The computational power and fault tolerance of future large-scale quantum processors derive in large part from the connectivity between the qubits. One approach to increase connectivity is to engineer qubit–qubit interactions at a distance. Alternatively, the connectivity can be increased by physically displacing the qubits. For semiconductor spin qubits, several studies have investigated spin coherent shuttling of individual electrons, but high-fidelity transport over extended distances remains to be demonstrated. Here we report shuttling of an electron inside an isotopically purified Si/SiGe heterostructure using electric gate potentials. In a first set of experiments, we form static quantum dots and study how spin coherence decays during bucket-brigade shuttling, where we repeatedly move a single electron between up to five dots. Next, for conveyor-mode shuttling, we create a travelling-wave potential, formed with either one or two sets of sine waves, to transport an electron in a moving quantum dot. This method shows a spin coherence an order of magnitude better than the bucket-brigade shuttling. It allows us to displace an electron over an effective distance of 10 μm in under 200 ns while preserving the spin state with a fidelity of 99.5% on average. These results will guide future efforts to realize large-scale semiconductor quantum processors, making use of electron shuttling both within and between qubit arrays.

Micromagnet-enabled electric-dipole spin resonance (EDSR) is an established method for high-fidelity single-spin control in silicon, although so far experiments have been restricted to one-dimensional arrays. In contrast, qubit control based on hopping spins has recently emerged as a compelling alternative, with high-fidelity baseband control realized in sparse two-dimensional hole arrays in germanium. In this work, we commission a ²⁸Si/SiGe 2 × 2 quantum dot array both as a four-qubit device using EDSR and as a two-qubit device using baseband hopping control. We establish a lower bound on the fidelity of the hopping gate of 99.50(6)%, which is similar to the average fidelity of the resonant gate. The hopping gate also circumvents the transient pulse-induced resonance shift from heating observed during EDSR operation. To motivate hopping spins as an attractive means of scaling silicon spin-qubit arrays, we propose an extensible nanomagnet design that enables engineered baseband control of large spin arrays.

Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating gate errors are useful to improve gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor, allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gate-set tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity, controlled-phase gate.

Quantum systems with engineered Hamiltonians can be used to study many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for realizing generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium 4×2 quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays.

The electrical characterisation of classical and quantum devices is a critical step in the development cycle of heterogeneous material stacks for semiconductor spin qubits. In the case of silicon, properties such as disorder and energy separation of conduction band valleys are commonly investigated individually upon modifications in selected parameters of the material stack. However, this reductionist approach fails to consider the interdependence between different structural and electronic properties at the danger of optimising one metric at the expense of the others. Here, we achieve a significant improvement in both disorder and valley splitting by taking a co-design approach to the material stack. We demonstrate isotopically purified, strained quantum wells with high mobility of 3.14(8) × 10⁵ cm² V⁻¹ s⁻¹ and low percolation density of 6.9(1) × 10¹⁰ cm⁻². These low disorder quantum wells support quantum dots with low charge noise of 0.9(3) μeV Hz^−1/2 and large mean valley splitting energy of 0.24(7) meV, measured in qubit devices. By striking the delicate balance between disorder, charge noise, and valley splitting, these findings provide a benchmark for silicon as a host semiconductor for quantum dot qubits. We foresee the application of these heterostructures in larger, high-performance quantum processors.

Qubits that can be efficiently controlled are essential for the development of scalable quantum hardware. Although resonant control is used to execute high-fidelity quantum gates, the scalability is challenged by the integration of high-frequency oscillating signals, qubit cross-talk, and heating. Here, we show that by engineering the hopping of spins between quantum dots with a site-dependent spin quantization axis, quantum control can be established with discrete signals. We demonstrate hopping-based quantum logic and obtain single-qubit gate fidelities of 99.97%, coherent shuttling fidelities of 99.992% per hop, and a two-qubit gate fidelity of 99.3%, corresponding to error rates that have been predicted to allow for quantum error correction. We also show that hopping spins constitute a tuning method by statistically mapping the coherence of a 10-quantum dot system. Our results show that dense quantum dot arrays with sparse occupation could be developed for efficient and high-connectivity qubit registers.

