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

Sivert Aasnaess (University of Oxford)

Okay, Roberts, Bartlett and Raussendorf recently introduced a new cohomological obstruction to contextuality in measurement based quantum computing. 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 Čech cohomology obstruction of Abramsky, Mansfield and Barbosa and give a direct proof that Čech cohomology is more powerful.