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Photonics

Hybrid Quantum–Classical Computing for Multi-Objective Resource Allocation in Elastic Optical Networks

Bakhe Nleya, Beverly Pule

Published May 9, 2026• 1 citation
Publisher

Abstract

The rapid advancement of beyond-5G and 6G services is creating computational challenges that classical optimisation methods for Elastic Optical Networks (EONs) cannot effectively handle. Specifically, the multi-objective Routing and Spectrum Assignment (RSA) problem—aimed at minimising blocking probability, maximising spectral efficiency, and reducing fragmentation—poses significant challenges and is NP-hard, particularly in dynamic traffic. This paper introduces a hybrid framework that combines quantum and classical computing, dividing the optimisation tasks into classical pre-processing, a quantum optimisation core, and classical post-processing with Pareto frontier management. The RSA problem is modelled using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation that accounts for blocking, efficiency, and a quadratic fragmentation metric. Simulations conducted on NSFNET and UBN topologies under Poisson traffic conditions revealed that even in realistic, noisy quantum environments, this hybrid method reduces the blocking probability by 14% and improves fragmentation by 7.3% compared to the top classical heuristics. A scaling analysis indicates a key point of around 220 variables where this hybrid strategy surpasses traditional meta-heuristics in both solution quality and execution time, emphasising its significant potential in the current NISQ era.

