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.
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.
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum computing (AQC) is discussed. A performance comparison between two deterministic DD schemes is given, where preference towards one particular method is found due to sequence structure and procedure from which higher accuracy sequences are generated.
Dynamical decoupling (DD) is a widely used and resource-efficient technique for error suppression, but conventional DD relies on periodically repeating a short pulse block to refocus the qubit state during idle periods. Imperfections in this block cause residual errors to accumulate, ultimately degrading state recovery over long idle times. Here, we introduce a universal optimal tracking approach that extends the original tracking concept to a fully state-independent setting for designing DD sequences. By monitoring the qubit's evolution at predefined waypoints during optimization, the method dynamically compensates residual errors while preserving regular refocusing. Experimental demonstrations on a superconducting-qubit platform confirm the suppression of error accumulation under static control imperfections, in agreement with numerical predictions. Complementary simulations further show that optimal-tracking-based sequences maintain strong performance under time-dependent noise. These results establish optimal tracking as a practical and hardware-agnostic approach to designing short, robust DD sequences suitable for noisy quantum devices.
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.
Dynamical decoupling (DD) is perhaps the simplest and least resource-intensive error-suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences from ten families, including basic as well as advanced sequences with high-order error cancelation properties and built-in robustness. The survey is performed using three different superconducting-qubit IBMQ devices, with the goal of assessing the relative performance of the different sequences in the setting of arbitrary quantum state preservation. We find that the high-order universally robust (UR) and quadratic DD (QDD) sequences generally outperform all other sequences across devices and pulse-interval settings. Surprisingly, we find that DD performance for basic sequences such as the Carr-Purcell-Meiboom-Gill and XY4 sequences can be made to nearly match that of UR and QDD sequences by optimizing the pulse interval, with the optimal interval being substantially larger than the minimum interval possible on each device.
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.
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses does not outweigh the increased ability in averaging away the original background noise. We present break-even conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.