Study of localization in the quantum sawtooth map emulated on a quantum   information processor
  Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution. 
Michael K. Henry, Joseph Emerson, Rudy Martinez, and David G. Cory