Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2311.08508 · Physical Review A

Decoherence reduction via continuous dynamical decoupling: Analytical study of the role of the noise spectrum

Jose M. Gomez Llorente, I. Gomez-Ojeda, Jesús Plata

Published Nov 13, 2023• 3 citations
arXivHTMLPDF

Abstract

We analyze the robust character against the nonstatic noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in $^{87}\mathrm{Rb}$. The emergence of features specific to the quadratic corrections to the linear Zeeman effect is evaluated. Our analytical approach, which combines methods of stochastic analysis with time-dependent perturbation theory, allows tracing the deco- herence process for generic noise sources. Working first with a basic CDD scheme, it is shown that the amplitude and frequency of the (sinusoidal driving) field of control can be appropriately chosen to force the nonstatic random input to have a (time-dependent) perturbative character. Moreover, in the dressed-state picture, the effect of noise is described in terms of an operative random variable whose properties, dependent on the driving field, can be analytically characterized. In this framework, the relevance of the spectral density of the fluctuations to the performance of the CDD technique is precisely assessed. In particular, the range of noise correlation times where the method of decoherence reduction is still efficient is identified. The results obtained in the basic CDD framework are extrapolated to concatenated schemes. The generality of our approach allows its applicability beyond the specific atomic system considered.

DOI
10.1103/physreva.108.052412

Related papers

Robust applicability of continuous dynamical decoupling to decoherence reduction in longitudinal and transverse-noise settings: The role of anisotropy

S. Afonso, J. M. Gomez Llorente, J. Plata

We analytically evaluate the efficiency of continuous dynamical decoupling (CDD) to curb decoherence in generic qubit setups where diverse sources of noise can be present. Previous theoretical approaches to CDD have mainly focused on its potential to cope with longitudinal fluctuations. Here, the basic scenario tackled with CDD is generalized. Apart from dealing with pure dephasing induced by diagonal noise, we consider the impact of transverse fluctuations, usually present in the practical arrangements. In particular, the implications of anisotropic noisy inputs are studied. Additionally, we analyze the role of the fluctuations in the dressing of the qubit by the CDD field of control: since the driving field is usually switched on through linear ramps of its characteristic parameters, the associated dressing of the original states can be described in terms of noisy Landau-Zener transitions. In our approach, based on a sequence of unitary transformations, the noise entering the system is cast into effective stochastic terms whose spectral characteristics are dependent on the driving parameters. This description allows the design of strategies to mitigate the impact of the fluctuations using controlled changes in the effective-noise properties. Significant robustness of CDD against the generalization of the basic scenario can be achieved through an appropriate choice of the parameters of control.

quant-pharXiv:2606.08114•Physical Review A•Jun 9, 2026•0 citations

Robust dynamical decoupling with concatenated continuous driving

J-M Cai, Boris Naydenov, R Pfeiffer +5 more

The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.

arXiv:1111.0930•New Journal of Physics•Nov 20, 2012•214 citations

Estimation of the Laser Frequency Noise Spectrum by Continuous Dynamical Decoupling

Manchao Zhang, Yi Xie, Jie Zhang +5 more

Decoherence induced by laser frequency noise is one of the most important obstacles in quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2\ensuremath{\pi})530$ kHz by monitoring the transverse relaxation from an initial state $+X$, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by encoding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth is assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.

arXiv:2005.03908•Physical Review Applied•Jan 20, 2021•8 citations

Dynamical-decoupling noise spectroscopy at an optimal working point of a qubit

Łukasz Cywiński

I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of $n$ pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $\ensuremath{\xi}(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large $n$, and well-established methods of noise spectroscopy can be used to reconstruct the spectrum of ${\ensuremath{\xi}}^{2}(t)$ noise. On the other hand, for noise of dominant low-frequency character $(1/{f}^{\ensuremath{\beta}}$ noise with $\ensuremath{\beta}>1)$, an infinite-order resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a power-law tail at long times. In this case, the coherence at time $t$ depends both on spectral density of $\ensuremath{\xi}(t)$ noise at $\ensuremath{\omega}=n\ensuremath{\pi}/t$, and on the effective low-frequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.

arXiv:1308.3102•Physical Review A•Oct 6, 2014•60 citations

Continuous dynamical decoupling utilizing time‐dependent detuning

I. Cohen, N. Aharon, Alex Retzker

Resilience to noise and to decoherence processes is an important ingredient for the implementation of quantum information processing, and quantum technologies. To this end, techniques such as pulsed and continuous dynamical decoupling have been proposed to reduce noise effects. In this paper, we suggest a new approach to implementing continuous dynamical decoupling techniques, that uses an extra control parameter; namely, the ability to shape the time dependence of the detuning. This approach reduces the complexity of the experimental setup, such that we are only left with noise originating from the frequency of the driving field, which is much more robust than the amplitude (Rabi frequency) noise. As an example, we show that our technique can be utilized for improved sensing.

arXiv:1606.03960•Fortschritte der Physik•Nov 15, 2016•48 citations

Simulation-Based Comparative Study of Dynamical Decoupling Sequences under Structured Noise Models

