Quantum computing of delocalization in small-world networks
  We study a quantum small-world network with disorder and show that the system exhibits a delocalization transition. A quantum algorithm is built up which simulates the evolution operator of the model in a polynomial number of gates for exponential number of vertices in the network. The total computational gain is shown to depend on the parameters of the network and a larger than quadratic speed-up can be reached.   We also investigate the robustness of the algorithm in presence of imperfections. 
O. Giraud, B. Georgeot and D.L. Shepelyansky