Stability of Continuous Time Quantum Walks in Complex Networks

We investigate the stability of continuous time quantum walks (CTQWs) in a range of network topologies under different decoherence mechanisms, defining stability as the system's ability to preserve quantum properties over time. The networks studied range from homogeneous to heterogeneous structures, including cycle, complete, Erdős-Rényi, small-world, scale-free, and star topologies. The decoherence models considered are intrinsic decoherence, Haken-Strobl noise, and quantum stochastic walks (QSWs). To assess quantum stability, we employ several metrics: node occupation probabilities, the ₁-norm of coherence, fidelity with the initial state, quantum-classical distance, and von Neumann entropy. Our results reveal that the interplay of both network topology and decoherence model influences coherence preservation. Intrinsic decoherence results in the slowest decay of coherence, followed by Haken-Strobl noise, while QSW causes the most rapid loss of coherence. The stability ranking among network topologies varies depending on the decoherence model and quantifier used. For example, under Haken-Strobl and intrinsic decoherence, the quantum-classical distance ranks the cycle network more stable than scale-free networks, although other metrics consistently favour scale-free topologies. In general, heterogeneous networks, such as star and scale-free networks, exhibit the highest stability, whereas homogeneous topologies, such as cycle and Erdős-Rényi networks, are more vulnerable to decoherence. The complete graph, despite its homogeneity, remains highly stable due to its dense connectivity. Furthermore, in heterogeneous networks, the centrality of the initialised node, measured by degree or closeness, has a pronounced impact on stability, underscoring the role of local topological features in quantum dynamics.