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

• URL: http://arxiv.org/abs/2005.00213v1
• Date: Fri, 1 May 2020 04:15:23 GMT
• Title: Cohomology and the Algebraic Structure of Contextuality in Measurement Based Quantum Computation
• Authors: Sivert Aasn{\ae}ss (Department of Computer Science, University of Oxford)
• Abstract summary: Roberts, Bartlett and Raussendorf recently introduced a new cohomological approach to contextuality in 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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