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arXiv:2503.07924 · International Conference on Communications

Multi-Objective Routing Optimization Using Coherent Ising Machine in Wireless Multihop Networks

Yuxuan Lin, Chunxue Xu, Chuan Xi Wang

Published Jun 8, 2025• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/icc52391.2025.11162085

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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.
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 ) ) .
Public transport systems play a crucial role in the development of large cities. Bus network design to optimize passenger flow coverage in a global metropolis is a challenging task. As an essential part of bus travel planning, considering the bus transfer factor in the existing extremely complex and extensive public bus network usually leads to a optimization problem characterized by high-dimensionality and non-linearity. While classical computers struggle to deal with this kind of problems, quantum computers shed new light into this field. The coherent Ising machine (CIM), a specialized optical quantum computer using a photonic dissipative architecture, has shown its remarkable computational power in combinatorial optimization problems. We construct the classical model and the quadratic unconstrained binary optimization (QUBO) model of the bus route optimization problem, and solve it using a classical computer and CIM, respectively. Our experimental results demonstrate the significant acceleration capability of CIM over classical computers in finding the optimal or near-optimal solutions, albeit subject to the hardware limitations of the 100-qubit CIM.
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.
Optimizing routing in Wireless Sensor Networks (WSNs) is pivotal for minimizing energy consumption and extending network lifetime. This paper introduces a resource-efficient compilation method for distributed quantum circuits tailored to address large-scale WSN routing problems. Leveraging a hybrid classical-quantum framework, we employ spectral clustering for network partitioning and the Quantum Approximate Optimization Algorithm (QAOA) for optimizing routing within manageable subgraphs. We formulate the routing problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, providing comprehensive mathematical formulations and complexity analyses. Comparative evaluations against traditional classical algorithms demonstrate significant energy savings and enhanced scalability. Our approach underscores the potential of integrating quantum computing techniques into wireless communication networks, offering a scalable and efficient solution for future network optimization challenges.
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.
Sixth-generation wireless (6G) technology has been focused on in the wireless research community. Global coverage, massive spectrum usage, complex new applications, and strong security are among the new paradigms introduced by 6G. However, realizing such features may require computation capabilities transcending those of present (classical) computers. Large technology companies are already exploring quantum computers, which could be adopted as potential technological enablers for 6G. This is a promising avenue to explore because quantum computers exploit the properties of quantum states to perform certain computations significantly faster than classical computers. This paper focuses on routing optimization in wireless mesh networks using quantum computers, explicitly applying the quantum approximate optimization algorithm (QAOA). Single-objective and multi-objective examples are presented as robust candidates for the application of quantum machine learning. Moreover, a discussion about quantum supremacy estimation for this problem is provided.