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arXiv:quant-ph/0309192 · Physical Review Letters

Dynamical Localization and Repeated Measurements in a Quantum Computation Process

M. Terraneo, Dima L. Shepelyansky

Published Jan 22, 2004• 8 citations
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Abstract

We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability spreading, our results demonstrate that localization can be preserved for repeated single-qubit measurements. We detect a transition from a localized to a delocalized phase, depending on the system parameters and on the choice of the measured qubit.

DOI
10.1103/physrevlett.92.037902

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We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability spreading, our results demonstrate that localization can be preserved for repeated single-qubit measurements. We detect a transition from a localized to a delocalized phase, depending on the system parameters and on the choice of the measured qubit.
This paper presents the first experimental evidence of the transition from dynamical localization to delocalization under the influence of a quasiperiodic driving on a quantum system. A quantum kicked rotator is realized by placing cold atoms in a pulsed, far-detuned, standing wave. If the standing wave is periodically pulsed, one observes the suppression of the classical chaotic diffusion, i.e., dynamical localization. If the standing wave is pulsed quasiperiodically, dynamical localization is observed or not, depending on the driving frequencies being commensurable or incommensurable. One can thus study the transition from the localized to the delocalized case as a function of the effective dimensionality of the system.
We investigate a quantum algorithm that simulates efficiently the quantum kicked rotator model, a system that displays rich physical properties and enables to study problems of quantum chaos, atomic physics, and localization of electrons in solids. The effects of errors in gate operations are tested on this algorithm in numerical simulations with up to 20 qubits. In this way various physical quantities are investigated. Some of them, such as second moment of probability distribution and tunneling transitions through invariant curves, are shown to be particularly sensitive to errors. However, investigations of the fidelity and the Wigner and Husimi distributions show that these physical quantities are robust in presence of imperfections. This implies that the algorithm can simulate the dynamics of quantum chaos in presence of a moderate amount of noise.