In a paper published in the journal Photonics, researchers presented a quantum-based solution for the routing and spectrum assignment (RSA) problem in elastic optical networks (EONs). By framing RSA as a quadratic unconstrained binary optimization (QUBO) model, they utilized the quantum approximate optimization algorithm (QAOA) to minimize delay while meeting spectrum constraints.
Simulations with a small network topology confirmed the approach’s efficiency, achieving an optimal solution in under 30 iterations. This study highlighted the potential of quantum computing for scalable RSA solutions in EONs.
Study: Novel Application of Quantum Computing for Routing and Spectrum Assignment in Flexi-Grid Optical Networks. Image Credit: metamorworks/Shutterstock.com
Related Work
Past work on EONs highlighted the limitations of traditional fixed-grid systems, emphasizing the need for flexible, scalable solutions as data traffic grows. While integer linear programming (ILP) and deep reinforcement learning (DRL) have been applied to the RSA problem, they struggle with high computational demands and adapting to real-time traffic changes.
Quantum computing (QC) offers a promising alternative by leveraging quantum parallelism to efficiently address RSA’s nondeterministic polynomial-time (NP)-hard complexity.
Quantum Solutions for RSA Optimization
This work explores recent advancements in QC for solving the RSA problem in EON, focusing on noisy intermediate-scale quantum (NISQ) devices. Variational quantum algorithms (VQAs), particularly the QAOA, were used to map the RSA problem as a QUBO model.
The QAOA’s hybrid quantum-classical loop iteratively optimized circuit parameters, effectively finding solutions with manageable noise. The proposed QC approach enables efficient spectrum allocation, advancing QC’s application potential in large-scale optimization tasks.
QAOA for Efficient RSA Solutions
The section explains how the QAOA is applied to the RSA problem within EONs. The RSA problem in EONs is formulated mathematically to optimize path selection and spectrum allocation for traffic demands constrained by delay, spectrum contiguity, and continuity.
This model represents the network as a directed graph where nodes correspond to optical switches and edges to optical links, each accommodating a fixed number of frequency slots (FSs). Available slots are in blue, and occupied ones are in red for spectrum allocation. Traffic demands, defined by their source, destination, and requested slots, must meet contiguity and continuity requirements across links.
The RSA problem consists of routing for optimal path determination and spectrum assignment for contiguous FS allocation, modeled with decision variables and constraints to ensure flow conservation and spectrum capacity while minimizing total delay for each allocation. To solve RSA with QAOA, the problem is mapped to a QUBO format, translating constraints into a quadratic cost function.
Decision variables are represented in a binary vector, with a penalty matrix enforcing constraints. The QAOA Ansatz circuit uses qubits to represent FS availability. An initial layer of Hadamard gates creates a superposition, followed by cost function-specific operations to find optimal FS allocations.
This mapping allows the RSA problem to be addressed using quantum computation, aiming for efficient solutions in complex optical networks.
Simulation Results and Analysis
The simulation results are discussed, focusing on a case study to evaluate the proposed QC-based approach for solving the RSA problem. A comparative analysis was conducted against classical methods, specifically ILP and DRL, examining factors such as solution quality, time-to-solution, scalability, and real-time adaptability.
The simulations were executed on various graphs using the Qiskit framework quantum simulator with 32 qubits. The optimization parameters were adjusted using the constrained optimization by linear approximation (COBYLA) optimizer.
The simulation graph represented a scenario involving five available FS per edge and a traffic request from node 0 to node 3 requiring two contiguous spectrum slots. The tuning penalties were set to maintain the constraints during the simulations.
The QAOA algorithm utilized parameters β and γ to effectively explore the solution space, with β facilitating configuration exploration and γ minimizing the QUBO function for optimal routing paths and spectrum assignments, ultimately converging to a minimum energy state.
The results indicated a notable drop in energy, particularly at iteration 24, suggesting convergence towards optimal configurations with a significant sampling probability of the optimal bitstring.
The overall optimization process was completed efficiently, taking approximately 10.7 seconds, and the QAOA algorithm achieved an approximation ratio of 0.788, demonstrating its ability to identify correct routing paths and spectrum assignments. However, the objective value could have been more perfectly optimal.
The discussion highlighted the limitations of current quantum hardware, noting that the number of qubits needed for the QAOA scales with network size. At the same time, a comparative analysis of QAOA, ILP, and DRL emphasized the challenges of scalability and training time. Despite the promise of quantum computing methods like QAOA, their practical application necessitates further research and development.
Conclusion
To sum up, the paper presented a quantum-based solution for the RSA problem in EONs by formulating it as a QUBO model for the QAOA. The algorithm converged to an optimal solution in under 30 iterations, achieving a solution quality of 78.8% within a runtime of approximately 10.7 seconds.
A comparative analysis showed that while ILP provided optimal solutions, it lacked scalability, and DRL required extensive training. The findings highlighted QAOA's potential for scalability and time-to-solution, suggesting that ongoing advancements in quantum technology could enhance its applicability in large-scale networks.
Journal Reference
Bouchmal, O., et al. (2024). Novel Application of Quantum Computing for Routing and Spectrum Assignment in Flexi-Grid Optical Networks. Photonics, 11:11, 1023. DOI:10.3390/photonics11111023. https://www.mdpi.com/2304-6732/11/11/1023
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