Quantum computation of the Anderson transition in presence of imperfections

Andrei A. Pomeransky, Dima L. Shepelyansky

Published 2003-06-30Version 1

We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a quadratic speedup in computation of diffusion rate and localization length, comparing to the known classical algorithms. We show that the Anderson transition can be detected on quantum computers with $7 - 10$ qubits.