Inferring quantum network topologies using genetic optimization of indirect measurements

The characterization of quantum networks is fundamental to understanding how energy and information propagates through complex systems, with applications in control, communication, error mitigation, and energy transfer. In this work, we explore the use of external probes to infer the network topology in the context of continuous-time quantum walks, where a single excitation traverses the network with a pattern strongly influenced by its topology. The probes act as decay channels for the excitation and can be interpreted as performing an indirect measurement on the network dynamics. By making use of a genetic optimization algorithm, we demonstrate that the data collected by the probes can be used to successfully reconstruct the topology of any quantum network with high success rates, where performance is limited only by computational resources for large network sizes. Moreover, we show that increasing the number of probes significantly simplifies the reconstruction task, revealing a trade-off between the number of probes and the required computational power.