In-Network Hamiltonian Engineering for 6G: Addressing the Quantum-Classical Temporal Mismatch via P4-Programmable Control Planes

The convergence of 6G telecommunications and distributed quantum computing (DQC) necessitates a paradigm shift from passive data transport to active, intelligent control fabrics. While 6G architectures increasingly embrace In-Network Computing (INC) to reduce latency, a fundamental temporal mismatch remains between the microsecond-scale jitter of packet switching and the nanosecond-scale coherence requirements of quantum systems (Urgelles et al., 2024). This paper proposes “Compute-on-Network Hamiltonian Engineering,” a novel architecture that embeds stochastic Hamiltonian control protocols directly into P4-programmable data planes. We introduce a Coherence-Aware Scheduling algorithm with admission control that synchronizes classical network control loops with quantum $T_2^*$ decay rates. Using a calibrated simulation environment validated against recent infrastructure prototypes (NTT Group, 2025), we demonstrate that our approach restores quantum fidelity from a baseline of 0.16 to 0.82 in distributed Variational Quantum Eigensolver (VQE) tasks. These findings suggest that 6G networks can serve as effective quantum control planes, provided that Hamiltonian dynamics are explicitly accounted for in the packet scheduling logic.