Gate-defined quantum dots define an attractive platform for quantum computation and have been used to confine individual charges in a planar array. Here, we demonstrate control over vertical double quantum dots confined in a strained germanium double quantum well. We sense individual charge transitions with a single-hole transistor. The vertical separation between the quantum wells provides a sufficient difference in capacitive coupling to distinguish quantum dots located in the top and bottom quantum wells. Tuning the vertical double quantum dot to the (1,1) charge state confines a single-hole in each quantum well beneath a single plunger gate. By simultaneously accumulating holes under two neighboring plunger gates, we are able to tune to the (1,1,1,1) charge state. These results motivate quantum dot systems that exploit the third dimension, opening new opportunities for quantum simulation and quantum computing.

Direct interactions between quantum particles naturally fall off with distance. However, future quantum computing architectures are likely to require interaction mechanisms between qubits across a range of length scales. In this work, we demonstrate a coherent interaction between two semiconductor spin qubits 250 μm apart using a superconducting resonator. This separation is several orders of magnitude larger than for the commonly used direct interaction mechanisms in this platform. We operate the system in a regime in which the resonator mediates a spin–spin coupling through virtual photons. We report the anti-phase oscillations of the populations of the two spins with controllable frequency. The observations are consistent with iSWAP oscillations of the spin qubits, and suggest that entangling operations are possible in 10 ns. These results hold promise for scalable networks of spin qubit modules on a chip.

Silicon-based spin qubits offer a potential pathway toward realizing a scalable quantum computer owing to their compatibility with semiconductor manufacturing technologies. Recent experiments in this system have demonstrated crucial technologies, including high-fidelity quantum gates and multiqubit operation. However, the realization of a fault-tolerant quantum computer requires a high-fidelity spin measurement faster than decoherence. To address this challenge, we characterize and optimize the initialization and measurement procedures using the parity-mode Pauli spin blockade technique. Here, we demonstrate a rapid (with a duration of a few μs) and accurate (with >99% fidelity) parity spin measurement in a silicon double quantum dot. These results represent a significant step forward toward implementing measurement-based quantum error correction in silicon.

Electrically driven spin resonance is a powerful technique for controlling semiconductor spin qubits. However, it faces challenges in qubit addressability and off-resonance driving in larger systems. We demonstrate coherent bichromatic Rabi control of quantum dot hole spin qubits, offering a spatially selective approach for large qubit arrays. By applying simultaneous microwave bursts to different gate electrodes, we observe multichromatic resonance lines and resonance anticrossings that are caused by the ac Stark shift. Our theoretical framework aligns with experimental data, highlighting interdot motion as the dominant mechanism for bichromatic driving.

The co-integration of spin, superconducting, and topological systems is emerging as an exciting pathway for scalable and high-fidelity quantum information technology. High-mobility planar germanium is a front-runner semiconductor for building quantum processors with spin-qubits, but progress with hybrid superconductor-semiconductor devices is hindered by the difficulty in obtaining a superconducting hard gap, that is, a gap free of subgap states. Here, we address this challenge by developing a low-disorder, oxide-free interface between high-mobility planar germanium and a germanosilicide parent superconductor. This superconducting contact is formed by the thermally-activated solid phase reaction between a metal, platinum, and the Ge/SiGe semiconductor heterostructure. Electrical characterization reveals near-unity transparency in Josephson junctions and, importantly, a hard induced superconducting gap in quantum point contacts. Furthermore, we demonstrate phase control of a Josephson junction and study transport in a gated two-dimensional superconductor-semiconductor array towards scalable architectures. These results expand the quantum technology toolbox in germanium and provide new avenues for exploring monolithic superconductor-semiconductor quantum circuits towards scalable quantum information processing.

The small footprint of semiconductor qubits is favorable for scalable quantum computing. However, their size also makes them sensitive to their local environment and variations in the gate structure. Currently, each device requires tailored gate voltages to confine a single charge per quantum dot, clearly challenging scalability. Here, we tune these gate voltages and equalize them solely through the temporary application of stress voltages. In a double quantum dot, we reach a stable (1,1) charge state at identical and predetermined plunger gate voltage and for various interdot couplings. Applying our findings, we tune a 2 × 2 quadruple quantum dot such that the (1,1,1,1) charge state is reached when all plunger gates are set to 1 V. The ability to define required gate voltages may relax requirements on control electronics and operations for spin qubit devices, providing means to advance quantum hardware.

