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arXiv:2504.09767

Implementing and benchmarking dynamically corrected gates on superconducting devices using space curve quantum control

Hisham Amer, Evangelos Piliouras, Edwin Barnes, Sophia E. Economou

Published Apr 14, 2025• 0 citations
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Abstract

We use Space Curve Quantum Control (SCQC) to design, experimentally demonstrate, and benchmark dynamically corrected single-qubit gates on IBM hardware, comparing their performance to that of the standard gates provided by IBM. Our gates are designed to dynamically suppress both detuning and pulse-amplitude noise, with gate times as short as 88 ns. We compare our gates against those of IBM on two separate IBM devices and across sets of up to 18 qubits. Randomized benchmarking is done utilizing our detuning- and amplitude-robust gates in randomized Clifford circuits containing up to 4000 gates. Our gates achieve error-per-Clifford rates that reach as low as 7$\times10^{-5}$ ($\pm10^{-6}$) and which remain nearly constant as the compound noise is increased up to 4% amplitude noise and up to a detuning noise of 342 kHz; this is in contrast to the IBM gates, which exhibit rates that drop to order $10^{-3}$ across this range. This range is consistent with the commonly reported frequency fluctuations and with the upper bound of the statistical uncertainty in gate calibration. In addition, we investigate the performance across larger noise ranges of up to 20% amplitude and 3.5 MHz detuning noise using quantum process tomography. Finally, we experimentally demonstrate how SCQC can be tailored to different practical use cases by trading off amplitude-robustness for ultrafast 60 ns dephasing-only robust pulses. Our work establishes experimental guidelines for implementing SCQC-designed dynamically corrected gates on a broad range of qubit hardware to limit the effect of noise-induced errors and decoherence.

DOI
10.48550/arxiv.2504.09767

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We use Space Curve Quantum Control (SCQC) to design, experimentally demonstrate, and benchmark dynamically corrected single-qubit gates on IBM hardware, comparing their performance to that of the standard gates provided by IBM. Our gates are designed to dynamically suppress both detuning and pulse-amplitude noise, with gate times as short as 88 ns. We compare our gates against those of IBM on two separate IBM devices and across sets of up to 18 qubits. Randomized benchmarking is done utilizing our detuning- and amplitude-robust gates in randomized Clifford circuits containing up to 4000 gates. Our gates achieve error-per-Clifford rates that reach as low as 7×10−5\times10^{-5}×10−5 (±10−6\pm10^{-6}±10−6) and which remain nearly constant as the compound noise is increased up to 4% amplitude noise and up to a detuning noise of 342 kHz; this is in contrast to the IBM gates, which exhibit rates that drop to order 10−310^{-3}10−3 across this range. This range is consistent with the commonly reported frequency fluctuations and with the upper bound of the statistical uncertainty in gate calibration. In addition, we investigate the performance across larger noise ranges of up to 20% amplitude and 3.5 MHz detuning noise using quantum process tomography. Finally, we experimentally demonstrate how SCQC can be tailored to different practical use cases by trading off amplitude-robustness for ultrafast 60 ns dephasing-only robust pulses. Our work establishes experimental guidelines for implementing SCQC-designed dynamically corrected gates on a broad range of qubit hardware to limit the effect of noise-induced errors and decoherence.
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State-of-the-art single-qubit gates on superconducting transmon qubits can achieve the fidelities required for error-corrected computations. However, parameter fluctuations due to qubit instabilities, environmental changes, and control inaccuracies make it difficult to maintain this performance. To mitigate the effects of these parameter variations, we numerically derive gates robust to amplitude and frequency errors using gradient ascent pulse engineering (GRAPE). We analyze how fluctuations in qubit frequency, drive amplitude, and coherence affect gate performance over time. The robust pulses suppress coherent errors from drive amplitude drifts over 15 times more than a Gaussian pulse with derivative removal by adiabatic gate (DRAG) corrections. Furthermore, the robust gates, originally designed to compensate for quasi-static errors, also demonstrate resilience to stochastic, time-dependent noise, which is reflected in the dephasing time. They suppress added errors during increases in dephasing by up to 1.7 times more than DRAG.
Noise-induced gate errors remain one of the main obstacles to realizing a broad range of quantum information technologies. Dynamical error suppression using carefully designed control schemes is critical for overcoming this challenge. Such schemes must be able to correct against multiple noise sources simultaneously afflicting a qubit to reach error-correction thresholds. Here we present a general framework for designing control fields that simultaneously suppress both noise in the fields themselves as well as transverse dephasing noise. Using the recently developed space curve quantum control formalism, in which robust quantum evolution is mapped to closed geometric curves in a multidimensional Euclidean space, we derive the minimal conditions necessary to guarantee the simultaneous cancellation of both types of noise to leading order. In particular, we find that the cancellation of control field noise requires the derivative of the space curve to have zero-area projections, which is a much more subtle property compared to the closed-curve condition needed to suppress transverse dephasing. We present several techniques for solving both these conditions simultaneously and provide explicit examples of error-resistant control fields. Our work also sheds light on the relation between holonomic evolution and the suppression of control field errors.
Achieving very fast gates that undercut the natural limits set by decoherence requires going into the strong driving limit. Realizing single-qubit control predicted beyond semi-classical, time-dependent modeling has yet to be experimentally realized on superconducting and most other computing platforms. In this regime, the common model of dynamics within a three-level manifold breaks down, and instead, we see new quantum error channels growing abruptly with decreasing time. To identify these error processes we systematically calculate the effect of multi-photon transitions that occur out of the computational space. We then derive analytical formulas to suppress these effects, as well as amplitude and phase errors on the qubit space; we term these R1D for suppressing the ∣0⟩−∣2⟩|0\rangle-|2\rangle∣0⟩−∣2⟩ transition and R2D when also suppressing ∣1⟩−∣3⟩|1\rangle-|3\rangle∣1⟩−∣3⟩ leakage. We also answer long-standing questions about the optimal values of the DRAG prefactor as well as constant detuning, when accounting for time-ordering, and also show how to calibrate other prefactors for further performance improvement. Upon correcting these varied sources of error, we numerically demonstrate gate infidelities below 10−510^{-5}10−5 for a 7ns πππ-rotation when incorporating existing decoherence rates.
As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting their performance in realistic circuits. To overcome this problem, we must improve their robustness against pertinent error models besides isolated fidelity. Here, we report the experimental realization of robust quantum gates in superconducting quantum circuits based on a geometric framework for diagnosing and correcting various gate errors. Using quantum process tomography and randomized benchmarking, we demonstrate robust single-qubit gates against quasistatic noise and spatially correlated noise in a broad range of strengths, which are common sources of coherent errors in large-scale quantum circuits. We also apply our method to nonstatic noises and to realize robust two-qubit gates. Our Letter provides a versatile toolbox for achieving noise-resilient complex quantum circuits.