Connectivity--Interference Competition in Coherent Transport on Percolated Hierarchical Small-World Networks

• URL: http://arxiv.org/abs/2608.19130v1
• Date: Wed, 19 Aug 2026 17:26:32 GMT
• Title: Connectivity--Interference Competition in Coherent Transport on Percolated Hierarchical Small-World Networks
• Abstract summary: Adding links generally improves classical transport by increasing the number of available paths.<n>We show that coherent quantum transport can display the opposite behavior.<n>Results provide a design principle for coherent transport in disordered photonic and quantum-network architectures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Adding links generally improves classical transport by increasing the number of available paths. We show that coherent quantum transport can display the opposite behavior. Using continuous-time quantum walks on a percolated hierarchical small-world network, we identify a coherent overconnectivity penalty: root-to-boundary transport is maximized at intermediate bond probability and decreases as the network approaches full connectivity. The effect is quantified by the final-layer limiting probability $χ_N$ and by the penalty $P_Q=1-χ_N(p=1)/\max_pχ_N(p)$, which measures the loss caused by making the architecture fully connected. The optimum results from a competition between shortcut-assisted spreading and interference-induced intra-layer recirculation. Spectral analysis shows that bond dilution creates motif-induced degeneracies and reorganizes the eigenstates connecting the root to the outermost layer. A comparison with dephased and classical transport shows that the non-monotonic landscape is not a purely geometrical percolation effect, but a coherent architecture-dependent phenomenon. These results provide a design principle for coherent transport in disordered photonic and quantum-network architectures.

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