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Cited by 95Quantum Mechanics and ApplicationsQuantum Information and CryptographyAdvanced Thermodynamics and Statistical Mechanics

Classical-driving-assisted quantum speed-up

Open access
Zhang, Ying-Jie, Han, Wei, Xia, Yun-Jie, Cao, Jun-Peng, Fan, Heng·2015·Physical Review A
DOI 10.1103/physreva.91.032112
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Abstract

We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong system-environment couplings. By considering the relationship between non-Makovianity of environment and the classical field, we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of the classical field. That is the intrinsic physical reason that the classical field may induce the speed-up process. In addition, the role of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.

Verified 2026-10-06 · 36 references not checked yet

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes using an external classical driving field to speed up the evolution of a qubit coupled to a zero-temperature structured reservoir. It shows that the driving field can induce a transition from Markovian to non-Markovian dynamics, which is identified as the physical reason for the quantum speed-up.

Key findings

  • In the weak-coupling regime, a sudden transition from no speed-up to speed-up occurs at a critical driving strength Ωc; for λ = 3R, 6R, and 9R, the paper reports Ωc = 5.31R, 10.89R, and 16.41R, respectively, with actual driving time τD = 1.
  • In the strong-coupling regime, the quantum speed limit time (QSLT) shows a plateau independent of Ω for moderate driving strengths and then periodically decreases for large driving strengths, allowing control of speed-up or speed-down.
  • The classical field can change the original Markovian dynamics to non-Markovian dynamics, and the transition point equals the critical driving strength Ωc where uniform evolution becomes speed-up.
  • For the whole decoherence process, increasing the driving strength Ω reduces the decay rate of QSLT in the speed-up process and the increasing rate in the speed-down process, leading to smaller acceleration and smaller deceleration.

Methods

  • Theoretical model: a two-level atom/qubit interacting with a zero-temperature structured reservoir and driven by a classical field; the Hamiltonian is transformed into an effective form in the dressed-state basis under the rotating-wave approximation.
  • The reservoir is described by a Lorentzian spectral density S(ω) = (1/2π) λR / [(ω − ωc)² + λ²], with weak coupling λ > 2R giving Markovian behavior and strong coupling λ < 2R giving non-Markovian behavior; the amplitude c+(t) is obtained via Laplace transform.
  • The QSLT is calculated using the Deffner-Lutz unified bound, with the ML-type operator-norm bound (p = ∞) used as the sharpest bound; non-Markovianity is quantified via the Breuer et al. trace-distance measure, and numerical calculations are performed for QSLT, non-Markovianity, and population dynamics.

Limitations

  • The paper states no explicit limitations.
  • Evident from the text: the analysis is theoretical and numerical, with no experimental demonstration; potential experimental platforms are only suggested as candidates.
  • Evident from the text: results are illustrated for specific model choices, including a zero-temperature Lorentzian reservoir, a two-level atom, the rotating-wave approximation, and selected parameters such as λ = 3R, λ = 0.05R, and τD = 1, so generality beyond these conditions is not established.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1103/physreva.91.032112

Cites

16 of 52 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 8 cited sources checked · 0 supported · 0 flagged

  • Findingnone given
    § Classical-driving-assisted quantum speed-up · p. 1

    The original Markovian dynamics can be changed to non-Markovian dynamics by choosing an agreeable driving strength of the classical field.

    “the original Markovian dynamics can be changed to the non-Markovian dynamics by choosing an agreeable driving strength of the classical field.”
    • Also stated in: § Classical-driving-assisted quantum speed-up · p. 1 · plain
      “we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of classical field.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.
  • Findingown data
    § Classical-driving-assisted quantum speed-up · p. 3

    In the weak-coupling regime, the external classical field can reduce the QSLT below its value, thereby obtaining a speed-up of the evolution of an open quantum system.

    “So we therefore reach the interesting result that the external classical field can be used to reduced the QSLT below its value in the weak-coupling regime. Thus we obtain the speed-up of the evolution of an open quantum system in the weak-coupling regime.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.
  • Findingreasoning
    § Classical-driving-assisted quantum speed-up · p. 1

    With a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment coupling regime and the strong system-environment coupling regime.

