Spin qubits in germanium gate-defined quantum dots have made considerable progress within the last few years, partially due to their strong spin-orbit coupling and site-dependent g-tensors. While this characteristic of the g-factors removes the need for micromagnets and allows for the possibility of all-electric qubit control, relying on these g-tensors necessitates the need to understand their sensitivity to the confinement potential that defines the quantum dots. Here, we demonstrate a S − T_ qubit whose frequency is a strong function of the voltage applied to the barrier gate shared by the quantum dots. We find a g-factor that can be approximately increased by an order of magnitude adjusting the barrier gate voltage only by 12 mV. We show how this strong dependence could potentially be attributed to the dots moving through a variable strain environment in our device. This work not only reinforces previous findings that site-dependent g-tensors in germanium can be utilized for qubit manipulation, but reveals the sensitivity and tunability these g-tensors have to the electrostatic confinement of the quantum dot.

Disorder in the heterogeneous material stack of semiconductor spin qubit systems introduces noise that compromises quantum information processing, posing a challenge to coherently control large-scale quantum devices. Here we exploit low-disorder epitaxial, strained quantum wells in Ge/SiGe heterostructures grown on Ge wafers to comprehensively probe the noise properties of complex micrometre-scale devices, comprising quantum dots arranged in a two-dimensional array. We demonstrate an average low charge noise across different locations on the wafer, providing a benchmark for quantum confined holes. We then establish spin qubit control and extend our investigation from electrical to magnetic noise through spin echo measurements. Exploiting dynamical decoupling sequences, we quantify the power spectral density components arising from the hyperfine interaction with 73Ge spinful isotopes and identify coherence modulations associated with the interaction with the 29Si nuclear spin bath near the Ge quantum well, underscoring the need for full isotopic purification of the qubit host environment.

Quantum computers require the systematic operation of qubits with high fidelity. For holes in germanium, the spin-orbit interaction allows for 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.

As quantum computing advances towards practical applications, reducing errors remains a crucial frontier for developing near-term devices. Errors in the quantum gates and quantum state readout result in noisy circuits, which would prevent the acquisition of the exact expectation values of the observables. Although ultimate robustness to errors is known to be achievable by quantum error correction-based fault-tolerant quantum computing, its successful implementation demands large-scale quantum processors with low average error rates that are not yet widely available. In contrast, quantum error mitigation offers more immediate and practical techniques, which do not require extensive resources and can be readily applied to existing quantum devices to improve the accuracy of the expectation values. Here, we report the implementation of a zero-noise extrapolation-based error mitigation technique on a silicon spin qubit platform. This technique has recently been successfully demonstrated for other platforms such as superconducting qubits, trapped-ion qubits, and photonic processors. We first explore three methods for amplifying noise on a silicon spin qubit: global folding, local folding, and pulse stretching, using a standard randomized benchmarking protocol. We then apply global folding-based zero-noise extrapolation to the state tomography and achieve a state fidelity of 99.96% (98.52%), compared to the unmitigated fidelity of 75.82% (82.16%) for different preparation states. These results show that the zero-noise extrapolation technique is a versatile approach that is generally adaptable to quantum computing platforms with different noise characteristics through appropriate noise amplification methods.

Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors. High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment. However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings. While virtual gates offer a practical solution, determining all the required cross-capacitance matrices accurately and efficiently in large quantum dot registers is an open challenge. Here, we establish a modular automated virtualization system (MAViS)—a general and modular framework for autonomously constructing a complete stack of multilayer virtual gates in real time. Our method employs machine learning techniques to rapidly extract features from two-dimensional charge stability diagrams. We then utilize computer vision and regression models to self-consistently determine all relative capacitive couplings necessary for virtualizing plunger and barrier gates in both low- and high-tunnel-coupling regimes. Using MAViS, we successfully demonstrate accurate virtualization of a dense two-dimensional array comprising ten quantum dots defined in a high-quality Ge/SiGe heterostructure. Our work offers an elegant and practical solution for the efficient control of large-scale semiconductor quantum dot systems.

Addressing and mitigating decoherence sources plays an essential role in the development of a scalable quantum computing system, which requires low gate errors to be consistently maintained throughout the circuit execution. While nuclear spin-free materials, such as isotopically purified silicon, exhibit intrinsically promising coherence properties for electron spin qubits, the omnipresent charge noise, when converted to magnetic noise under a strong magnetic field gradient, often hinders stable qubit operation within a time frame comparable to the data acquisition time. Here, we demonstrate both open- and closed-loop suppression techniques for the transduced noise in silicon spin qubits, resulting in a more than two-fold (ten-fold) improvement of the inhomogeneous coherence time (Rabi oscillation quality) that leads to a single-qubit gate fidelity of over 99.6% even in the presence of a strong decoherence field gradient. Utilizing gate set tomography, we show that adaptive qubit control also reduces the non-Markovian noise in the system, which validates the stability of the gate fidelity. The technique can be used to learn multiple Hamiltonian parameters and is useful for the intermittent calibration of the circuit parameters with affordable experimental overhead, providing a useful subroutine during the repeated execution of general quantum circuits.

