Quantum computing of delocalization in small-world networks

O. Giraud, B. Georgeot, and D. L. Shepelyansky

Phys. Rev. E 72, 036203 – Published 2 September 2005

Abstract

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 an 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 speedup can be reached. We also investigate the robustness of the algorithm in presence of imperfections.