Exchanging particles on graphs, or more concretely networks of quantum wires, has been proposed as a means to perform fault-tolerant computation. This was inspired by braiding anyons in planar systems. However, exchanges graph are not governed the usual braid group but instead group. By imposing compatibility with fusion topological charges, we obtain generalized hexagon equations. We find anyo...

Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara, Bravyi, and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs that satisfy certain constraints. Finding such hypergraphs and computing their parameters, however, is a nontrivial task. We propose families of topological ...

We investigate generalized quadrangles Γ that admit at least two projective axes of symmetry. We show that if there are three such axes incident with a common point x, then x is a translation point of Γ. In case that Γ is moreover a compact connected quadrangle with topological parameters (p, p), p ∈ N, then Γ is a topological translation generalized quadrangle. We further investigate the case ...

‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p, q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p, q). On the other hand, we construct a consistent example of a Tychonov countably compact semigroup containing a copy of C(p, q). In this paper we study the structural prope...