Quantum heuristic algorithm for traveling salesman problem

I came across this paper on arXiv: Quantum heuristic algorithm for traveling salesman problem by Jeongho Bang, Seokwon Yoo, James Lim, Junghee Ryu, Changhyoup Lee, and Jinhyoung Lee. Here's the abstract:

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.

The paper is a short read at 5 pages too. I remember discussing the traveling salesman problem in the Summer of 2007 when discussing graph theory in a survey course at Colorado Tech with Dr. Willshire, Dr. Sanden, and Dr. Calongne. It wasn't all that long after I started getting into quantum computing as my research there. I remember at the time thinking it just seemed like a problem that a quantum computer could somehow be utilized for.