A new study reveals that adding links to a network does not always improve coherent quantum transport, and can even penalize it. Unlike classical transport, where more connections generally facilitate flow, researchers have identified a "coherent overconnectivity penalty" in percolated hierarchical small-world networks. Coherent quantum transport from the root to the boundary of the network is maximized at an intermediate bond probability and decreases as the network approaches full connectivity. This unexpected behavior stems from a complex interplay between shortcut-assisted spreading and interference-induced intra-layer recirculation.

The authors quantify this effect using the final-layer limiting probability, $\chi_N$, and a penalty $P_Q = 1 - \chi_N(p=1) / \max_p \chi_N(p)$, which measures the performance loss when the architecture is fully connected. Spectral analysis suggests that bond dilution creates motif-induced degeneracies and reorganizes the eigenstates connecting the root to the outermost layer. This reorganization is key to understanding why lower connectivity can be beneficial.

Comparison with classical and dephased transport demonstrates that this non-monotonic landscape is not merely a geometrical percolation effect, but a coherent architecture-dependent phenomenon. These findings provide a fundamental design principle for coherent transport in disordered photonic and quantum-network architectures, suggesting that optimization does not lie in maximum connectivity, but in a balance that avoids destructive interference.