF
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