Multi-objective optimization is a ubiquitous problem that arises naturally in many scientific and industrial areas. Network routing optimization with multi-objective performance demands falls into this problem class, and finding good quality solutions at large scales is generally challenging. In this work, we develop a scheme with which near-term quantum computers can be applied to solve multi-objective combinatorial optimization problems. We study the application of this scheme to the network routing problem in detail, by first mapping it to the multi-objective shortest path problem. Focusing on an implementation based on the quantum approximate optimization algorithm (QAOA) – the go-to approach for tackling optimization problems on near-term quantum computers – we examine the Pareto plot that results from the scheme, and qualitatively analyze its ability to produce Pareto-optimal solutions. We further provide theoretical and numerical scaling analyses of the resource requirements and performance of QAOA, and identify key challenges associated with this approach. Finally, through Amazon Braket we execute small-scale implementations of our scheme on the IonQ Harmony 11-qubit quantum computer.
Multi-objective optimization is a ubiquitous problem that arises naturally in many scientific and industrial areas. Network routing optimization with multi-objective performance demands falls into this problem class, and finding good quality solutions at large scales is generally challenging. In this work, we develop a scheme with which near-term quantum computers can be applied to solve multi-objective combinatorial optimization problems. We study the application of this scheme to the network routing problem in detail, by first mapping it to the multi-objective shortest path problem. Focusing on an implementation based on the quantum approximate optimization algorithm (QAOA) – the go-to approach for tackling optimization problems on near-term quantum computers – we examine the Pareto plot that results from the scheme, and qualitatively analyze its ability to produce Pareto-optimal solutions. We further provide theoretical and numerical scaling analyses of the resource requirements and performance of QAOA, and identify key challenges associated with this approach. Finally, through Amazon Braket we execute small-scale implementations of our scheme on the IonQ Harmony 11-qubit quantum computer.
A multi-objective optimization problem involves optimizing two or more conflicting objectives simultaneously. This type of problem arises in many scientific and industrial areas and it is classified as NP-Hard. Network routing optimization with multiple objectives falls into this category. In the context of 6G networks, solving this problem will become even more challenging due to the exponential growth of Internet of Things devices and the high quality of service requirements. Finding good quality solutions for large-scale networks will be increasingly difficult. In this paper, we introduce a quantum-inspired routing optimization scheme in which noisy-intermediate scale quantum computers (NISQ) can be used to solve the Multi-Objective Routing Problem (MORP). We evaluate the application of the proposed scheme in detail by first developing the mathematical formulas for both single-objective and multi-objective routing and mapping the problem onto gate-based models by using the quadratic unconstrained binary optimization (QUBO) approach. To validate the proposed scheme, we use the quantum approximate optimization algorithm (QAOA), the go-to approach for solving combinatorial optimization problems that are classically intractable. For the simulation, we use the IBM-Qasm simulator and Qiskit framework. Additionally, we use the Chernoff Bound as a standard technique to estimate the sample complexity of QAOA. Finally, we provide a detailed numerical and theoretical analysis of the proposed scheme, including its time complexity, resource requirements, and the challenges associated with it. Our results demonstrate that the proposed approach operates with a time complexity of O ( E 2 ) per iteration in both single and multi-objective scenarios, with an overall runtime of ( n iteration + n CB ) ⋅ O ( E 2 ) influenced by the sampling overhead, significantly outperforming Dijkstra’s algorithm in the multi-objective case, where the complexity increases to O ( 2 k ( N ( k + log N ) + 2 k E ) ) .
Multi-objective combinatorial optimization in wireless communication networks is a challenging task, particularly for large-scale and diverse topologies. Recent advances in quantum computing offer promising solutions for such problems. Coherent Ising Machines (CIM), a quantum-inspired algorithm, leverages quantum properties of coherent light, enabling faster convergence to the ground state. This paper applies CIM to multiobjective routing optimization in wireless multi-hop networks. We formulate the routing problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, and map it onto an Ising model, allowing CIM to solve it. CIM demonstrates strong scalability across diverse network topologies without requiring topology-specific adjustments, overcoming the limitations of traditional quantum algorithms like Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). Our results show that CIM provides feasible and near-optimal solutions for networks containing hundreds of nodes and thousands of edges. Additionally, a complexity analysis highlights CIM's increasing efficiency as network size grows.
Optimization problems are fundamental in a wide range of fields, including telecommunications, where efficient resource allocation is critical to ensure good network performance and high scalability. In the context of elastic optical networks (EONs), the multi-objective routing and spectrum assignment (MO-RSA) problem represents a key challenge, as it involves selecting a valid path and assigning frequency slots while fulfilling continuity and contiguity constraints and optimizing multiple conflicting objectives. This paper presents a novel, to the best of our knowledge, quantum-based approach to solving the MO-RSA problem. We first formulate the MO-RSA problem as a quadratic unconstrained binary optimization (QUBO) problem and then solve it using the quantum approximate optimization algorithm (QAOA). Our method accounts for both minimizing the total number of used links (or any non-negative additive metric) and maximizing the optical signal-to-noise ratio. For our simulations, we employed the Qiskit framework and IBM’s sampler-based quantum backend to implement and test the proposed approach. Our results demonstrate that by encoding the MO-RSA problem into a QUBO model and optimizing it with QAOA, we achieved an approximation ratio of 88% and a computational complexity of O ( n 2 ) , which represents a significant improvement over the exponential complexity of traditional integer linear programming methods.
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
Multi-objective routing in communication networks requires simultaneous optimization of delay, congestion, and reliability—posing challenges for classical single-metric routing protocols. This paper presents a rigorous quantitative benchmarking framework comparing classical deterministic routing paradigms, namely Routing Information Protocol and Open Shortest Path First, against a quantum-assisted routing formulation based on the Quantum Approximate Optimization Algorithm (QAOA). The routing problem is encoded as a constrained Quadratic Unconstrained Binary Optimization (QUBO) model incorporating flow-conservation and path-continuity constraints. Random connected weighted graphs (10–20 nodes) were evaluated across 50 independent runs per topology size under a unified scalarized cost function (0.5D + 0.3C + 0.2L). Results demonstrate that deterministic link-state routing achieves optimal path selection with minimal computational complexity O(m log n), while QAOA attains near-optimal solutions (3–8% deviation) at significantly higher computational overhead due to qubit scaling and variational optimization loops. Scalability analysis reveals quadratic qubit growth with network size, limiting NISQ-era applicability. The study establishes a structured comparative benchmark and positions quantum routing as a complementary exploratory mechanism rather than a replacement for classical routing.