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INVARIANT SUBSPACES AND CONTROL OF DECOHERENCE

Paolo Facchi A, V.L. LEPORE, Saverio Pascazio

Published Mar 1, 2006• 0 citations
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Abstract

We discuss three control strategies, all aimed at countering the effects of deciherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses) and the third of a strong, continuous coupling. Decoherence is suppressed if the frequency N of the measurements/pulses is large enough or if the coupling K is sufficiently strong. However, if N or K are large, but not sufficiently large, all procedures accelerate decoherence.

DOI
10.1142/9789812774491_0008

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We discuss three control strategies, all aimed at countering the effects of deciherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses) and the third of a strong, continuous coupling. Decoherence is suppressed if the frequency N of the measurements/pulses is large enough or if the coupling K is sufficiently strong. However, if N or K are large, but not sufficiently large, all procedures accelerate decoherence.
We discuss three control strategies, whose objective is to counter the effects of decoherence: the first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses), and the third of a strong, continuous coupling. Decoherence can be suppressed only if the frequency τ-1 of the measurements/pulses is large enough or if the coupling K is sufficiently strong. Otherwise, if τ-1 or K are large, but not sufficiently large, all these control procedures accelerate decoherence.
We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (``bang-bang'' pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency NNN of the measurements or pulses is large enough or if the coupling KKK is sufficiently strong. Otherwise, if NNN or KKK is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.
We discuss three control strategies aimed at countering the effects of decoherence: the first hinges on frequent projective measurements, the second on frequent unitary "kicks" ("bang-bang" pulses) and the third on a strong continuous coupling. Decoherence is suppressed if the frequency N of the measurements/kicks is large enough or if the coupling K is sufficiently strong: in all these cases, the Hilbert space of the system splits into invariant subspaces, among which any transition is hindered. However, if N or K are large, but not extremely large, all these control procedures accelerate decoherence.
To suppress the decoherence, in addition to error-correcting codes and the error-avoiding codes, bang-bang control has also been introduced. Here in this work, we discuss how to suppress decoherence in quantum systems using bang-bang control, two cases have been discussed, adiabatic decoherence alone, and decoherence with both phase and amplitude damping. We also discussed the different cases when the system is made up of one atom or multi-atom and when such atom with two level or multi-level. It is found that in all the above cases, bang-bang control can suppress decoherence effectively.
We present a strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir. We discuss the applicability of this strategy by studying the dependence of the decoherence suppression on the shape of the coupling spectral density. We find that the effectiveness of this strategy arises from the non-Markovian nature of dynamical motion of the reservoir.