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

Achieving high-fidelity and robust qubit manipulations is a crucial requirement for realizing fault-tolerant 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 noise-resilient 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. Geometric quantum gates—engineered evolution paths for qubit control—promise noise resilience but have shown limited fidelity in prior implementations in semiconductor quantum computation. Here the authors demonstrate high-fidelity single-qubit gates in a single-hole quantum dot in Ge, outperforming conventional dynamical gates.