We detect correlations in qubit-energy fluctuations of non-neighboring qubits defined in isotopically purified Si/Si-Ge quantum dots. At low frequencies (where the noise is strongest), the correlation coefficient reaches 10% for a next-nearest-neighbor qubit-pair separated by 200 nm. Correlations with the charge-sensor signal reach up to 70%, proving that the observed noise is of electrical origin. A simple theoretical model quantitatively reproduces the measurements and predicts a polynomial decay of correlations with interqubit distance. Our results quantify long-range correlations of noise in quantum-dot spin-qubit arrays, essential for their scalability and fault tolerance.

As spin-based quantum processors grow in size and complexity, maintaining high fidelities and minimizing crosstalk will be essential for the successful implementation of quantum algorithms and error-correction protocols. In particular, recent experiments have highlighted pernicious transient qubit frequency shifts associated with microwave qubit driving. Work-Arounds for small devices, including prepulsing with an off-resonant microwave burst to bring a device to a steady state, wait times prior to measurement, and qubit-specific calibrations all bode ill for device scalability. Here, we make substantial progress in understanding and overcoming this effect. We report a surprising nonmonotonic relation between mixing chamber temperature and spin Larmor frequency which is consistent with observed frequency shifts induced by microwave and baseband control signals. We find that purposefully operating the device at 200 mK greatly suppresses the adverse heating effect while not compromising qubit coherence or single-qubit fidelity benchmarks. Furthermore, systematic non-Markovian crosstalk is greatly reduced. Our results provide a straightforward means of improving the quality of multispin control while simplifying calibration procedures for future spin-based quantum processors.

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

A strained Ge quantum well, grown on a SiGe/Si virtual substrate and hosting two electrostatically defined hole spin qubits, is nondestructively investigated by synchrotron-based scanning X-ray diffraction microscopy to determine all its Bravais lattice parameters. This allows rendering the three-dimensional spatial dependence of the six strain tensor components with a lateral resolution of approximately 50 nm. Two different spatial scales governing the strain field fluctuations in proximity of the qubits are observed at <100 nm and >1 μm, respectively. The short-ranged fluctuations have a typical bandwidth of 2 × 10-4 and can be quantitatively linked to the compressive stressing action of the metal electrodes defining the qubits. By finite element mechanical simulations, it is estimated that this strain fluctuation is increased up to 6 × 10-4 at cryogenic temperature. The longer-ranged fluctuations are of the 10-3 order and are associated with misfit dislocations in the plastically relaxed virtual substrate. From this, energy variations of the light and heavy-hole energy maxima of the order of several 100 μeV and 1 meV are calculated for electrodes and dislocations, respectively. These insights over material-related inhomogeneities may feed into further modeling for optimization and design of large-scale quantum processors manufactured using the mainstream Si-based microelectronics technology.

We grow strained Ge/SiGe heterostructures by reduced-pressure chemical vapor deposition on 100 mm Ge wafers. The use of Ge wafers as substrates for epitaxy enables high-quality Ge-rich SiGe strain-relaxed buffers with a threading dislocation density of ( 6 ± 1 ) × 10 5 cm − 2 , nearly an order of magnitude improvement compared to control strain-relaxed buffers on Si wafers. The associated reduction in short-range scattering allows for a drastic improvement of the disorder properties of the two-dimensional hole gas, measured in several Ge/SiGe heterostructure field-effect transistors. We measure an average low percolation density of ( 1.22 ± 0.03 ) × 10 10 cm − 2 and an average maximum mobility of ( 3.4 ± 0.1 ) × 10 6 cm 2 / Vs and quantum mobility of ( 8.4 ± 0.5 ) × 10 4 cm 2 / Vs when the hole density in the quantum well is saturated to ( 1.65 ± 0.02 ) × 10 11 cm − 2 . We anticipate immediate application of these heterostructures for next-generation, higher-performance Ge spin-qubits, and their integration into larger quantum processors.