Quantum speedup in a memory environment

Xu, Zhenyu; Luo, Shunlong; Yang, Wanli; Liu, Chen; Zhu, Shiqun

doi:10.1103/physreva.89.012307

Cited by 159 publications

(162 citation statements)

References 79 publications

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“…It indicates that the system presents a dramatic speedup and nonMarkovian effect. Although this result confirms the previous result that the quantum speedup connects directly with the non-Markovianity [25,28,33], the existence of the obvious threshold point η c inspires us to further pursue the hidden physical reason for the quantum speedup. Our main point is that the non-Markovian dynamics of an open system connects tightly with the energyspectrum characters of the total system consisting of the system and its environment.…”

supporting

confidence: 88%

“…The generic bound on the QSL time for both mixed and pure initial states has been obtained by introducing the relative purity [26] and the Hilbert-Schmidt product of operators [27,28] as distance measure. Deffner and Lutz [25] showed that non-Markovian effect characterized by non-Markovianity [29][30][31][32] can speed up quantum evolution, which has been verified in different settings [26,28,33,34]. A first experimental observation in cavity QED systems [35], where an atomic beam is treated as a controllable environment for the cavity field system, has confirmed such non-Markovianity-assisted speedup.…”

mentioning

confidence: 95%

“…Different from the widely studied Lorentzian spectrum [25,26,28,33,34], we here study the Ohmic kind of spectra with the spectral density J(ω) = ηω s ω…”

mentioning

confidence: 99%

“…Thus it is generic in open systems. Note that our mechanism cannot be captured by the previous treatment with Lorentzian spectrum [25,26,28,33,34], where the lower limit of the frequency integration in f (t − τ ) is artificially extended from 0 to −∞. This approximation is mathematically convenient but loses the availability of the bound state [40].…”

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confidence: 99%

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Mechanism for quantum speedup in open quantum systems

Liu

Yang

et al. 2016

Phys. Rev. A

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The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interests in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.PACS numbers: 03.65.Yz, 03.67.-a Introduction.-As one of the fundamental laws of nature, quantum mechanics imposes a bound on the evolution speed to quantum systems, the so-called quantum speed limit (QSL) [1][2][3][4][5]. It has recently attracted considerable attention and played remarkable roles in various areas of quantum physics including nonequilibrium thermodynamics [6], quantum metrology [7][8][9][10], quantum optimal control [11][12][13][14][15][16], quantum computation [17][18][19], and quantum communication [1,20]. The QSL time sets a bound on the minimal time a system needs to evolve between two distinguishable states, and it can be understood as a generalization of the time-energy uncertainty principle. For isolated systems, the QSL time under unitary evolution is determined by the maximum [21] of the Mandelstam-Tamm bound τ MT = π /(2∆E) [2,3] and Margolus-Levitin bound τ ML = π /(2Ē) [22], where ∆E andĒ are the fluctuation and mean value of the initialstate energy, respectively.Because of the inevitable interactions with the environments, quantum systems should be generally regarded as open systems. The decoherence effect resulting from the system-environment interactions would introduce remarkable influences on the QSL. Much effort has been made to explore the QSL of open system under the environment governed nonunitary evolution. A MandelstamTamm-type bound on the QSL time for pure initial states has been derived by using positive nonunitary maps [23,24]. Using a geometric approach, a unified bound on the QSL time including both Mandelstam-Tamm and Margolus-Levitin types has also been formulated [25]. The generic bound on the QSL time for both mixed and pure initial states has been obtained by introducing the relative purity [26] and the Hilbert-Schmidt product of operators [27,28] as distance measure. Deffner and Lutz [25] showed that non-Markovian effect character-

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supporting

confidence: 88%

mentioning

confidence: 95%

“…Different from the widely studied Lorentzian spectrum [25,26,28,33,34], we here study the Ohmic kind of spectra with the spectral density J(ω) = ηω s ω…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Mechanism for quantum speedup in open quantum systems

Liu

Yang

et al. 2016

Phys. Rev. A

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“…To apply the influence functional method to an open quantum system, the first step towards the dynamics of the reduced system is to compute the forward and backward propagators between certain initial and final states of the full system by choosing a convenient representation [14][15][16][17][18][19] . In the present work we use the coherent state representation, in which the basis of the Hilbert space for the environment consists of multi-mode bosonic coherent states…”

Section: ̂=̂+̂+̂mentioning

confidence: 99%

The Propagation of Spin Coherent States

2017

JCBSC

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Quantum speedup via engineering multiple environments

Wang

2017

Annalen der Physik

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Evolution speed of an open quantum system is vividly influenced by the structure of environments. The strong systemenvironment coupling is found to be able to accelerate quantum evolution. In this work, we propose a different method of governing the quantum speedup via engineering multiple environments. It is shown that, with a judicious choice of the number of coupling environments, the quantum speedup of an open system can be achieved even under weak system-environment coupling conditions. The mechanism for the speedup is due to the switch between Markovian and non-Markovian regions by manipulating the number of the surrounding environments. In addition, we verify the above phenomena by using quantum dots embedded in a planar photonic crystal under current technologies. These results provide a new degree of freedoms to accelerate quantum evolution of open systems. The strong systemenvironment coupling can speed up the quantum evolution process. This work shows that, via engineering multiple environments, one can speed up the evolution process even under weak coupling conditions.

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Quantum speedup in a memory environment

Cited by 159 publications

References 79 publications

Mechanism for quantum speedup in open quantum systems

Mechanism for quantum speedup in open quantum systems

The Propagation of Spin Coherent States

Quantum speedup via engineering multiple environments

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