A Quantum Stochastic Walk Approach to Dynamic Multipath Routing under Correlated Cryptographic Degradation

Classical multipath routing protocols, including Equal-Cost Multi-Path (ECMP) and Shortest Path First (SPF), optimize for physical link metrics and are mathematically incapable of representing correlated algorithmic failure across cryptographic primitives. As financial-grade network architectures migrate to Post-Quantum Cryptography (PQC) under NIST mandate, this representational gap introduces a systemic risk: a zero-day compromise of a lattice-based algorithm (e.g., Module Learning With Errors, Module-LWE) leaves classical load balancers routing traffic into cryptographically compromised paths while all physical links remain active. This paper presents a Quantum Stochastic Walk (QSW) control plane operating over a Software-Defined Network (SDN), designed to detect and respond to correlated cryptographic degradation events. The architecture encodes heterogeneous PQC overhead Kyber (lattice, low latency), SPHINCS+ (hash, medium latency), and McEliece (code, high latency) into a utility vector u, and captures shared failure probability via a dual-covariance matrix Σ that decomposes network-layer and cryptographic-layer correlations with equal weight. A discretized approximation of the Gorini-Kossakowski- Lindblad-Sudarshan (GKLS) master equation evolves a density matrix ρ over N = 30 logical routing paths, blending coherent quantum channel dynamics with a classical Google-matrix baseline at mixing parameter ω = 0.2. The coherent update (V ρtV †) and stochastic update together carry an O(N3) periteration complexity, tractable for physical port densities up to N = 128. Upon simulation of a lattice-compromise shock event, the QSW engine redistributed traffic away from the compromised cluster reducing lattice-path utilization from 43.7% to 25.3% and increasing hash-based and code-based path utilization to 40.4% and 34.2%, respectively while maintaining 100% packet reachability throughout the transition. GPU/CPU convergence was achieved in 8.32 ms under the shock state. A 50-stream Non-Homogeneous Poisson Process (NHPP) traffic load with micro-burst injection confirmed correct multipath saturation at 188 Mbit/s aggregate throughput. The Python-based OpenFlow update latency of tflow mod ≈ 42 ms is identified as the binding deployment constraint, arising from OS-level user/kernel-space serialization; the required production path is migration to a P4 programmable data plane with native C++ or SmartNIC execution of the O(N3) tensor operations.