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arXiv:2606.08114 · Physical Review A

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

quant-phstat.APSubmitted Jun 6, 2026• Announced Jun 9, 2026• 0 citations

Abstract

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.

Journal reference: Phys. Rev. A 113, 062412 (2026)
DOI: 10.1103/gb82-y4z3

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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.

Environmental noise that couples longitudinally to a quantum system dephases that system and can limit its coherence lifetime. Performance using quantum superposition in clocks, information processors, communication networks, and sensors depends on careful state and external field selection to lower sensitivity to longitudinal noise. In many cases time varying external control fields--such as the Hahn echo sequence originally developed for nuclear magnetic resonance applications--can passively correct for longitudinal errors. There also exist continuous versions of passive correction called continuous dynamical decoupling (CDD), or spin-locking depending on context. However, treating quantum systems under CDD as qubits has not been well explored. Here, we develop universal single-qubit gates that are ``fast'' relative to perturbative Rabi gates and applicable to any CDD qubit architecture. We demonstrate single-qubit gates with fidelity

\mathcal{F}=0.9947(1)

on a frequency tunable CDD transmon superconducting circuit operated where it is strongly sensitive to longitudinal noise, thus establishing this technique as a potentially useful tool for operating qubits in applications requiring high fidelity under non-ideal conditions.

Both longitudinal and transverse relaxations exist in the practical environment. Their simultaneous eliminations are extremely demanding in real applications. Previous experimental work has focused mainly on the suppression of transverse relaxation. In this paper we investigate the performance of three important dynamical decoupling schemes---quadratic dynamical decoupling, periodic dynamical decoupling, and concatenated dynamical decoupling---in an environment with hybrid errors. We propose a method to engineer arbitrary environment by modulating the control field. The technique developed here is universal and can be applied to other quantum information processing systems. Three-dimensional filter functions technique is utilized to analyze the fidelity decay of a one-qubit state protected by dynamical decoupling sequences. This enables us to quantitatively compare the performance of different dynamical decoupling sequences and demonstrate the superiority of quadratic dynamical decoupling in experiments for the first time. Our work reveals that quadratic dynamical decoupling is optimal conditioned on the appropriate noise properties. The difference of constructing dynamical decoupling sequences with various Pauli pulses is also investigated.

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