    “It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong systemenvironment couplings.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.
  • Findingreasoning
    § Classical-driving-assisted quantum speed-up · p. 1

    A speed-up evolution of an open system can be achieved by manipulating the driving strength of an external classical field for a qubit in a zero-temperature structured reservoir.

    “We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir.”
    • Also stated in: § Classical-driving-assisted quantum speed-up · p. 4 · boosted
      “we demonstrated that a speed-up evolution of an open system could be achieved by manipulating the driving strength of an external classical field.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.
  • Findingown data
    § Classical-driving-assisted quantum speed-up · p. 3

    The transition point from Markovian dynamics to non-Markovian dynamics equals the critical driving strength Ω_c where the uniform evolution speed becomes the speed-up dynamical process of the system.

    “And the transition point from Markovian dynamics to non-Markovian dynamics is equal to the critical driving strength of the classical field Ω c where the uniform evolution speed becomes the speed-up dynamical process of the system.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.
  • May combine two claims. 7
  • Classified as probably not a substantial claim. 3

  • May combine two claims.

    Findingreasoning
    § Classical-driving-assisted quantum speed-up · p. 3

    For λ = 3R, Ω_c = 5.31R; for λ = 6R, Ω_c = 10.89R; and for λ = 9R, Ω_c = 16.41R.

    “when λ = 3 R , we find the value of the critical driving strength is Ω c = 5 . 31 R . While in the cases λ = 6 R and λ = 9 R , we can acquire Ω c = 10 . 89 R and Ω c = 16 . 41 R , respectively.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • May combine two claims.

    Findingown data
    § Classical-driving-assisted quantum speed-up · p. 3

    The critical driving strength Ω_c is determined by the spectral width λ; the larger λ is, the larger Ω_c must be.

    “numerical calculation also shows that the critical driving strength Ω c is determined by the value of the spectral width λ . The larger the value of λ is, the lager the value of the critical driving strength Ω c should be requested.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • May combine two claims.

    Findingown data
    § Classical-driving-assisted quantum speed-up · p. 3

    The population 1 - PτD(|+><+|) converges to zero for a strong driving classical field in both the weak-coupling regime (no oscillations) and the strong-coupling regime (oscillations present).

    “Figs. 2( b ) and 2( d ) show that the population 1 -P τ D ( | + 〉〈 + | ) converges to zero for the strong driving classical field in the weak-coupling regime (no oscillations) and the strong-coupling regime (oscillations are present).”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • Classified as probably not a substantial claim.

    Findingnone given
    § Classical-driving-assisted quantum speed-up · p. 4

    The results illustrated in this paper involve amplitude damping channels for controlling Markovian and non-Markovian dynamics.

    “In comparison, the results we illustrated here involve the amplitude damping channels for the controlling of Markovian and non-Markovian dynamics.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • May combine two claims.

    Findingreasoning
    § Classical-driving-assisted quantum speed-up · p. 3

    The QSLT is strictly related to the non-Markovianity of the evolution from ρ0 to ρτD and the population of the dressed state |+> at time τD.

    “It is easy to find that the QSLT is strictly related to the non-Markovianity of the evolution from ρ 0 to ρ τ D and the population of the dressed-state | + 〉 at time τ D .”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • May combine two claims.

    Findingown data
    § Classical-driving-assisted quantum speed-up · p. 3

    The QSLT can still be reduced by the classical field, meaning that the external classical field can be used to control the speed of evolution of quantum systems.

    “So the QSLT can still be reduced by the classical field, that means the external classical field can be used to control the speed of evolution of quantum systems.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Classical-driving-assisted quantum speed-up · p. 2

    A unified lower bound including both MT and ML types has been derived by Deffner and Lutz.

