Paper
Stability of Continuous Time Quantum Walks in Complex Networks
Authors
Adithya L J, Johannes Nokkala, Jyrki Piilo, Chandrakala Meena
Abstract
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 energy-based intrinsic decoherence, node-based Haken-Strobl noise, and edge-based quantum stochastic walks (QSWs). To assess quantum stability, we employ several metrics: node occupation probabilities, -norm of coherence fidelity with the initial state, quantum-classical distance, and von Neumann entropy. The stability ranking among network topologies varies depending on the decoherence model and the quantifier used. For example, we show that for Haken-Strobl noise, topologies like complete, star and scale-free with high degree nodes are most stable. Conversely, under the QSW decoherence, these same networks with initialization on high degree node becomes uniquely fragile, exhibiting rapid coherence loss. In general, networks such as star and scale-free networks, exhibit the highest stability in all cases except for QSW. However, these same networks, due to their high degree of localization, also show lower values of coherence even in the noiseless case, highlighting a fundamental trade-off between localization and coherence. Furthermore, in heterogenous networks, the centrality (degree or closeness) of the initialized node has a pronounced impact on stability, underscoring the critical role of local topological features in quantum dynamics.