Optimizing Fractional Routing with Algebraic Transformations, AI, and Quantum Computing for Next-Generation Networks

In fractional routing, the flows are distributed through different paths; this allows the maximum efficiency to be achieved by using several partial capacities to balance flow. However, the mathematical formalism for dynamic and scalable implementation is yet to be developed. This paper proposes the aforementioned hybrid framework of edge-linear transformations, AIs, and QCs for fractional routing optimizations. The system encodes flows by means of vector linear transformations over finite fields, supports real-time reconfiguration via deep reinforcement learning, and employs quantum algorithms such as QAOA and HHL for efficient minimization of path costs. The Python 3-based implementations of the model were utilized to test DAGs of a small- and medium-scale, showing a 30% increase in computational efficiency and a 25% drop in runtime compared to classical implementations. The evidence states that the practical-scalability results can be used for the real-time applications of emerging IoT and 6G networks.