Exponential Gain in Quantum Computing of Quantum Chaos and Localization
  We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps. 
B. Georgeot and D. L. Shepelyansky (CNRS, Toulouse)