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

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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.
Original languageEnglish
Number of pages1
Publication statusUnpublished - 4 Apr 2017
EventHeilbronn Quantum Algorithms Day 2017 - HH Wills Physics Laboratory, Bristol, United Kingdom
Duration: 4 Apr 2017 → …
http://heilbronn.ac.uk/2017/01/26/quantum-algorithms-day-2017/

Workshop

WorkshopHeilbronn Quantum Algorithms Day 2017
CountryUnited Kingdom
CityBristol
Period4/04/17 → …
Internet address

Structured keywords

  • QITG
  • Bristol Quantum Information Institute

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