



01584nas a2200133   4500008004100000245006400041210006400105300001200169490000700181520117000188100001901358700001901377856005401396       2012                        eng d00aQuantum Algorithms for Invariants of Triangulated Manifolds0 aQuantum Algorithms for Invariants of Triangulated Manifolds  a843-8630 v123 a<p>One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor networks. The graph underlying these networks is given by the triangulation of a manifold, and the structure of the tensors ensures that the overall tensor is independent of the choice of internal triangulation. This leads to quantum algorithms for additively approximating certain invariants of triangulated manifolds. We discuss the details of this construction in two specific cases. In the first case, we consider triangulated surfaces, where the triangle tensor is defined by the multiplication operator of a finite group; the resulting invariant has a simple closed-form expression involving the dimensions of the irreducible representations of the group and the Euler characteristic of the surface. In the second case, we consider triangulated 3-manifolds, where the tetrahedral tensor is defined by the so-called Fibonacci anyon model; the resulting invariant is the well-known Turaev-Viro invariant of 3-manifolds.</p>1 aAlagic, Gorjan1 aBering, E., A.  uhttp://dl.acm.org/citation.cfm?id=2481580.2481588