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Wireless multihop networks (WMHNs) have to strike a trade-off among diverse and often conflicting quality-of-service requirements. The resultant solutions may be included by the Pareto front under the concept of Pareto optimality. However, the problem of finding all the Pareto-optimal routes in WMHNs is classified as non-deterministic polynomial-hard, since the number of legitimate routes increases exponentially, as the nodes proliferate. Quantum computing offers an attractive framework of rendering the Pareto-optimal routing problem tractable. In this context, a pair of quantum-assisted algorithms has been proposed, namely the non-dominated quantum optimization and the non-dominated quantum iterative optimization. However, their complexity is proportional to $\sqrt {N}$ , where $N$ corresponds to the total number of legitimate routes, thus still failing to find the solutions in “polynomial time.” As a remedy, we devise a dynamic programming framework and propose the so-called evolutionary quantum pareto optimization (EQPO) algorithm. We analytically characterize the complexity imposed by the EQPO algorithm and demonstrate that it succeeds in solving the Pareto-optimal routing problem in polynomial time. Finally, we demonstrate by simulations that the EQPO algorithm achieves a complexity reduction, which is at least an order of magnitude when compared to its predecessors, albeit at the cost of a modest heuristic accuracy reduction. [ABSTRACT FROM AUTHOR]

Routing in wireless multihop networks (WMHNs) relies on a delicate balance of diverse and often conflicting parameters, when aiming for maximizing the WMHN performance. Classified as a non-deterministic polynomial-time hard problem, routing in WMHNs requires sophisticated methods. As a benefit of observing numerous variables in parallel, quantum computing offers a promising range of algorithms for complexity reduction by exploiting the principle of quantum parallelism (QP), while achieving the optimum full-search-based performance. In fact, the so-called non-dominated quantum optimization (NDQO) algorithm has been proposed for addressing the multiobjective routing problem with the goal of achieving a near-optimal performance, while imposing a complexity of the order of O(N) and O(N√N) in the best and worst case scenarios, respectively. However, as the number of nodes in the WMHN increases, the total number of routes increases exponentially, making its employment infeasible despite the complexity reduction offered. Therefore, we propose a novel optimal quantum-assisted algorithm, namely, the non-dominated quantum iterative optimization (NDQIO) algorithm, which exploits the synergy between the hardware and the QP for the sake of achieving a further complexity reduction, which is on the order of O(√N) and O(N√N) in the best and worst case scenarios, respectively. In addition, we provide simulation results for demonstrating that our NDQIO algorithm achieves an average complexity reduction of almost an order of magnitude compared with the near-optimal NDQO algorithm, while having the same order of power consumption.