We consider an agent on a fixed but arbitrary node of a known threshold network, with the task of detecting an unknown missing link. We obtain analytic formulas for the probability of success when the agent’s tool is the free evolution of a single excitation on an $\mathit{XX}$ spin system paired with the network. We completely characterize the parameters, which allows us to obtain an advantageous solution. From the results emerges an optimal (deterministic) algorithm for quantum search, from which a quadratic speedup with respect to the optimal classical analog and in line with well-known results in quantum computation is gained. When attempting to detect a faulty node, the chosen setting appears to be very fragile and the probability of success too small to be of any direct use.

• Received 21 September 2010

DOI:https://doi.org/10.1103/PhysRevA.83.012310