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. Also this work demonstrates that the TSP Library is a source of benchmarks for quantum processing of combinatorial problems. The hybrid solvers combine quantum and classical methods in a manner that is D_Wave proprietary information. The results from Kerberos were closer to optimal than the results from LeapHybridSampler. We show that the error percent from optimal increases as the problem size increases, which is consistent with results on D-Wave_s quantum computer for other optimization problems. An appendix contains outcomes from the two hybrid solvers for two asymmetric traveling salesman problems that are in the TSP Library. Again, the Kerberos results were closer to optimal than those from LeapHybridSampler, which indicates that Kerberos is superior to LeapHybridSampler on traveling salesman problems.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. Also this work demonstrates that the TSP Library is a source of benchmarks for quantum processing of combinatorial problems. The hybrid solvers combine quantum and classical methods in a manner that is D_Wave proprietary information. The results from Kerberos were closer to optimal than the results from LeapHybridSampler. We show that the error percent from optimal increases as the problem size increases, which is consistent with results on D-Wave_s quantum computer for other optimization problems. An appendix contains outcomes from the two hybrid solvers for two asymmetric traveling salesman problems that are in the TSP Library. Again, the Kerberos results were closer to optimal than those from LeapHybridSampler, which indicates that Kerberos is superior to LeapHybridSampler on traveling salesman problems.

arXiv:2106.05948Jun 8, 20214 citations

Framework for Small Traveling Salesman Problems

Richard H. Warren

We study small traveling salesman problems (TSPs) because current quantum computers can find optional solutions for TSPs with up to 14 cities. Also, we study small TSPs because TSPs have been recommended to be benchmarks to measure quantum optimization on all types of quantum hardware. This means comparisons of quantum data about small TSPs. We extent previous numerical results that were reported in “Small Traveling Salesman Problems” for 6, 8 and 10 cities. The new results in this paper are for 10 – 14 cities in symmetric TSPs. The data for this new range of cities is consistent with the previous data and can be the basis for estimates of results from quantum computers that are upgraded to handle more than 14 cities. The work and analysis suggest two conjectures that we discuss. The paper also contains an annotated survey of recent publications about TSPs.We study small traveling salesman problems (TSPs) because current quantum computers can find optional solutions for TSPs with up to 14 cities. Also, we study small TSPs because TSPs have been recommended to be benchmarks to measure quantum optimization on all types of quantum hardware. This means comparisons of quantum data about small TSPs. We extent previous numerical results that were reported in “Small Traveling Salesman Problems” for 6, 8 and 10 cities. The new results in this paper are for 10 – 14 cities in symmetric TSPs. The data for this new range of cities is consistent with the previous data and can be the basis for estimates of results from quantum computers that are upgraded to handle more than 14 cities. The work and analysis suggest two conjectures that we discuss. The paper also contains an annotated survey of recent publications about TSPs.

International Journal on Applied Physics and EngineeringNov 12, 20241 citation

The travelling salesman problem and adiabatic quantum computation: an algorithm

Tien D. Kieu

arXiv:1801.07859Quantum Information ProcessingFeb 9, 201924 citations

Quantum Algorithm for the Traveling Salesperson Problem

Andrew Haverly, M. A. Novotny, Shahram Rahimi

The traveling salesperson problem (TSP) is “if a traveling salesman wishes to visit exactly once each of a list of $m$ cities (where the cost of traveling from city $i$ to city $j$ is $c_{ij}$ ) and then return to the home city, what is the least costly route the traveling salesman can take [1]?” The TSP is an NP-Complete problem. This paper introduces a solution to the TSP using Grover's quantum algorithm. This paper also introduces a quantum algorithm to the minimum (and maximum) spanning tree problem. The full circuit implementation is presented using the open-source Qiskit environment [2]. This paper provides the number of qubits required, the quantum depth, and the quantum volume of the algorithm for the TSP. This paper also shows how to solve the minimum (and maximum) spanning tree using Grover's algorithm.The traveling salesperson problem (TSP) is “if a traveling salesman wishes to visit exactly once each of a list of$m$cities (where the cost of traveling from city$i$to city$j$is$c_{ij}$) and then return to the home city, what is the least costly route the traveling salesman can take [1]?” The TSP is an NP-Complete problem. This paper introduces a solution to the TSP using Grover's quantum algorithm. This paper also introduces a quantum algorithm to the minimum (and maximum) spanning tree problem. The full circuit implementation is presented using the open-source Qiskit environment [2]. This paper provides the number of qubits required, the quantum depth, and the quantum volume of the algorithm for the TSP. This paper also shows how to solve the minimum (and maximum) spanning tree using Grover's algorithm.

IEEE Asia-Pacific Conference on Computer Science and Data Engineering (CSDE)Dec 4, 20231 citation

A Magnetism-Inspired Quantum Algorithm to Solve the Traveling Salesman Problem

Luke Ellert-Beck, Michael J. Lawler, Samuel Gosin

Bulletin of the American Physical SocietyMar 19, 20210 citations

The traveling salesperson problem (TSP) is “if a traveling salesman wishes to visit exactly once each of a list of

m

cities (where the cost of traveling from city

i

to city

j

c_{ij}

) and then return to the home city, what is the least costly route the traveling salesman can take [1]?” The TSP is an NP-Complete problem. This paper introduces a solution to the TSP using Grover's quantum algorithm. This paper also introduces a quantum algorithm to the minimum (and maximum) spanning tree problem. The full circuit implementation is presented using the open-source Qiskit environment [2]. This paper provides the number of qubits required, the quantum depth, and the quantum volume of the algorithm for the TSP. This paper also shows how to solve the minimum (and maximum) spanning tree using Grover's algorithm.