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arXiv:1208.5218 · Physical Review A

Design method of dynamical decoupling sequences integrated with optimal control theory

Yutaka Tabuchi, Makoto Negoro, Masahiro Kitagawa

Published Aug 31, 2017• 5 citations
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Abstract

A method for synthesizing dynamical decoupling (DD) sequences is presented, which can tailor these sequences to a given set of qubits, environments, instruments, and available resources using partial information of the system. The key concept behind the generation of the DD sequences involves not only extricating the strong dependence on the coupling strengths according to the ``optimal control,'' but also exploiting the ``refocus'' technique used conventionally to obtain DD sequences. The concept is a generalized one that harmonizes optimal control and designing of DD sequences.

DOI
10.1103/physreva.96.022331

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A method for synthesizing dynamical decoupling (DD) sequences is presented, which can tailor these sequences to a given set of qubits, environments, instruments, and available resources using partial information of the system. The key concept behind the generation of the DD sequences involves not only extricating the strong dependence on the coupling strengths according to the optimal control,'' but also exploiting the refocus'' technique used conventionally to obtain DD sequences. The concept is a generalized one that harmonizes optimal control and designing of DD sequences.
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.
Abstract Dynamical decoupling (DD), usually implemented by sophisticated sequences of instantaneous control pulses, is a well-established quantum control technique for quantum information and quantum sensing. In practice, the pulses are inevitably imperfect with many systematic errors that may influence the performances of DD. In particular, Rabi error and detuning are primary systemic errors arising from finite pulse duration, incorrect time control, and frequency instability. Here, we propose a phase-modulated DD with staggered global phases for the basic units of the pulse sequences to suppress these systemic errors. By varying the global phases appended to the pulses in the dynamical decoupling unit alternatively with 0 or π, our protocol can significantly reduce the influences of Rabi error and detuning. Our protocol is general and can be combined with the most existing DD sequences such as universal DD, knill DD, XY, etc. As an example, we further apply our method to quantum lock-in detection for measuring time-dependent alternating signals. Our study paves the way for a simple and feasible way to realize robust dynamical decoupling sequences, which can be applicable for various quantum sensing scenarios.
Dynamical decoupling (DD) sequences were invented to eliminate the direct coupling between a qubit and its environment. We further investigate the possibility of decoupling the indirect qubit–qubit interaction induced by a common environment, and successfully find simplified solutions that preserve the bipartite quantum states to arbitrary order. Through analysing the exact dynamics of the controlled two-qubit density matrix, we have proven that applying independent Uhrig DD (UDD) on each qubit will effectively eliminate both the qubit–environment and indirect qubit–qubit couplings to the same order as in the single-qubit case, only if orders of the two UDD sequences have different parities. More specifically, UDD(n) on one qubit with UDD(m) on another are able to produce min (n, m)th-order suppression while n + m is odd. Our results can be used to reduce the pulse number in relevant experiments for protecting bipartite quantum states, or dynamically manipulating the indirect interaction within a certain quantum gate and quantum bus.
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.
Near-term quantum devices are subject to errors and decoherence error is one of the non-negligible sources. Dynamical decoupling (DD) is a well-known technique to protect idle qubits from decoherence error. However, the optimal approach to inserting DD sequences still remains unclear. In this paper, we identify different conditions that lead to idle qubits and evaluate strategies for DD insertion under these specific conditions. Specifically, we divide the idle qubit into crosstalk-idle or idle-idle qubit depending on its coupling with other qubits and report the DD insertion strategies for the two types of idle qubits. We also perform Ramsey experiment to understand the reasons behind the strategy choice. Finally, we provide design guidelines for DD insertion for small circuits and insights for large-scale circuit design.
Dynamical decoupling (DD) is a low-overhead method for quantum error suppression. Despite extensive work in DD design, finding pulse sequences that optimally decouple computational qubits is not well understood. Using IBM’s superconducting-qubit-based quantum processors, we demonstrate how to empirically tailor DD strategies for an arbitrary quantum circuit and device. These learned DD strategies significantly improve error suppression relative to canonical sequences, with relative improvement increasing with problem size and circuit sophistication. We leverage this to study mirror randomized benchmarking on 100 qubits, Greenberger-Horne-Zeilinger state preparation on 50 qubits, and the Bernstein-Vazirani algorithm on 27 qubits. Our empirical learning method finds strategies, in constant time independent of circuit width and depth, provides stable performance over long time periods without retraining, and generalizes to larger circuits when trained on small subcircuit structures.