A two-dimensional 10-qubit array in germanium with robust and localised qubit control

TL;DR

This work demonstrates a two-dimensional, 10-qubit array in a Ge/SiGe platform with robust, highly localised qubit control via electric-dipole spin resonance (EDSR). By integrating material growth, device fabrication, gate virtualization, and comprehensive modelling, the authors show that plunger-gate driving can strongly enhance EDSR in three-hole dot configurations, producing localized qubit drives despite pronounced g-tensor anisotropy. The study combines extensive experimental data (RB fidelities, exchange spectroscopy, and LSES/EDSR measurements) with analytical and numerical models (g-matrix formalism, four-band Luttinger-Kohn, and full configuration interaction) to reveal how intradot Coulomb interactions, dot symmetry, and magnetic-field orientation shape qubit control. Importantly, the results illustrate the potential for scalable quantum processors: robust, addressable qubits with controllable exchange and predictable gating behavior across a 2D array, aided by gate virtualization and disorder-aware design. The insights into multi-hole dot physics and many-body contributions provide a path toward higher-fidelity, scalable spin-qubit architectures in semiconductor platforms.

Abstract

Quantum computers require the systematic operation of qubits with high fidelity. For holes in germanium, the spin-orbit interaction allows for \textit{in situ} electric fast and high-fidelity qubit gates. However, the interaction also causes a large qubit variability due to strong g-tensor anisotropy and dependence on the environment. Here, we leverage advances in material growth, device fabrication, and qubit control to realise a two-dimensional 10-spin qubit array, with qubits coupled up to four neighbours that can be controlled with high fidelity. By exploring the large parameter space of gate voltages and quantum dot occupancies, we demonstrate that plunger gate driving in the three-hole occupation enhances electric-dipole spin resonance (EDSR), creating a highly localised qubit drive. Our findings, confirmed with analytical and numerical models, highlight the crucial role of intradot Coulomb interaction and magnetic field direction. Furthermore, the ability to engineer qubits for robust control is a key asset for further scaling.

Figures (17)

• Figure S1: Scanning electron microscope image of a device nominally identical to the one utilised in the experiments without any false colouring.
• Figure S2: Single-qubit gate benchmark on the 10 qubits. The black dots correspond to the averaged randomised benchmarking data over 10 randomisations, the red line is the exponential fit to extract the gate fidelity $F_\mathrm{gate}$ and the grey area covers the standard deviation of the data. The error bar only denotes the precision of the fit. We also remark that while the sequence lengths of 100 Clifford yields saturation for fidelities below 99.4%, larger length sequences may be needed to probe the precise fidelities of the better performing qubits.
• Figure S3: a-j. Exchange splitting for all ten qubits. The observed splitting of the qubit resonance frequency as a function of virtual barrier voltage is directly proportional to the exchange coupling between qubits.
• Figure S4: a-d. Examplary data of exchange interaction between qubit pairs.
• Figure S5: Effective g-factor values of the 10 qubits in the single, three and five-hole occupation.