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arXiv:2109.05309 · IEEE/ACM International Symposium on Microarchitecture (MICRO)

ADAPT: Mitigating Idling Errors in Qubits via Adaptive Dynamical Decoupling

Poulami Das, Swamit Tannu, Siddharth Dangwal, Moinuddin Qureshi

Published Oct 17, 2021• 69 citations
arXivHTMLPDF

Abstract

The fidelity of applications on near-term quantum computers is limited by hardware errors. In addition to errors that occur during gate and measurement operations, a qubit is susceptible to idling errors, which occur when the qubit is idle and not actively undergoing any operations. To mitigate idling errors, prior works in the quantum devices community have proposed Dynamical Decoupling (DD), that reduces stray noise on idle qubits by continuously executing a specific sequence of single-qubit operations that effectively behave as an identity gate. Unfortunately, existing DD protocols have been primarily studied for individual qubits and their efficacy at the application-level is not yet fully understood.

DOI
10.1145/3466752.3480059

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The fidelity of applications on near-term quantum computers is limited by hardware errors. In addition to errors that occur during gate and measurement operations, a qubit is susceptible to idling errors, which occur when the qubit is idle and not actively undergoing any operations. To mitigate idling errors, prior works in the quantum devices community have proposed Dynamical Decoupling (DD), that reduces stray noise on idle qubits by continuously executing a specific sequence of single-qubit operations that effectively behave as an identity gate. Unfortunately, existing DD protocols have been primarily studied for individual qubits and their efficacy at the application-level is not yet fully understood.
Abstract Dynamical decoupling (DD) is one of the simplest error suppression methods, aiming to enhance the coherence of qubits in open quantum systems. Moreover, DD has demonstrated effectiveness in reducing coherent crosstalk, one major error source in near-term quantum hardware, which manifests from two types of interactions. Static crosstalk exists in various hardware platforms, including superconductor and semiconductor qubits, by virtue of always-on qubit-qubit coupling. Additionally, driven crosstalk may occur as an unwanted drive term due to leakage from driven gates on other qubits. Here we explore a novel staggered DD protocol tailored for multi-qubit systems that suppresses the decoherence error and both types of coherent crosstalk. We develop two experimental setups—an ‘idle–idle’ experiment in which two pairs of qubits undergo free evolution simultaneously and a ‘driven-idle’ experiment in which one pair is continuously driven during the free evolution of the other pair. These experiments are performed on an IBM Quantum superconducting processor and demonstrate the significant impact of the staggered DD protocol in suppressing both types of coherent crosstalk. When compared to the standard DD sequences from state-of-the-art methodologies with the application of X 2 sequences, our staggered DD protocol enhances circuit fidelity by 19.7% and 8.5%, respectively, in addressing these two crosstalk types.
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.
Achieving high-precision quantum computation requires effective suppression of idling errors that occur when qubits remain inactive during waiting periods within a quantum circuit. Conventional mitigation techniques, such as dynamical decoupling, suppress decoherence by periodically refreshing quantum states through the insertion of additional control gates. In this paper, we propose an alternative approach that suppresses idling errors through quantum circuit scheduling without introducing any additional gate operations. By appropriately adjusting the execution timing of quantum gates with scheduling flexibility, we demonstrate through both numerical simulations and hardware experiments that the overall computational accuracy can be significantly influenced and, in many cases, improved. In addition, we analytically derive the density-matrix evolution under idling noise and provide a theoretical framework that explains the observed behavior.
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.
Dynamic quantum circuits integrate mid-circuit measurements and feed-forward operations to enable real-time classical processing and conditional quantum logic. These capabilities are central to key quantum protocols such as quantum error correction, and have recently demonstrated significant potential for reducing quantum resources, including circuit depth and gate count, across a range of applications. However, executing dynamic circuits on real quantum hardware introduces a critical trade-off: while resource requirements decrease, circuit fidelity degrades due to high error rates of mid-circuit measurements, as well as the decoherence errors accumulated during the extended idle periods introduced by both mid-circuit measurements and feed-forward operations. In this paper, we systematically investigate the impact of standard error mitigation techniques on dynamic circuit applications pertaining to Hamiltonian simulation and ground state estimation of physically relevant systems like the Heisenberg model. We explore dynamical decoupling (DD) as a strategy to suppress decoherence and crosstalk errors during idle windows introduced by mid-circuit measurements and feed-forward delays, and also examine error mitigation via zero-noise extrapolation (ZNE). Through experiments conducted on IBM quantum hardware, we benchmark effective combinations of these strategies that maximize the practical benefits of dynamic quantum circuits in these applications. We demonstrate that a combination of DD and ZNE is effective in mitigating the errors introduced during mid-circuit measurements and feed-forward operations, as well as the errors arising from faulty measurements. This approach yields a energy gap improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.
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.