Towards Efficiently Solving Quantum Traveling Salesman Problem

Quantum heuristic algorithm for traveling salesman problem

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.

Solving combinatorial problems by two D_Wave hybrid solvers: a case study of traveling salesman problems in the TSP Library

The D_Wave quantum computer is an analog device that approximates optimal solutions to optimization problems. The traveling salesman problems in the TSP Library are too large to process on the D_Wave quantum computer DW_2000Q_6. We report favorable approximations for solving the smallest, symmetric traveling salesman problems in the TSP Library by two D_Wave hybrid solvers, Kerberos and LeapHybridSampler. This is useful work about results from new quantum tools on problems that have been studied. It is expected to show a quantum way forward with larger problems when the hardware is upgraded. A…

Quantum Elastic Net and the Traveling Salesman Problem

Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical computers. Similarly, quantum wave packet reduction allows to devise the Grover search algorithm which outperforms any classical one. In the present paper we argue that the quantum incoherent tunneling can be used for elaboration of new algorithms able to solve some NP-hard problems, such as the Traveling Salesman Problem, considered to be intractable in th…

通过量子优化的切平面方法解决旅行商问题

Cutting-plane methodology via quantum optimization for solving the Traveling Salesman Problem

本文提出通过量子优化的切平面方法解决旅行商问题，通过动态生成子游走消除约束和预处理减少候选边，提升计算性能。

Designing Adiabatic Quantum Optimization: A Case Study for the Traveling Salesman Problem

With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal design of adiabatic algorithms plays an important role in their assessment, we illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP). We demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dyn…

量子局部搜索结合路径切片策略求解旅行商问题

Quantum Local Search for Traveling Salesman Problem with Path-Slicing Strategy

本文提出结合路径切片策略的量子局部搜索方法，通过k-means等聚类划分TSP子问题，混合量子经典求解，在TSPlib实例上高效获得近优解，提升求解效率与资源利用。