This paper explores the enhancement of quantum networks, both standard and entanglement-based, by enabling them to handle superposed tasks and superposed addressing. This is achieved using a quantum control register that specifies tasks and their weights coherently. While directly adding coherent control to classical tasks is generally impossible, the authors introduce protocols that mimic this behavior by always performing the classical task on either the desired state or a dummy state. Examples illustrate the advantages of superposed tasks, including preparing superpositions of target states, sending quantum information through superposed paths, and addressing devices in superposition. The work extends known techniques such as quantum forking and introduces a quantum addressing procedure for complete functionality.

J. Miguel-Ramiro, A. Pirker, W. Dür