Metaheuristics on quantum computers: Inspiration, simulation and real execution

Quantum-inspired metaheuristics are solvers that incorporate principles inspired from quantum mechanics into classical-approximate algorithms using non-quantum machines. Due to the uniqueness of quantum principles, the inspiration of quantum phenomena and the way it is done in fundamentally different non-quantum systems rather than real or simulated quantum computers raise important questions about these algorithms’ design and the reproducibility of their results in real or simulated quantum devices. Thus, this work’s contribution stands in a first step towards answering those questions as an attempt to identify key findings in the existing literature that should be considered or adapted in order to build hybrid or fully-quantum algorithms that can be used in quantum machines. This is done by proposing and studying four inspired, simulated and real quantum cellular genetic algorithms that, as far as the authors’ knowledge, are the first quantum structured metaheuristics studied in the three quantum realms using a quantum simulator with 32 quantum bits and a real quantum machine employing 15 superconducting quantum bits. The users’ mobility management in cellular networks is taken as a validation problem using 13 real-world instances. The comparisons have been made against 6 diverse algorithms using 9 comparison metrics. Thorough statistical tests and parameters’ sensitivity analysis have been also conducted. The experiments allowed answering several questions, including how quantum hardware influences the studied-algorithms’ search process. They also enabled opening new perspectives in quantum metaheuristics’ design.Authors acknowledge that this research is partially funded by the Universidad de Málaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under grant number UMA18-FEDERJA-003 (PRECOG); under grant PID 2020-116727RB-I00 (HUmove) funded by MCIN/AEI/10.13039/501100011033; and TAILOR ICT-48 Network (No 952215) funded by EU Horizon 2020 research and innovation programme. Funding for open access charge is supported by the Universidad de Málaga/CBUA. The authors also acknowledge that an instance studied in this work was inspired from the CRAWDAD dataset spitz/cellular. The authors acknowledge also the use of the IBMQ for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBMQ team. Finally, the authors would like to state that the views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission