Unveiling noiseless clusters in complex quantum networks

The transport and storage of quantum information, excitations, and entanglement, within and across complex quantum networks is crucially affected by the presence of noise induced by their surroundings. Generally, the interaction with the environment deteriorates quantum properties initially present, thus limiting the efficiency of any quantum-enhanced protocol or phenomenon. This is of key relevance, for example, in the design of quantum communication networks and for understanding and controlling quantum harvesting on complex systems. Here, we show that complex quantum networks, such as random and small-world ones,
can admit noiseless clusters for collective dissipation. We characterize these noiseless structures in connection to their topology addressing their abundance, extension, and configuration, as well as their robustness to noise and experimental imperfections. We
show that the network degree variance controls the probability to find noiseless modes and that these are mostly spanning an even number of nodes, like breathers. For imperfections across the network, a family of quasi-noiseless modes is also identified shielded by noise up to times decreasing linearly with frequency inhomogeneities. Large noiseless components are shown to be more resilient to the presence of detuning than to differences in their coupling strengths. Finally, we investigate the emergence of both stationary and transient quantum synchronization showing that this is a rather resilient phenomenon in these networks.