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Results in Physics

Quantum speed limits of quantum system in colored environments

Longli Zheng, Yonggang Peng

Published Jan 6, 2024• 4 citations
Publisher

Abstract

In this paper, we investigate quantum speed limits (QSLs) of a two-level system in the colored environments which are described by stochastic processes. We present QSL can be affected by the correlation time, the partitions of the constituent elements of the two-level system in different colored environments: the Ornstein–Uhlenbeck environment, simple fluctuating bottleneck environment, and the Dichotomic (two-state) environment. The investigations provide us a potential way to manipulate the quantum speed limit time (QSLT) of the quantum system in the colored environments. Our results could provide different insights on quantum control technologies of QSL and decoherent dynamics for the quantum computation.

DOI
10.1016/j.rinp.2023.107315

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Limitations to the speed of evolution of quantum systems, typically referred to as quantum speed limits (QSLs), have important consequences for quantum control problems. However, in its standard formulation, is not straightforward to obtain meaningful QSL bounds for time-dependent Hamiltonians with unknown control parameters. In this paper we present a short introductory overview of quantum speed limit for unitary dynamics and its connection to quantum control. We then analyze potential methods for obtaining new bounds on control times inspired by the QSL. We finally extend the work in [Poggi, Lombardo and WisniackiEPL104 40005 (2013)] by studying the properties and limitations of these new bounds in the context of a driven two-level quantum system.

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In this paper, we investigate quantum speed limits (QSLs) of a two-level system in the colored environments which are described by stochastic processes. We present QSL can be affected by the correlation time, the partitions of the constituent elements of the two-level system in different colored environments: the Ornstein–Uhlenbeck environment, simple fluctuating bottleneck environment, and the Dichotomic (two-state) environment. The investigations provide us a potential way to manipulate the quantum speed limit time (QSLT) of the quantum system in the colored environments. Our results could provide different insights on quantum control technologies of QSL and decoherent dynamics for the quantum computation.
Abstract The time required for a given quantum system to evolve is known as the quantum speed limit (QSL), which can be used to characterize the speed of evolution of a quantum system. We study QSL time for Markovian and non-Markovian dynamics. Investigating the effect of QSL under non-unitary evolution is of fundamental interest. In this work, we derive QSL time for maximally entangled state and apply its results under various noise channels. We discuss measure of QSL, how correlations affect the rate of QSL. Further, we carried an investigation on connection between non-Markovianity and QSL. We show that the non Markovian evolution can speed up quantum evolution, therefore lead to smaller QSL time. We have established the connections between correlated channels, information loss and non-Markovianity. This theory may suggest some further connections to retrieve back information from surrounding and preserves decoherence.
Abstract In this paper, we have investigated the behavior alterations and properties of the quantum speed limit time (QSLT) under different parameters’ modulations, as well as its relation to the non-Markovianity of the system in the presence of random telegraph noise (RTN) and colored noise (CN). We found that when the switching rate of RTN and the power-law exponent of CN are varied, both QSLT and the non-Markovianity of the system change, and a specific negative correlation exists between them. We have also explored the consistency of the above-mentioned conclusions for both pure and mixed initial states. Our findings may be conducive to uncovering the mechanism of non-Markovian regulation of QSLT and providing possible artificial control schemes for this behavior.
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.
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.
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.
Limitations to the speed of evolution of quantum systems, typically referred to as quantum speed limits (QSLs), have important consequences for quantum control problems. However, in its standard formulation, is not straightforward to obtain meaningful QSL bounds for time-dependent Hamiltonians with unknown control parameters. In this paper we present a short introductory overview of quantum speed limit for unitary dynamics and its connection to quantum control. We then analyze potential methods for obtaining new bounds on control times inspired by the QSL. We finally extend the work in [Poggi, Lombardo and WisniackiEPL104 40005 (2013)] by studying the properties and limitations of these new bounds in the context of a driven two-level quantum system.