Quantum computing of delocalization in small-world networks

Olivier Giraud (1) , Bertrand Georgeot (1, 2) , Dima Shepelyansky (1)

1 ICQ - Cohérence Quantique (LPT)
2 LPT - Laboratoire de Physique Théorique

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.

Mots clés: ordinateur quantique; reseau small-world; localisation

Domaines: Physique Quantique [quant-ph]; Adaptation et Systèmes auto-organisés [nlin.AO]; Mécanique statistique [cond-mat.stat-mech]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Olivier Giraud, Bertrand Georgeot, Dima Shepelyansky. Quantum computing of delocalization in small-world networks. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2005, 72, pp.036203. ⟨10.1103/PhysRevE.72.036203⟩. ⟨hal-00004563⟩