Abstract
Quantum technology enters in the new era of Noisy Intermediate-Scale Quantum (NISQ) with 50-100 qubits quantum computers already available. It is now important to compare quantum methods with the classical approach to solve optimization problems in order to determine if there is a potential speed-up and what quantum technologies will be able to perform. The Quantum Approximate optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. We provide the method to apply QAOA on a shortest path problem and a study of the performance of this quantum method by using heuristic strategies based on observed patterns in optimal parameters. First, we will present the state of the art of quantum hybrid algorithms and technologies. Then we will discuss the effect of the shape of the graph, the number of valid solutions, and the number of nodes of the graph we consider on the quality of the QAOA’s results and on the patterns in optimal variational parameters.
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