Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Algorithms for Invariants of Triangulated Manifolds   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.

24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an