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:1101.5430 · Physical Review A

Efficiency of dynamical decoupling sequences in the presence of pulse errors

Zhihao Xiao, Lewei He, Wen-ge Wang

Published Mar 30, 2011• 16 citations
arXivHTMLPDF

Abstract

For a generic dynamical decoupling sequence employing a single-axis control, we study its efficiency in the presence of small errors in the direction of the controlling pulses. In the case that the corresponding ideal dynamical decoupling sequence produces sufficiently good results, the impact of the errors is found to scale as $\ensuremath{\xi}{}^{2}$, with negligible first-order effect, where $\ensuremath{\xi}$ is the dispersion of the random errors. This analytical prediction is numerically tested in a model in which the environment is modeled by one qubit coupled to a quantum kicked rotator in chaotic motion. In this model, with periodic pulses applied to the qubit in the environment, it is found numerically that periodic bang-bang control may outperform Uhrig dynamical decoupling.

DOI
10.1103/physreva.83.032322

Related papers

Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences

Kaveh Khodjasteh, Daniel A. Lidar

Dynamical decoupling can be used to preserve arbitrary quantum states despite undesired interactions with the environment, using control Hamiltonians affecting the system only. We present a system-independent analysis of dynamical decoupling based on leading order decoupling error estimates, valid for bounded-strength environments. Using as a key tool a renormalization transformation of the effective system-bath coupling Hamiltonian, we delineate the reliability domain of dynamical decoupling used for quantum state preservation, in a general setting for a single qubit. We specifically analyze and compare two deterministic dynamical decoupling schemes---periodic and concatenated---and distinguish between two limiting cases of fast versus slow environments. We prove that concatenated decoupling outperforms periodic decoupling over a wide range of parameters. These results are obtained for both ``ideal'' (zero-width) and realistic (finite-width) pulses This work extends and generalizes our earlier work [Phys. Rev. Lett. 95, 180501 (2005)].

arXiv:quant-ph/0607086•Physical Review A•Jun 8, 2007•215 citations

Aperiodic dynamical decoupling sequences in the presence of pulse errors

Zhi‐Hui Wang, V. V. Dobrovitski

Dynamical decoupling (DD) is a promising tool for preserving the quantum states of qubits. However, small imperfections in the control pulses can seriously affect the fidelity of decoupling, and qualitatively change the evolution of the controlled system at long times. Using both analytical and numerical tools, we theoretically investigate the effect of the pulse errors accumulation for two aperiodic DD sequences, the Uhrig's DD UDD) protocol [G. S. Uhrig, Phys. Rev. Lett. {\bf 98}, 100504 (2007)], and the Quadratic DD (QDD) protocol [J. R. West, B. H. Fong and D. A. Lidar, Phys. Rev. Lett {\bf 104}, 130501 (2010)]. We consider the implementation of these sequences using the electron spins of phosphorus donors in silicon, where DD sequences are applied to suppress dephasing of the donor spins. The dependence of the decoupling fidelity on different initial states of the spins is the focus of our study. We investigate in detail the initial drop in the DD fidelity, and its long-term saturation. We also demonstrate that by applying the control pulses along different directions, the performance of QDD protocols can be noticeably improved, and explain the reason of such an improvement. Our results can be useful for future implementations of the aperiodic decoupling protocols, and for better understanding of the impact of errors on quantum control of spins.

arXiv:1101.0292•Journal of Physics B Atomic Molecular and Optical Physics•Jul 25, 2011•15 citations

Quadratic dynamical decoupling: Universality proof and error analysis

Wan-Jung Kuo, Daniel A. Lidar

We prove the universality of the generalized QDD${}_{{N}_{1}{N}_{2}}$ (quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using ${N}_{1}$ and ${N}_{2}$ pulses, respectively, can eliminate decoherence to $O({T}^{N})$ using $O({N}^{2})$ unequally spaced ``ideal'' (zero-width) pulses, where $T$ is the total evolution time and $N={N}_{1}={N}_{2}$. A proof of the universality of QDD has been given for even ${N}_{1}$. Here we give a general universality proof of QDD for arbitrary ${N}_{1}$ and ${N}_{2}$. As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of ${N}_{1}$ and ${N}_{2}$. We prove that using QDD${}_{{N}_{1}{N}_{2}}$ decoherence can always be eliminated to $O({T}^{\mathrm{min}{{N}_{1},{N}_{2}}})$.

arXiv:1106.2151•Physical Review A•Oct 17, 2011•42 citations

Faster Randomized Dynamical Decoupling

Changhao Yi, Leeseok Kim, Milad Marvian

We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system's Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. We also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.

arXiv:2409.18369•Physical Review Letters•Dec 18, 2025•3 citations

Optimized dynamical decoupling via genetic algorithms

Gregory Quiroz, Daniel A. Lidar

We utilize genetic algorithms aided by simulated annealing to find optimal dynamical decoupling (DD) sequences for a single-qubit system subjected to a general decoherence model under a variety of control pulse conditions. We focus on the case of sequences with equal pulse intervals and perform the optimization with respect to pulse type and order. In this manner, we obtain robust DD sequences, first in the limit of ideal pulses, then when including pulse imperfections such as finite-pulse duration and qubit rotation (flip-angle) errors. Although our optimization is numerical, we identify a deterministic structure that underlies the top-performing sequences. We use this structure to devise DD sequences which outperform previously designed concatenated DD (CDD) and quadratic DD (QDD) sequences in the presence of pulse errors. We explain our findings using time-dependent perturbation theory and provide a detailed scaling analysis of the optimal sequences.

