Exponential Gain in Quantum Computing of Quantum Chaos and Localization

Abstract

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.

final published version

References in corpus (6)

• Quantum Mechanics helps in searching for a needle in a haystack
• Quantum Computing
• Spin-spin interaction and spin-squeezing in an optical lattice
• Experimental evidence of dynamical localization and delocalization in a quasi-periodic driven system
• Using a quantum computer to investigate quantum chaos
• Quantum computing of quantum chaos and imperfection effects

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