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Quantum Optimization
Quantum speedup of the Travelling Salesman Problem for bounded-degree graphs
arXiv
Authors: Alexandra E. Moylett, Noah Linden, Ashley Montanaro
Year
2016
Paper ID
41742
Status
Preprint
Abstract Read
~2 min
Abstract Words
95
Citations
N/A
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.
Why This Paper Matters
- This paper contributes to the Quantum Optimization research area in the Quantum Articles archive.
- It adds a 2016 reference point for readers tracking recent quantum research.
- The Travelling Salesman Problem is one of the most famous problems in graph theory.
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