Solving NP-hard Problems with Quantum Annealing

Quadratic unconstrained binary optimization (QUBO) formulas of quantum annealing (QA) algorithms are classified into four categories. QA algorithms using different QUBO formulas solve specific NP-hard problems as examples of the classification. The NP-hard problems solved are the subset sum, the vertex cover, the graph coloring, and the traveling salesperson problems. The QA algorithms are compared with their classical counterparts in terms of the quality of the solution and the time to the solution. Based on the comparison results, observations and suggestions are given for each QUBO formula category, so that proper actions can be adopted to improve the performance of QA algorithms. Compared with classical algorithms, QA algorithms are competitive in the current noisy intermediate-scale quantum (NISQ) era and beyond.