UBC

A computationally universal phase of quantum matter [Published March 4, 2019] We provide the first example of a symmetry protected quantum phase that has universal computational power. This two-dimensional phase is protected by one-dimensional line-like symmetries that can be understood in terms of local symmetries of a tensor network. These local symmetries imply that every ground state in the phase is a universal resource for measurement based quantum computation... Homotopical approach to quantum contextuality We extend Arkhipov's graph theoretic characterization of magic arrangements to arbitrary collection of contexts by relaxing the requirement that each observable belongs to exactly two contexts. We introduce the notion of a topological realization of a given set of operator constraints by cell complexes of algebraic topology. We prove that an arrangement is magic only if the first homotopy group (fundamental group) of any topological realization is non-trivial... Here, we..

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