Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity

Abstract

Spin qubits defined by valence band hole states are attractive for quantum information processing due to their inherent coupling to electric fields, enabling fast and scalable qubit control. Heavy holes in germanium are particularly promising, with recent demonstrations of fast and high-fidelity qubit operations. However, the mechanisms and anisotropies that underlie qubit driving and decoherence remain mostly unclear. Here we report the highly anisotropic heavy-hole g-tensor and its dependence on electric fields, revealing how qubit driving and decoherence originate from electric modulations of the g-tensor. Furthermore, we confirm the predicted Ising-type hyperfine interaction and show that qubit coherence is ultimately limited by 1/f charge noise, where f is the frequency. Finally, operating the qubit at low magnetic field, we measure a dephasing time of $${T}_{2}^{* }$$ T 2 * = 17.6 μs, maintaining single-qubit gate fidelities well above 99% even at elevated temperatures of T > 1 K. This understanding of qubit driving and decoherence mechanisms is key towards realizing scalable and highly coherent hole qubit arrays.

Operating semiconductor quantum processors with hopping spins

“…The observed variability in this distribution is likely a result of multiple factors: the heterogeneity inherent in the shapes of the quantum dots (dot-to-dot variability), the presence of strain gradients in the quantum well arising from the gates above or the SiGe strained relaxed buffer below, and the impact of interface charges. The average g -factor that we obtained was considerably lower than what has been observed in the literature ( 10 , 24 , 26 , 30 ). We suggest that this reduction is primarily due to two phenomena: a precise in-plane magnetic field configuration and an appreciable renormalization of the gyromagnetic ratio from the pure heavy-hole value of ~0.18 ( 27 , 28 , 42 ).…”

“…Consequently, a small tilt of the applied magnetic field from the in-plane g -tensor will lead to a strong reorientation of the spin quantization axis in the out-of-plane direction. Subsequently, when an in-plane magnetic field is applied, the orientation of the spin quantization axis is highly sensitive to the local g -tensor, and thus to confinement, strain, and electric fields, thus becoming a site-dependent property ( 21 , 24 , 28 , 29 ). Here, we exploited this aspect to establish hopping-based quantum operations in two different devices: a four-quantum dot array ( 30 ) arranged in a 2 × 2 configuration and a 10–quantum dot system arranged in a 3-4-3 configuration.…”

“…A key advantage in such a hopping-based operation is that the spin rotation frequency is given by the Larmor precession. The latter remains sizeable even at small magnetic fields where quantum coherence is substantially improved ( 23 , 24 ). This enabled us to perform universal quantum control with error rates exceeding the thresholds predicted for practical quantum error correction ( 25 ) while also operating with low-frequency baseband signals.…”

“…High-fidelity single-qubit operations and long qubit coherence times at low magnetic field A large difference in the orientation of the spin quantization axes between quantum dots is essential for hopping-based qubit operations. Holes in planar germanium heterostructures manifest a pronounced anisotropic g-tensor, with an out-of-plane g-factor, g ⊥ , that can be two orders of magnitude larger than the inplane component, g || (20,24,26,27). Consequently, a small tilt of the applied magnetic field from the in-plane g-tensor will lead to a strong reorientation of the spin quantization axis in the out-of-plane direction.…”