Blended Dynamics and Emergence in Open Quantum Networks

In this paper, we develop a blended dynamics framework for open quantum networks with diffusive couplings. The network consists of qubits interconnected through Hamiltonian couplings, environmental dissipation, and consensus-like diffusive interactions. Such networks commonly arise in spontaneous emission processes and non-Hermitian quantum computing, and their evolution follows a Lindblad master equation. Blended dynamics theory is well established in the classical setting as a tool for analyzing emergent behaviors in heterogeneous networks with diffusive couplings. Its key insight is to blend the local dynamics rather than the trajectories of individual nodes. Perturbation analysis then shows that, under sufficiently strong coupling, all node trajectories tend to stay close to those of the blended system over time. We first show that this theory extends naturally to the reduced-state dynamics of quantum networks, revealing classical-like clustering phenomena in which qubits converge to a shared equilibrium or a common trajectory determined by the quantum blended reduced-state dynamics. We then extend the analysis to qubit coherent states using quantum Laplacians and induced graphs, proving orbit attraction of the network density operator toward the quantum blended coherent dynamics, establishing the emergence of intrinsically quantum and dynamically clustering behaviors. Finally, numerical examples validate the theoretical results.