HackerPapers

arXiv:1612.06203quant-ph

Quantum speedup of the Travelling Salesman Problem for bounded-degree graphs

Alexandra E. Moylett, Noah Linden, Ashley Montanaro

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

Abstract

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.

arXiv comments
12 pages, 3 figures, 1 table
Journal reference
Phys. Rev. A 95, 032323 (2017)
DOI
doi:10.1103/PhysRevA.95.032323
Subjects
quant-phQuantum Physics cs.DSData Structures and Algorithms

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Feb 2018 to Feb 2018.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. Review of Vivek Wadhwa’s Washington Post Column on Quantum Computing 1 comment

    • Now I was wondering about TSP why it was mentioned at all and if there were any new results since I dabbled in quantum computing. It seems with some constraints on vertex degrees, which seems to be practical, it's possible to do have some speedup (not polynomial of course). For…

      rdtscView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.