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arXiv:2609.33251 · Nature Communications

High-fidelity geometric quantum gates exceeding 99.9% in germanium quantum dots

Yu-Chen Zhou, Rong-Long Ma, Zhenzhen Kong, Ao-Ran Li, Chengxian Zhang, Xin Zhang, Yang Liu, Hao-Tian Jiang, Zhi-Tao Wu, Gui-Lei Wang, Gang Cao, Guang-Can Guo, Hai-Ou Li, Guo-Ping Guo

quant-phcond-mat.mes-hallSubmitted Sep 27, 2026• Announced Sep 29, 2026• 12 citations
arXivHTMLPDF

Abstract

Achieving high-fidelity and robust qubit manipulations is a crucial requirement for realizing faulttolerant quantum computation. Here, we demonstrate a single-hole spin qubit in a germanium quantum dot and characterize its control fidelity using gate set tomography. The maximum control fidelities reach 97.48%, 99.81%, 99.88% for the I, X/2 and Y /2 gate, respectively. These results reveal that off-resonance noise during consecutive I gates in gate set tomography sequences severely limits qubit performance. Therefore, we introduce geometric quantum computation to realize noiseresilient qubit manipulation. The geometric gate control fidelities remain above 99% across a wide range of Rabi frequencies. The maximum fidelity surpasses 99.9%. Furthermore, the fidelities of geometric X/2 and Y /2 (I) gates exceed 99% even when detuning the microwave frequency by +-2.5 MHz (+-1.2 MHz), highlighting the noise-resilient feature. These results demonstrate that geometric quantum computation is a potential method for achieving high-fidelity qubit manipulation reproducibly in semiconductor quantum computation.

Journal reference
Nature Communications 16, 7953 (2025)
DOI
10.5281/zenodo.16450274
Comments
13 pages, 4 figures

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Achieving high-fidelity and robust qubit manipulations is a crucial requirement for realizing faulttolerant quantum computation. Here, we demonstrate a single-hole spin qubit in a germanium quantum dot and characterize its control fidelity using gate set tomography. The maximum control fidelities reach 97.48%, 99.81%, 99.88% for the I, X/2 and Y /2 gate, respectively. These results reveal that off-resonance noise during consecutive I gates in gate set tomography sequences severely limits qubit performance. Therefore, we introduce geometric quantum computation to realize noiseresilient qubit manipulation. The geometric gate control fidelities remain above 99% across a wide range of Rabi frequencies. The maximum fidelity surpasses 99.9%. Furthermore, the fidelities of geometric X/2 and Y /2 (I) gates exceed 99% even when detuning the microwave frequency by +-2.5 MHz (+-1.2 MHz), highlighting the noise-resilient feature. These results demonstrate that geometric quantum computation is a potential method for achieving high-fidelity qubit manipulation reproducibly in semiconductor quantum computation.
Hole spin qubits based on semiconductor quantum dots are promising for building future large-scale quantum computers owing to their all-electrical manipulation. However, abundant physical mechanisms of valence band holes lead to anisotropic qubit properties. There is an opportunity to prolong the coherence time and achieve high-fidelity qubit manipulations. Here, we report a single-hole spin qubit in a planar germanium quantum dot and investigate its anisotropic susceptibility to charge noise under an in-plane magnetic field. By correlating the longitudinal spin-electric susceptibility with qubit coherence and control performance, we identify an optimal operating point where the sensitivity to charge noise is minimized. We find that optimizing the magnetic-field orientation reduces the spin-electric susceptibility, resulting in a five-fold enhancement of the Hahn-echo coherence time and a nearly tenfold suppression of control infidelity. At the optimal operating point, gate set tomography demonstrates the maximum gate fidelity of 99.82 %. Our finding enhances the prospects of hole spin qubits for scalable quantum information processing.
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Achieving high-fidelity two-qubit gates is crucial for spin qubits in silicon-based double quantum dots. However, these gates are sensitive to charge noise in experimental settings, which remains a significant challenge. Geometric gates, which utilize pure geometric phases for gate operations, are a promising approach to achieving robust control. In this work, we theoretically propose a feasible strategy to implement geometric two-qubit gates for silicon-based spin qubits considering experimental control environments. By operating in the suitable region where the local magnetic field gradient is significantly larger than the exchange interaction, we can implement both entangling and nonentangling geometric gates through analytical and numerical methods. It is found that the geometric gates obtained are highly compatible with existing experimental techniques using electric dipole spin resonance in silicon. Moreover, the implemented geometric controlled-ZZZ (CZ) gates can achieve fidelities exceeding 99% under experimental noise levels and the gate times are as short as 20 ns. Our work paves the way for the realization of high-fidelity geometric two-qubit gates for spin qubits in silicon.
Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.
Abstract We implement resonant single qubit operations on a semiconductor hybrid qubit hosted in a three-electron Si/SiGe double quantum dot structure. By resonantly modulating the double dot energy detuning and employing electron tunnelling-based readout, we achieve fast (>100 MHz) Rabi oscillations and purely electrical manipulations of the three-electron spin states. We demonstrate universal single qubit gates using a Ramsey pulse sequence as well as microwave phase control, the latter of which shows control of an arbitrary rotation axis on the X–Y plane of the Bloch sphere. Quantum process tomography yields π rotation gate fidelities higher than 93 (96)% around the X (Z) axis of the Bloch sphere. We further show that the implementation of dynamic decoupling sequences on the hybrid qubit enables coherence times longer than 150 ns.
Geometric gates that use the global property of the geometric phase is believed to be a powerful tool to realize fault-tolerant quantum computation. However, for singlet-triplet qubits in semiconductor quantum dot, the low Rabi frequency of the microwave control leads to overly long gating time, and thus the constructing geometric gate suffers more from the decoherence effect. Here we investigate the key issue of whether the fast geometric gate can be realized for singlet-triplet qubits without introducing an extra microwave-driven pulse, while maintaining the high-fidelity gate operation at the same time. We surprisingly find that both the single- and two-qubit geometric gates can be implemented via only modulating the time-dependent exchange interaction of the Hamiltonian, which can typically be on the order of $\ensuremath{\sim}\mathrm{GHz}$, and thus the corresponding gate time is of several nanoseconds. Furthermore, the obtained geometric gates are superior to their counterparts, i.e., the conventional dynamical gates for singlet-triplet qubits, with a relatively high fidelity surpassing 99%. Therefore our scheme is particularly applied to singlet-triplet qubits to obtain fast and high-fidelity geometric gates. Our scheme can also be extended to other systems without a microwave drive.