Restricting the search space to boost Quantum Annealing performance

We are interested in Quantum Annealing (QA), an algorithm inspired by quantum theory and Simulated Annealing (SA). It is based on quantum replicas, which explore an energy surface, and are less prone to be trapped in local minima. Moreover, kinetic energy helps replicas to find a global minimum. This method has proved its efficiency for several optimization problems. We start this study by presenting the application of QA to a new problem: the Multidimensional Knapsack Problem (MKP). We then present a new idea to speed up the quantum annealing process by detecting the resemblance between replicas. If many of the replicas exhibit the same properties, our assumption is that these properties will also be present with a high probability in a global solution. Consequently, the QA may restrict certain mutations in order to preserve those similarities. We call this algorithm Restrictive Quantum Annealing (RQA). We establish that RQA has better performances than QA and SA by carrying out an adequate analysis of the RQA performance, taking the Traveling Salesman Problem (TSP) and the above-mentioned MKP as references. We also advance guidelines indicating types of NP-hard problems for which our algorithm is particularly well adapted.