We show how to make quantum networks, both standard and entanglement-based, genuine
quantum by providing them with the possibility of handling superposed tasks and
superposed addressing. This extension of their functionality relies on a quantum control
register, which specifies not only the task of the network, but also the corresponding weights
in a coherently superposed fashion. Although adding coherent control to classical tasks,
such as sending or measuring—or not doing so—is in general impossible, we introduce …