Some of the Heterogeneous Network (HetNet) components may act autonomously for the sake of achieving the best possible performance. The attainable routing performance depends on a delicate balance of diverse and often conflicting Quality-of-Service (QoS)requirements. Finding the optimal solution typically becomes an NP-hard problem, as the network size increases in terms of the number of nodes. Moreover, the employment of user defined utility functions for the aggregation of the different objective functions often leads to suboptimal solutions. On the other hand, Pareto Optimality is capable of amalgamating the different design objectives by relying on an element of elitism. Although there is a plethora of bio-inspired algorithms that attempt to address the associated multi-component optimization problem, they often fail to generate all the routes constituting the Optimal Pareto Front (OPF). As a remedy, we initially propose an optimal multi-objective quantum-assisted algorithm, namely the Non-dominated Quantum Optimization (NDQO) algorithm, which evaluates the legitimate routes using the concept of Pareto Optimality at a reduced complexity. We then compare the performance of the NDQO algorithm to the state-of-the-art evolutionary algorithms, demonstrating that the NDQO algorithm achieves a near-optimal performance. Furthermore, we analytically derive the upper and lower bounds of the NDQO’s algorithmic complexity, which is of the order of O(N) and O(N√N) in the best- and worst-case scenario, respectively. This corresponds to a substantial complexity reduction of the NDQO from the order of O(N2)imposed by the brute-force (BF) method. However again, as the number of nodes 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 parallelism and the quantum parallelism 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. 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 activating the same order of comparison operators. Apart from the traditional QoS requirements, the network design also has to consider the nodes’ user-centric social behavior. Hence, the employment of socially-aware load balancing becomes imperative for avoiding the potential formation of bottlenecks in the network’s packet-flow. Therefore, we also propose a novel algorithm, referred to as the Multi-Objective Decomposition Quantum Optimization (MODQO) algorithm, which exploits the quantum parallelism to its full potential by exploiting the database correlations for performing multi-objective routing optimization, while at the same time balancing the tele-traffic load among the nodes without imposing a substantial degradation on the network’s delay and power consumption. Furthermore, we introduce a novel socially-aware load balancing metric, namely the normalized entropy of the normalized composite betweenness of the associated socially-aware network, for striking a better trade-off between the network’s delay and power consumption. We analytically prove that the MODQO algorithm achieves the full-search based accuracy at a significantly reduced complexity, which is several orders of magnitude lower than that of the full-search. Finally, we compare the MODQO algorithm to the classic NSGA-II evolutionary algorithm and demonstrate that the MODQO succeeds in halving the network’s average delay, whilst simultaneously reducing the network’s average power consumption by 6 dB without increasing the computational complexity.