Exploring Dynamical Localization on a Quantum Information Processor

An experiment which investigates dynamical localization in an implementation of the quantum sawtooth map is presented. In the appropriate parameter regimes, the quantum sawtooth map produces localized states which have a characteristic localization length. This unique quantum behavior, which we observe in a nuclear magnetic resonance quantum information processor, can be used to assess the accuracy of control achieved in a quantum computation device. Measurement of the predicted localization length provides a quantitative measure of experimental control of quantum coherence.