Stability of continuous time quantum walks in complex networks

Abstract

Understanding how decoherence disrupts quantum walks is vital for developing robust quantum technologies, as environmental interactions often degrade quantum properties or induce transitions to classical random walks. We investigate the stability of continuous-time quantum walks across different network topologies subjected to three distinct decoherence mechanisms: energy-based intrinsic decoherence, node-based Haken–Strobl noise, and edge-based quantum stochastic walk. By defining stability as the preservation of quantum properties, we find that densely connected networks, such as the complete network, and hub dominated networks, such as scale-free and star topologies, are stable under Haken–Strobl noise but become uniquely vulnerable under quantum stochastic walk. However, these same networks exhibit lower coherence in the noiseless regime due to their inherent localization, highlighting a fundamental trade-off between localization and coherence. Furthermore, the centrality of the initialization node has a pronounced impact on relaxation time, underscoring the critical role of local topological features in quantum dynamics.