Quantum heuristic algorithm for traveling salesman problem

Details Quantum heuristic algorithm for traveling salesman problem Quantum heuristic algorithm for traveling salesman problem

2010-04-23

arxiv.org/abs/1004.4124v2

Physics

Quantum Physics

Revised the introduction, and corrected some typos

Scientific paper

We propose a quantum heuristic algorithm to solve a traveling salesman problem by generalizing Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with extremal costs, reaching almost to unity and they are shown characterized by statistical properties of tour costs. In particular for a Gaussian distribution of the tours along the cost we show that the quantum algorithm exhibits the quadratic speedup of its classical counterpart, similarly to Grover search.

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