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Scientific Reports

Control quantum evolution speed of a single dephasing qubit for arbitrary initial states via periodic dynamical decoupling pulses

Ya‐Ju Song, Qing-Shou Tan, Le‐Man Kuang

Published Mar 8, 2017• 22 citations
Publisher

Abstract

We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).

DOI
10.1038/srep43654

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International Journal of Modern Physics B•Jan 29, 2021•0 citations
We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).
Quantum state change can not occurs instantly, but the speed of quantum evolution is limited to an upper bound value, called quantum speed limit (QSL). Engineering QSL is an important task for quantum information and computation science and technologies. This paper devotes to engineering QSL and quantum correlation in simple two-qubit system suffering dephasing via Periodic Dynamical Decoupling (PDD) method in both Markovian and non-Markovian dynamical regimes. The results show that when decoupling pulses are applied to both qubits this method removes all undesirable effects of the dephasing process, completely. Applying the PDD on only one of the qubits also works but with lower efficiency. Additionally, ultra-high speedup of the quantum processes become possible during the pulse application period, for enough large number of pulses. The results is useful for high speed quantum gate implementation application.
Quantum state change cannot occur instantly, but the speed of quantum evolution is limited to an upper bound value, called quantum speed limit (QSL). Understanding the quantum speed limit time (QSLT) is fundamental to advancing the control and optimization of quantum systems under decoherence. While significant progress has been made for single-qubit systems, the dynamics of two-qubit systems remain less explored. Studying the effects of dynamical decoupling (DD), such as periodic dynamical decoupling (PDD), on QSLT in two-qubit systems provides an opportunity to explore how to approach coherence preservation, entanglement stabilization, and environmental noise suppression. This exploration can lead to optimized strategies for controlling the evolution of two-qubit systems, which serve as the foundation of quantum gates and scalable quantum architectures. By analyzing QSLT in two-qubit systems, this research seeks to find how DD techniques can be adapted to mitigate the adverse effects of decoherence and extend their coherence times. The insights from this work will also shed light on the role of non-Markovian effects in two-qubit systems, offering potential pathways for leveraging such phenomena to maintain quantum coherence. The results reveal that under special conditions when decoupling pulses are applied to both qubits, the PDD method can completely remove all undesirable effects of the pure dephasing process. Eventually, these findings try to bridge the gap between theoretical frameworks and practical applications in quantum technologies, aiming to develop high-performance quantum processors.
We present a method to accelerate the dynamical evolution of multiqubit open system by employing dynamical decoupling pulses (DDPs) when the qubits are initially in W-type states. It is found that this speed-up evolution can be achieved in both of the weak-coupling regime and the strong-coupling regime. The physical mechanism behind the acceleration evolution is explained as the result of the joint action of the non-Markovianity of reservoirs and the excited-state population of qubits. It is shown that both of the non-Markovianity and the excited-state population can be controlled by DDPs to realize the quantum speed-up.
We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform versus nonuniform delay times between pulses. In the limit of instantaneous bit-flip pulses, this is accomplished by establishing a different representation of the controlled qubit evolution, where the decoherence behavior after an arbitrary number of pulses is directly expressed in terms of the uncontrolled decoherence function. In particular, analytical expressions are obtained for approximation of the long- and short-term coherence behavior for both Ohmic and supra-Ohmic environments. By focusing on the realistic case of pure dephasing in an excitonic qubit, we quantitatively assess the impact of physical constraints on achievable pulse separations, and show that little advantage of high-level decoupling schemes based on concatenated or optimal design may be expected if pulses cannot be applied sufficiently fast. In such constrained scenarios, we demonstrate how simple modifications of repeated periodic-echo protocols can offer significantly improved coherence preservation in realistic parameter regimes. We expect similar conclusions to be relevant to other constrained qubit devices exposed to quantum or classical phase noise.
The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [ Phys. Rev. Lett . 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s . We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.
Dynamical decoupling (DD) technique is one of the most successful methods to suppress decoherence in qubit systems. In this paper, we studied a solvable pure dephasing model and investigated how DD sequences and initial correlations affect this system. We gave the analytical expressions of decoherence functions and compared the decoherence suppression effects of DD pulses in Ohmic, sub-Ohmic and super-Ohmic environments. Our results show that (1) The initial system-environment correlation will cause additional decoherence. In order to control the dynamic process of open quantum system more accurately and effectively, the initial correlation between the system and reservoir must be considered. (2) High frequency DD pulses can significantly reduce the amplitude of the decoherence function even in the presence of initial system-environment correlations.