Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum speedup of the Travelling Salesman Problem for bounded-degree
  graphs   The Travelling Salesman Problem is one of the most famous problems in graph
theory. However, little is currently known about the extent to which quantum
computers could speed up algorithms for the problem. In this paper, we prove a
quadratic quantum speedup when the degree of each vertex is at most 3 by
applying a quantum backtracking algorithm to a classical algorithm by Xiao and
Nagamochi. We then use similar techniques to accelerate a classical algorithm
for when the degree of each vertex is at most 4, before speeding up
higher-degree graphs via reductions to these instances.

9
The categories of this paper are: nlin
2
The categories of this paper are: math
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con