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arXiv:quant-ph/9803057 · Physical Review A

Dynamical suppression of decoherence in two-state quantum systems

Lorenza Viola, Seth Lloyd

Published Oct 1, 1998• 1,580 citations
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Abstract

The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.

DOI
10.1103/physreva.58.2733

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The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.
In this paper, we have detailedly studied the dynamical suppression of the phase damping for the two-qubit quantum memory of Ising model by the quantum ``bang-bang" technique. We find the sequence of periodic radio-frequency pulses repetitively to flip the state of the two-qubit system and quantitatively find that these pulses can be used to effectively suppress the phase damping decoherence of the quantum memory and freeze the system state into its initial state. The general sequence of periodic radio-frequency pulses to suppress the phase damping of multi-qubit of Ising model is also given.
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 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.
The pulse control of decoherence in a qubit interacting with a quantum environment is studied with focus on a general case where decoherence is induced by both pure dephasing and population decay. To observe how the decoherence is suppressed by periodic pi pulses, we present a simple method to calculate the time evolution of a qubit under arbitrary pulse sequences consisting of bit-flips and/or phase-flips. We examine the effectiveness of the two typical sequences: bb sequence consisting of only bit-flips, and bp sequence consisting of both bit- and phase-flips. It is shown that the effectiveness of the pulse sequences depends on a relative strength of the two decoherence processes especially when a pulse interval is slightly shorter than qubit-environment correlation times. In the short-interval limit, however, the bp sequence is always more effective than, or at least as effective as, the bb sequence.
Dynamical control of decoherence induced by the environment in a single quantum-bit system is investigated. We choose the suitable perturbations acting on the qubit system to decrease the decoherence due to pure amplitude damping. The scheme proposed here is based on the free-Hamiltonian-elimination technique and the parity-kick technique, which concludes two homogeneous classical large-blue-detuned optical fields with different frequencies added to the qubit system. By applying this scheme, the decoherence can be completely suppressed.
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.