| Summary: | 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 (NP-hard), 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 multi-objective routing problem with the goal of achieving a near-optimal performance, while imposing a complexity of the order of $O(N)$ and $O(N\sqrt{N})$ 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 quantum parallelism for the sake of achieving a further complexity reduction, which is on the order of $O(\sqrt{N})$ and $O(N\sqrt{N})$ in the best- and worst-case scenarios, respectively. Additionally, we provide simulation results for demonstrating that our NDQIO algorithm achieves an average complexity reduction of almost an order of magnitude compared to the near-optimal NDQO algorithm, while having the same order of power consumption
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