DOI
10.3390/photonics13050472

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The rapid advancement of beyond-5G and 6G services is creating computational challenges that classical optimisation methods for Elastic Optical Networks (EONs) cannot effectively handle. Specifically, the multi-objective Routing and Spectrum Assignment (RSA) problem—aimed at minimising blocking probability, maximising spectral efficiency, and reducing fragmentation—poses significant challenges and is NP-hard, particularly in dynamic traffic. This paper introduces a hybrid framework that combines quantum and classical computing, dividing the optimisation tasks into classical pre-processing, a quantum optimisation core, and classical post-processing with Pareto frontier management. The RSA problem is modelled using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation that accounts for blocking, efficiency, and a quadratic fragmentation metric. Simulations conducted on NSFNET and UBN topologies under Poisson traffic conditions revealed that even in realistic, noisy quantum environments, this hybrid method reduces the blocking probability by 14% and improves fragmentation by 7.3% compared to the top classical heuristics. A scaling analysis indicates a key point of around 220 variables where this hybrid strategy surpasses traditional meta-heuristics in both solution quality and execution time, emphasising its significant potential in the current NISQ era.
Flexi-grid technology has revolutionized optical networking by enabling Elastic Optical Networks (EONs) that offer greater flexibility and dynamism compared to traditional fixed-grid systems. As data traffic continues to grow exponentially, the need for efficient and scalable solutions to the routing and spectrum assignment (RSA) problem in EONs becomes increasingly critical. The RSA problem, being NP-Hard, requires solutions that can simultaneously address both spatial routing and spectrum allocation. This paper proposes a novel quantum-based approach to solving the RSA problem. By formulating the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model, we employ the Quantum Approximate Optimization Algorithm (QAOA) to effectively solve it. Our approach is specifically designed to minimize end-to-end delay while satisfying the continuity and contiguity constraints of frequency slots. Simulations conducted using the Qiskit framework and IBM-QASM simulator validate the effectiveness of our method. We applied the QAOA-based RSA approach to small network topology, where the number of nodes and frequency slots was constrained by the limited qubit count on current quantum simulator. In this small network, the algorithm successfully converged to an optimal solution in less than 30 iterations, with a total runtime of approximately 10.7 s with an accuracy of 78.8%. Additionally, we conducted a comparative analysis between QAOA, integer linear programming, and deep reinforcement learning methods to evaluate the performance of the quantum-based approach relative to classical techniques. This work lays the foundation for future exploration of quantum computing in solving large-scale RSA problems in EONs, with the prospect of achieving quantum advantage as quantum technology continues to advance.
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 exponential growth of global network traffic has made the expansion of network capacity increasingly urgent. Multi-band and flexible grid technologies have emerged as promising solutions to enhance network transmission capacity. Fast routing is an important measure to ensure the survivability of a multi-band flexible optical network (MB-FON) that carries massive services. However, the extensive network resources and the inter-channel stimulated Raman scattering (ISRS) effect between different bands pose a challenge to the efficient solution of classical routing, modulation, and spectrum allocation (RMSA) methods. This paper leverages the parallel computing advantage of quantum computing and proposes a hybrid quantum-classical computing mechanism for quality of transmission (QoT)-aware dynamic RMSA in MB-FON. In this mechanism, a decouple-then-integrate strategy is proposed to formulate the QoT-aware RMSA problem as a quadratic unconstrained binary optimization model. The augmented Lagrangian method is introduced to deal with the inequality constraint in an ISRS-aware formulation, and a path fragmentation metric is proposed to design the optimization objective. In addition, a coherent Ising machine is used to solve the problem by adjusting the parameters and precision in combination with classical computing methods. Experiments were conducted on network topologies of different sizes. The experimental results show that the solution time can be reduced from nearly 6 s to 537 µs compared with the auxiliary graph-based heuristic algorithm in a 142-node network. It also demonstrates that the proposed mechanism outperforms classical heuristic algorithms in terms of blocking probability and spectrum utilization.
Resource Allocation in quantum key distribution-enabled optical networks (QKD-ON) is an NP-hard combinatorial problem. Classical heuristics are greedy and suffer high blocking under dynamic traffic and security constraints, while deep reinforcement learning (DRL) methods can reduce blocking but introduce a processing bottleneck because their inference latency is often slower than the operational timescales of QKD-ON. We introduce hybrid quantum–classical frameworks using the quantum approximate optimization algorithm (QAOA) and variational quantum eigensolver (VQE) to perform request routing. The scheduling problem is encoded as a hamiltonian with penalty terms for wavelength and timeslot conflicts. We evaluate the approach on NSFNet and UBN topologies under dynamic traffic with time division multiplexing (TDM) and wavelength-time division multiplexing (WTDM). Our quantum-enhanced algorithms yield comparable or lower blocking with reduced inference latency, which can improve further on quantum hardware.
A challenge for scalability of demand-responsive, elastic optical Dense Wavelength Division Multiplexing (DWDM) and Flexgrid networks is the computational complexity of allocating many optical routes on large networks. We demonstrate that demand satisfaction problems in communication networks can be formulated as quadratic unconstrained binary optimisation (QUBO) problems, and solved using a hybrid quantum annealer. Efficient encodings are developed which solve both unicast and multicast multicommodity-flow problems, while also adhering to individual requirements for maximum latency and resilience for each route. We present several QUBO formulations and analyse the qubit scaling. We demonstrate solutions using a hybrid solver, D-Wave Quantum Advantage QPU. Progress in generating optimal solutions with efficient use of computational resources will be beneficial to telecoms operators, enabling them to run dynamic optical network infrastructures which use resources efficiently, are resilient to local faults and cyber-attacks, and can be elastically responsive to demands.
Optical communications provide high capacity and scalability, while quantum communications, particularly through quantum key distribution (QKD), enable information-theoretic security. However, it still remains challenging to deliver both high throughput communication and long-term security within a hybrid quantum-classical optical network. Specifically, classical optical resources can be reallocated to support QKD, aiming to achieve synergistic resource utilization that surpasses the sum of individual functionalities. In this work, we formulate a networking model that captures the resource allocation constraints, aiming to figure out the necessary conversion of classical optical resources to QKD capacity while maintain the connectivity of classical optical communication. Based on that, we propose a synergistic resource allocation strategy, implemented through heuristic routing, wavelength assignment, and power configuration (SRWP) algorithms. Simulation results demonstrate that the proposed SRWP algorithm, with the objective of network-wide average secret key rate (SKR) maximization (SRWP-ARM), enhances the average SKR from the order of kbit/s to Mbit/s at GHz-level pulse repetition rates. In a 9-node mesh network topology with 50 km links, the algorithm achieves this gain with zero service blocking under a traffic load of 100 erlangs. At a higher load of 300 erlangs, it maintains a service blocking probability as low as 1.24% while still achieving an average SKR of 18.05 kbit/s. This represents the best trade-off between classical service connectivity and secret key generation across all evaluated algorithms.