arXiv:1210.5538•Physical Review A•Nov 8, 2013•37 citations

Robustness of dynamical decoupling sequences

Mustafa Ahmed Ali Ahmed, Gonzalo A. Álvarez, Dieter Suter

Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.

arXiv:1211.5001•Physical Review A•Apr 8, 2013•66 citations
For a generic dynamical decoupling sequence employing a single-axis control, we study its efficiency in the presence of small errors in the direction of the controlling pulses. In the case that the corresponding ideal dynamical decoupling sequence produces sufficiently good results, the impact of the errors is found to scale as \ensuremathξ2\ensuremath{\xi}{}^{2}\ensuremathξ2, with negligible first-order effect, where \ensuremathξ\ensuremath{\xi}\ensuremathξ is the dispersion of the random errors. This analytical prediction is numerically tested in a model in which the environment is modeled by one qubit coupled to a quantum kicked rotator in chaotic motion. In this model, with periodic pulses applied to the qubit in the environment, it is found numerically that periodic bang-bang control may outperform Uhrig dynamical decoupling.
Dynamical decoupling can be used to preserve arbitrary quantum states despite undesired interactions with the environment, using control Hamiltonians affecting the system only. We present a system-independent analysis of dynamical decoupling based on leading order decoupling error estimates, valid for bounded-strength environments. Using as a key tool a renormalization transformation of the effective system-bath coupling Hamiltonian, we delineate the reliability domain of dynamical decoupling used for quantum state preservation, in a general setting for a single qubit. We specifically analyze and compare two deterministic dynamical decoupling schemes---periodic and concatenated---and distinguish between two limiting cases of fast versus slow environments. We prove that concatenated decoupling outperforms periodic decoupling over a wide range of parameters. These results are obtained for both ``ideal'' (zero-width) and realistic (finite-width) pulses This work extends and generalizes our earlier work [Phys. Rev. Lett. 95, 180501 (2005)].
Dynamical decoupling (DD) is a promising tool for preserving the quantum states of qubits. However, small imperfections in the control pulses can seriously affect the fidelity of decoupling, and qualitatively change the evolution of the controlled system at long times. Using both analytical and numerical tools, we theoretically investigate the effect of the pulse errors accumulation for two aperiodic DD sequences, the Uhrig's DD UDD) protocol [G. S. Uhrig, Phys. Rev. Lett. {\bf 98}, 100504 (2007)], and the Quadratic DD (QDD) protocol [J. R. West, B. H. Fong and D. A. Lidar, Phys. Rev. Lett {\bf 104}, 130501 (2010)]. We consider the implementation of these sequences using the electron spins of phosphorus donors in silicon, where DD sequences are applied to suppress dephasing of the donor spins. The dependence of the decoupling fidelity on different initial states of the spins is the focus of our study. We investigate in detail the initial drop in the DD fidelity, and its long-term saturation. We also demonstrate that by applying the control pulses along different directions, the performance of QDD protocols can be noticeably improved, and explain the reason of such an improvement. Our results can be useful for future implementations of the aperiodic decoupling protocols, and for better understanding of the impact of errors on quantum control of spins.
We prove the universality of the generalized QDDN1N2{}_{{N}_{1}{N}_{2}}N1​N2​​ (quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using N1{N}_{1}N1​ and N2{N}_{2}N2​ pulses, respectively, can eliminate decoherence to O(TN)O({T}^{N})O(TN) using O(N2)O({N}^{2})O(N2) unequally spaced ``ideal'' (zero-width) pulses, where TTT is the total evolution time and N=N1=N2N={N}_{1}={N}_{2}N=N1​=N2​. A proof of the universality of QDD has been given for even N1{N}_{1}N1​. Here we give a general universality proof of QDD for arbitrary N1{N}_{1}N1​ and N2{N}_{2}N2​. As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of N1{N}_{1}N1​ and N2{N}_{2}N2​. We prove that using QDDN1N2{}_{{N}_{1}{N}_{2}}N1​N2​​ decoherence can always be eliminated to O(TminN1,N2)O({T}^{\mathrm{min}{{N}_{1},{N}_{2}}})O(TminN1​,N2​).
We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system's Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. We also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.
We utilize genetic algorithms aided by simulated annealing to find optimal dynamical decoupling (DD) sequences for a single-qubit system subjected to a general decoherence model under a variety of control pulse conditions. We focus on the case of sequences with equal pulse intervals and perform the optimization with respect to pulse type and order. In this manner, we obtain robust DD sequences, first in the limit of ideal pulses, then when including pulse imperfections such as finite-pulse duration and qubit rotation (flip-angle) errors. Although our optimization is numerical, we identify a deterministic structure that underlies the top-performing sequences. We use this structure to devise DD sequences which outperform previously designed concatenated DD (CDD) and quadratic DD (QDD) sequences in the presence of pulse errors. We explain our findings using time-dependent perturbation theory and provide a detailed scaling analysis of the optimal sequences.
Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.