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arXiv:2411.05180

Quantum Speed Limit Time in two-qubit system by Dynamical Decoupling Method

Arefeh Aaliray, Hamidreza Mohammadi

Published Nov 7, 2024• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2411.05180

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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.
In this paper, we investigate the connection between quantum speed limit time and non-Markovianity by combining the concept of two-qubit maximally entangled mixed state for various correlated noise channels. In particular, we find an inverse relation between them, which means that the non-Markovian feature of the quantum process leads to speedup of evolution in terms of correlations between successive uses of noise channels because of various. Parameters, such as correlations, entanglement, get involved in it. As a result of this study, new insights are gained into the control of QSL time for open systems, which opens the door to further experimental development toward the development of quantum thermodynamic devices and quantum computers. Our results shed light into trace back of information from environment which might be useful for quantum information processing task.
We theoretically study the quantum speed limits (QSLs) of a qubit system coupled to a thermal dephasing environment with an Ohmic-like spectral density. Based on the geometric QSLs time bound, which is derived by employing the trace distance to quantify the geodesic between two distinguishable states in dynamical evolution, we study the influences of the temperature and spectral density of the environment on the QSLs time of the dephasing qubit. We also investigate the interplay between the QSLs time, the environmental temperature, and the spectral density of the environment. It has been demonstrated that the QSLs time closely depends on the transition frequency and the dynamical behavior (e.g., coherence trapping) of the dephasing qubit. For a fixed Ohmicity parameter of the environmental spectral density, the increase in environmental temperature can enhance the QSLs time bound. In addition, when the environmental temperature remains constant, the increase in the Ohmicity parameter initially leads to a reduction in the QSLs time bound, which is then followed by an increase in the time bound of QSLs. Our results can help to better understand the QSLs in the dynamics of open quantum systems and have potential application in the modulation of QSLs time in the dephasing qubit by engineering the spectral density of the environment.
Characterizing the most efficient evolution, the quantum speed limit (QSL) plays a significant role in quantum technology. How to generalize the well-established QSL from closed systems to open systems has attracted much attention. In contrast to the previous schemes to derive the QSL from the reduced dynamics of open systems, we propose a QSL bound from the point of view of the total system consisting of the open system and its environment using a quantum-state-diffusion method. The application of our scheme to a two-level system reveals that the system possesses an infinite speedup capacity in the noiseless case, which is destroyed by the environment under the Born-Markovian approximation. It is interesting to find that the capacity in the noiseless case is recovered in the non-Markovian dynamics as long as a bound state is formed in the energy spectrum of the total system. Enriching the characterization schemes of the QSL, our result provides an efficient way to control the QSL of open systems.
The quantum speed limit (QSL) is a theoretical lower bound of the time required for a quantum system to evolve from an arbitrary initial state to its orthogonal counterpart. This figure can be used to characterize the dynamics of open quantum systems, including non-Markovian maps. In this paper, we investigate the QSL time for a model that consists of a single qubit moving inside a leaky cavity. Notably, we show that for both weak and strong coupling regimes, the QSL time increases while we boost the velocity of the qubit inside the leaky cavity. Moreover, it is observed that by increasing the qubit velocity, the speed of the evolution tends to a constant value, and the system becomes more stable. The results provide a better understanding of the dynamics of atom-photon couplings and can be used to enhance the controllability of quantum systems.
Abstract The minimum evolution time between multi-qubit quantum states is estimated for non-Markovian quantum channels. We consider the maximally coherent pure and mixed states as well as multi-qubit X states as initial states and discuss the impact of initial coherence and the behaviour of coherence on their speed of evolution for both dephasing and dissipative processes. The role of the non-zero value of initial coherence under information backflow conditions for the non-unital dissipative process is revealed by the flow of quantum speed limit time ( τ QSL ). The trade-off between mixedness and coherence on the speed limit time reveals the nature of the quantum process the states undergo. The complementarity effect between mixedness and coherence is more prominent in the quantum non-unital dissipation process. The parametric trajectory of speed limit time vividly depicts the difference in the evolution of pure and mixed initial states, and this could be used to distinguish between the unital and non-unital channels studied in this work. Our investigation of quantum speed limit time on multi-qubit entangled X states reveals that τ QSL can be identified as a potential dynamical witness to distinguish multi-qubit states in the course of evolution.