Trivikramahimamshu S. Dorbala, Baladitya Suri

Abstract Dynamical decoupling (DD) is a quantum error-mitigation technique based on applying sequences of control pulses to suppress decoherence. Here we perform a numerical study to compare different DD protocols, namely Carr-Purcell-Meiboom-Gill (CPMG), Periodic Dynamical Decoupling (PDD), Concatenated Dynamical Decoupling (CDD) and Uhrig Dynamical Decoupling (UDD) applied to three commonly used noise power spectral densities: (i) white, (ii) 1/f, (iii) 1/f 2 and their hybrid combinations. By ignoring qubit relaxation, we simulate these protocols focusing purely on dephasing noise. We then consider independent multi-axial noise with uniaxial control pulses. The effective coherence times T2,eff are extracted for each case and compared with the baseline free induction decay T ∗ 2 [6]. In all these simulations, the time-domain decoherence profiles follow a stretched exponential form ∼ exp −(t/T2,eff) β with the effective coherence times dependent on the noise spectrum considered, the strength of the noise, and the DD sequence employed. An exception is observed for the UDD under specific noise conditions where it cannot be described by a simple stretched exponential decay form.

•Oct 1, 2025•0 citations
We analyze the robust character against the nonstatic noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in 87Rb^{87}\mathrm{Rb}87Rb. The emergence of features specific to the quadratic corrections to the linear Zeeman effect is evaluated. Our analytical approach, which combines methods of stochastic analysis with time-dependent perturbation theory, allows tracing the deco- herence process for generic noise sources. Working first with a basic CDD scheme, it is shown that the amplitude and frequency of the (sinusoidal driving) field of control can be appropriately chosen to force the nonstatic random input to have a (time-dependent) perturbative character. Moreover, in the dressed-state picture, the effect of noise is described in terms of an operative random variable whose properties, dependent on the driving field, can be analytically characterized. In this framework, the relevance of the spectral density of the fluctuations to the performance of the CDD technique is precisely assessed. In particular, the range of noise correlation times where the method of decoherence reduction is still efficient is identified. The results obtained in the basic CDD framework are extrapolated to concatenated schemes. The generality of our approach allows its applicability beyond the specific atomic system considered.
We analytically evaluate the efficiency of continuous dynamical decoupling (CDD) to curb decoherence in generic qubit setups where diverse sources of noise can be present. Previous theoretical approaches to CDD have mainly focused on its potential to cope with longitudinal fluctuations. Here, the basic scenario tackled with CDD is generalized. Apart from dealing with pure dephasing induced by diagonal noise, we consider the impact of transverse fluctuations, usually present in the practical arrangements. In particular, the implications of anisotropic noisy inputs are studied. Additionally, we analyze the role of the fluctuations in the dressing of the qubit by the CDD field of control: since the driving field is usually switched on through linear ramps of its characteristic parameters, the associated dressing of the original states can be described in terms of noisy Landau-Zener transitions. In our approach, based on a sequence of unitary transformations, the noise entering the system is cast into effective stochastic terms whose spectral characteristics are dependent on the driving parameters. This description allows the design of strategies to mitigate the impact of the fluctuations using controlled changes in the effective-noise properties. Significant robustness of CDD against the generalization of the basic scenario can be achieved through an appropriate choice of the parameters of control.
The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.
Decoherence induced by laser frequency noise is one of the most important obstacles in quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2\ensuremath{\pi})530$ kHz by monitoring the transverse relaxation from an initial state +X+X+X, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by encoding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth is assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of nnn pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $\ensuremath{\xi}(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large nnn, and well-established methods of noise spectroscopy can be used to reconstruct the spectrum of ${\ensuremath{\xi}}^{2}(t)$ noise. On the other hand, for noise of dominant low-frequency character $(1/{f}^{\ensuremath{\beta}}$ noise with $\ensuremath{\beta}>1)$, an infinite-order resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a power-law tail at long times. In this case, the coherence at time ttt depends both on spectral density of $\ensuremath{\xi}(t)$ noise at $\ensuremath{\omega}=n\ensuremath{\pi}/t$, and on the effective low-frequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.
Resilience to noise and to decoherence processes is an important ingredient for the implementation of quantum information processing, and quantum technologies. To this end, techniques such as pulsed and continuous dynamical decoupling have been proposed to reduce noise effects. In this paper, we suggest a new approach to implementing continuous dynamical decoupling techniques, that uses an extra control parameter; namely, the ability to shape the time dependence of the detuning. This approach reduces the complexity of the experimental setup, such that we are only left with noise originating from the frequency of the driving field, which is much more robust than the amplitude (Rabi frequency) noise. As an example, we show that our technique can be utilized for improved sensing.
Abstract Dynamical decoupling (DD) is a quantum error-mitigation technique based on applying sequences of control pulses to suppress decoherence. Here we perform a numerical study to compare different DD protocols, namely Carr-Purcell-Meiboom-Gill (CPMG), Periodic Dynamical Decoupling (PDD), Concatenated Dynamical Decoupling (CDD) and Uhrig Dynamical Decoupling (UDD) applied to three commonly used noise power spectral densities: (i) white, (ii) 1/f, (iii) 1/f 2 and their hybrid combinations. By ignoring qubit relaxation, we simulate these protocols focusing purely on dephasing noise. We then consider independent multi-axial noise with uniaxial control pulses. The effective coherence times T2,eff are extracted for each case and compared with the baseline free induction decay T ∗ 2 [6]. In all these simulations, the time-domain decoherence profiles follow a stretched exponential form ∼ exp −(t/T2,eff) β with the effective coherence times dependent on the noise spectrum considered, the strength of the noise, and the DD sequence employed. An exception is observed for the UDD under specific noise conditions where it cannot be described by a simple stretched exponential decay form.