    “A unified lower bound, including both MT and ML types, has been derived by Deffner and Lutz [25].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [25] S. Deffner, and E. Lutz, Phys. Rev. Lett. 111 , 010402 (2013). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Classical-driving-assisted quantum speed-up · p. 4

    The applied classical field can lead to smaller acceleration in the speed-up process and smaller deceleration in the speed-down process.

    “This can be understood that the applied classical field can lead to the smaller acceleration in the speed-up process, and also the smaller deceleration in the speed-down process.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.
    • Rests on an assumption: In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.
    • Rests on an assumption: The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

  • May combine two claims.

    Premisecitation
    § Classical-driving-assisted quantum speed-up · p. 1

    In weak system-environment couplings, the QSLT equals the actual driving time, while strong system-environment couplings can reduce the QSLT below the actual driving time.

    “the QSLT would equal to the actual driving time in the weak system-environment couplings, while the strong system-environment couplings can reduce the QSLT below the actual driving time [25].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [25] S. Deffner, and E. Lutz, Phys. Rev. Lett. 111 , 010402 (2013). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Classical-driving-assisted quantum speed-up · p. 4

    Recent experiments with photons allow one to drive an open system from the Markovian to the non-Markovian regime in dephasing channels.

    “Recent experiments with photons allow one to drive the open system from Markovian to nonMarkovian regime in the dephasing channels [38, 39].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [38] J. S. Tang, C. F. Li, Y. L. Li, X. B. Zou, G. C. Guo, H. P. Breuer, E. M. Laine, and J. Piilo, Europhys. Lett. 97 , 10002 (2012). source

      Not checked in the free run.

    • cites [39] B. H. Liu, L. Li, Y. F. Huang, C. F. Li, G. C. Guo, E. M. Laine, H. P. Breuer, and J. Piilo, Nature Phys. 7 , 931 (2011). source

      Not checked in the free run.

10 of 10

  • The paper relies on this without support.

    The environment can be described by an effective Lorentzian spectral density S(ω) = (1/2π) λR / ((ω - ωc)^2 + λ^2), where λ is the spectral width, R the coupling strength, and ωc the center frequency of the reservoir.

    “Here, the environment can be described by an effective Lorentzian spectral density of the form S ( ω ) = 1 2 π λR ( ω -ω c ) 2 + λ 2 , where λ is the spectral width, R the coupling strength, and ω c in the center frequency of the reservoir.”

  • The paper relies on this without support.

    In the weak-coupling regime (λ > 2R), the qubit-cavity system is Markovian with irreversible decay; in the strong-coupling regime (λ < 2R), non-Markovian dynamics occurs with oscillatory reversible decay.

    “Typically, in weak-coupling regime ( λ &gt; 2 R ), the behavior of the qubit-cavity system is Markovian and irreversible decay occurs. For strong-coupling regime ( λ &lt; 2 R ), non-Markovian dynamics occurs accompanied by an oscillatory reversible decay.”

  • The paper relies on this without support.

    The rotating-wave approximation is valid for the effective Hamiltonian of the driven qubit-reservoir system.

    “the total Hamiltonian in Eq. (1) can be transferred to an effective Hamiltonian in the rotating-wave approximation”
3 of 3

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Cites

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Research works printed but not linked: 1

  1. L. Mandelstam, 1945, J. Phys. (USSR), 9, 249

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Related

Authors
Zhang, Y.-J., Han, W., Xia, Y.-J., Cao, J.-P., & Fan, H.
Affiliations
  • Chinese Academy of Sciences (CN)
  • Qufu Normal University (CN)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2015-03-17
Volume
91
Issue
3
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.91.032112
OpenAlex
W2083178891
Cited by
95
References
52
Citations by year
2025: 7 · 2024: 8 · 2023: 9 · 2022: 4 · 2021: 7 · 2020: 15 · 2019: 10 · 2018: 11 · 2017: 11 · 2016: 9 · 2015: 4
FWCI
5.93
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
National Natural Science Foundation of China (11304179, 11247240, 11175248, 61178012, 11204156)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
quantum advantage, classical driving field, open quantum systems, qubits, structured reservoir, non-Markovianity, system-environment coupling, decoherence

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