Quantum-Based Resilient Routing in Networks: Minimizing Latency Under Dual-Link Failures

Abstract: Network optimization problems represent large combinatorial search spaces that grow exponentially with network size, making them computationally intensive to solve. This paper addresses the latency-resilient Layer 3 routing optimization problem in telecommunications networks with predefined Layer 1 optical links. We formulate this problem as a graph-based optimization problem with the objective of minimizing latency, creating vertex-disjoint paths from each site to the internet backbone, and maximizing overall resiliency by limiting the impact of dual-link failures. By framing the problem as finding two disjoint shortest paths, coupled together with a resiliency component to the objective function, we establish a single formulation to produce optimal path design. The mathematical formulation was adapted to solve the problem using quantum approximate optimization algorithm (QAOA) executed over both quantum simulator and quantum hardware. QAOA was tested on a toy graph topology with 5 vertices and 7 edges and considering two limiting scenarios respectively representing independent (uncorrelated) link failures and highly correlated failure for one pair of edges. Both explored scenarios produced the optimal network design-corresponding to the valid solution with highest frequency of occurrence and minimum energy state, hence, validating the proposed formulation for optimizing Layer 3 routing on quantum systems of the future.

• The paper introduces a dual-objective formulation that minimizes latency while enhancing resilience through a tunable trade-off factor for dual-link failures.
• It employs ILP and QUBO formulations to model disjoint paths, validated via QAOA on both simulators and current quantum hardware.
• Empirical results demonstrate that, despite hardware limitations, error mitigation and robust quantum algorithms can recover optimal solutions in complex networks.

Quantum-Based Resilient Routing for Dual-Link Failures: An Expert Analysis

Problem Formulation and Novelty

The work titled "Quantum-Based Resilient Routing in Networks: Minimizing Latency Under Dual-Link Failures" (2602.04495) addresses a critical challenge in telecommunications network design: optimizing routing for both minimum latency and high resilience to correlated or independent dual-link failures in meshy, backbone-connected Layer 3 (L3) topologies. The central task is to compute two vertex-disjoint paths from each secondary site to a pair of internet backbone hubs, such that total latency is minimized and network resilience—quantified via a joint failure exposure metric—is simultaneously maximized.

This problem formulation advances existing models of the disjoint paths problem by incorporating a composite objective that includes not only the sum of latencies but also a quadratic term encoding cross-path correlated failure exposures. The novelty lies in:

• The explicit introduction of a dual-objective function combining latency minimization with a penalty term for joint path vulnerability, parameterized by a tunable trade-off factor.
• A new resilience metric based on joint probabilities of edge failures, adaptable to both independent and fully correlated failure regimes.
• The formalization and conjecture of the "min-prod" disjoint paths problem, whose complexity is postulated to be NP-hard, representing a departure from classical min-sum, min-max, and min-min objectives.

Mathematical Approach: ILP and QUBO Formulations

The problem is first posed as an integer linear program (ILP), where the decision variables encode path membership for edges and vertices, and constraints ensure flow conservation and strict vertex-disjointedness. The resilience term introduces a quadratic interaction over pairs of path edges, penalizing solutions where dual-paths traverse links with substantial joint failure probability.

The authors then derive a Quadratic Unconstrained Binary Optimization (QUBO) mapping, which is required for quantum implementation. Classical constraints are embedded via large penalty terms to ensure their enforcement in the quantum energy landscape. Notably, the quadratic nature of failure exposure integrates naturally into the QUBO framework, facilitating direct implementation in quantum algorithms designed for binary variables and pairwise interactions.

Quantum Algorithm: QAOA Deployment and Circuit Considerations

Solution on quantum hardware leverages the Quantum Approximate Optimization Algorithm (QAOA), aligning the QUBO cost Hamiltonian with physical qubit interactions. The cost and mixer Hamiltonians are alternately applied to an initial superposition over all feasible bitstrings, with the variational circuit depth (number of QAOA layers) balancing solution quality against practical circuit depth limitations.

Simulation and hardware experiments were executed using both high-depth (20-layer) realizations on the Classiq simulator and minimally viable (8-layer) circuits on IonQ Forte hardware. The experiments required up to 24 logical qubits for the toy scenarios, with gates counts scaling to several thousand, and employed error mitigation (de-biasing) to partially compensate for low two-qubit gate fidelities (~99.6%).

Numerical Results and Empirical Validation

Numerical validation was conducted on a representative small topology (5 vertices, 7 edges). In all scenarios, the highest-frequency solutions generated by QAOA matched brute-force optimal solutions, for both independent and strongly correlated link failure models.

Key Results

• For independent link failures, the QAOA solution produced the minimum total latency disjoint paths.
• For fully correlated edge failures, the optimizer preferred paths that avoided simultaneously traversing risk-coupled links, sacrificing some latency for superior resilience.
• QAOA achieved correct optimal solutions with non-trivial probability on both simulator and real quantum hardware, even with circuit fidelities that predicted much lower success rates—demonstrating the robustness and feasibility of the approach within current quantum technological limits.
• Error-mitigation techniques produced a measurable increase in the observed frequency of optimal valid solutions.

It is particularly significant that the quantum hardware results, despite fidelity and shot limitations, were able to recover true optima in the presence of a vast solution space (e.g., $2^{24}$ configurations).

Theoretical and Practical Implications

From a theoretical perspective, this contribution demonstrates the tractability—at small scales—of optimizing combinatorially complex, resilience-aware disjoint paths using quantum algorithms. The "min-prod" objective introduces a rigorous new paradigm for resilient network design in the face of correlated risks.

Practically, the dual ILP/QUBO formalism and QAOA implementation validate the potential for near-term quantum advantage in layered network optimization tasks. The scalability analysis highlights clear bottlenecks: both qubit count and circuit depth (determined by the required number of two-qubit gates and QAOA layers) are major limitations for deployment on realistic, production-scale topologies. The path to scalability will depend on continued improvements in hardware error rates (approaching 99.99% two-qubit gate fidelity) and increases in available qubits.

The framework is directly relevant for operators seeking algorithms with tunable trade-offs between latency and survivability, particularly under uncertain or correlated physical risk models (fiber cuts, regional disasters). With quantum hardware and simulators becoming increasingly accessible and economical, prospects for the real-world application of this class of algorithms are strong, especially as error rates fall and allowable circuit complexity rises.

Prospects for Future Development

The current methodology can be expanded in several directions:

• Extension to larger, real-world network graphs as hardware scales.
• Integration with hybrid quantum-classical solvers for even larger instance sizes.
• Development of more sophisticated error mitigation and circuit compilation strategies to maximize solution quality within fixed hardware budgets.
• Generalization of the framework to multi-terminal and multi-path requirements beyond two-way disjoint paths.
• Investigation of dynamic and stochastic network conditions, where quantum machine learning policies might optimize path selection adaptively.

Conclusion

This work provides a precise mathematical and algorithmic blueprint for solving latency-resilient, two-path routing under dual-link failures using emerging quantum optimization technologies. The dual ILP-QUBO formalism enables both classical and quantum solution approaches, with numerical results establishing correctness and feasibility for current quantum hardware on moderate instance sizes. The research offers a substantial theoretical and practical step towards quantum-enabled optimization for resilient telecommunications network design, with future progress contingent on ongoing hardware advancements and the maturation of quantum-classical algorithmic ecosystems.