As one of the few group IV materials with the potential to host superconductor–semiconductor hybrid devices, planar germanium hosting proximitized quantum dots is a compelling platform to achieve and combine topological superconductivity with existing and new qubit modalities. We demonstrate a quantum dot in a Ge/SiGe heterostructure proximitized by a platinum germanosilicide (PtSiGe) superconducting lead, forming a superconducting lead–quantum dot–superconducting lead junction. We show tunability of the coupling strength between the quantum dot and the superconducting lead, and gate control of the ratio of charging energy and the induced gap, and we tune the ground state of the system between even and odd parity. Furthermore, we characterize critical magnetic field strengths, finding a critical out-of-plane field of 0.90 ± 0.04 T. Finally, we explore sub-gap spin splitting, observing rich physics in the resulting spectra, that we model using a zero-bandwidth model in the Yu–Shiba–Rusinov limit. Our findings open up the physics of alternative spin and superconducting qubits, and the physics of Josephson junction arrays, in germanium. The authors achieve gate-controlled proximitization of a quantum dot in a planar germanium heterostructure, an isotopically purifiable group IV material. A patterned Pt germanosilicide superconductor is introduced via a thermally activated reaction.

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.

We investigate the disorder properties of two-dimensional hole gases in Ge/SiGe heterostructures grown on Ge wafers, using thick SiGe barriers to mitigate the influence of the semiconductor-dielectric interface. Across several heterostructure field effect transistors, we measure an average maximum mobility of (4.4 +/- 0.2)x10(6) cm(2)/Vs at a saturation density of (1.72 +/- 0.03)x10(11) cm(-2), corresponding to a long mean free path of (30 +/- 1)mu m. The highest measured mobility is 4.68x106 cm(2)/Vs. We identify uniform background impurities and interface roughness as the dominant scattering mechanisms limiting mobility in a representative device, and we evaluate a percolation-induced critical density of (4.5 +/- 0.1)x10(9) cm(-2). This low-disorder heterostructure, according to simulations, may support the electrostatic confinement of holes in gate-defined quantum dots. C2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).https://doi.org/10.1063/5.0242746

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.

Atom probes generate three-dimensional atomic-scale tomographies of material volumes corresponding to the size of modern-day solid-state devices. Here, the capabilities of atom probe tomography are evaluated to analyze buried interfaces in semiconductor heterostructures relevant for electronic and quantum devices. Employing brute-force search, the current dominant reconstruction protocol to generate tomographic three-dimensional images from Atom Probe data is advanced to its limits. Using Si/SiGe heterostructure for qubits as a model system, the authors show that it is possible to extract interface properties like roughness and width that agree with transmission electron microscopy observations on the sub-nanometer scale in an automated and highly reproducible manner. The demonstrated approach is a versatile method for atomic-scale characterization of buried interfaces in semiconductor heterostructures.

Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. Thus far, developments have been limited to quantum dots defined in a single plane. Here, we propose to advance beyond planar systems by exploiting heterostructures with multiple quantum wells. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. In quantum transport measurements we observe stability diagrams corresponding to a double quantum dot system. We analyze the capacitive coupling to the nearby gates and find two quantum dots accumulated under the central plunger gate. We extract the position and estimated size, from which we conclude that the double quantum dots are vertically stacked in the two quantum wells. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.

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)×105 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)×1010 cm−2 and an average maximum mobility of (3.4±0.1)×106 cm2/Vs and quantum mobility of (8.4±0.5)×104 cm2/Vs when the hole density in the quantum well is saturated to (1.65±0.02)×1011 cm−2. We anticipate immediate application of these heterostructures for next-generation, higher-performance Ge spin-qubits, and their integration into larger quantum processors.

Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport. We find that the concentration fluctuations of Si and Ge atoms within the 3D landscape of Si/SiGe interfaces can explain the observed large spread of valley splitting from measurements on many quantum dot devices. Against the prevailing belief, we propose to boost these random alloy composition fluctuations by incorporating Ge atoms in the Si quantum well to statistically enhance valley splitting.

Brian Paquelet Wuetz,1, ∗ Merritt P. Losert,2, ∗ Sebastian Koelling,3, ∗ Lucas E.A. Stehouwer,1 Anne-Marije J. Zwerver,1 Stephan G. J. Philips,1 Mateusz T. Mądzik,1 Xiao Xue,1 Guoji Zheng,1 Mario Lodari,1 Sergey V. Amitonov,1 Nodar Samkharadze,4 Amir Sammak,4 Lieven M. K. Vandersypen,1 Rajib Rahman,5 Susan N. Coppersmith,5 Oussama Moutanabbir,3 Mark Friesen,2 and Giordano Scappucci1, † 1QuTech and Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands 2University of Wisconsin-Madison, Madison, WI 53706 USA 3Department of Engineering Physics, École Polytechnique de Montréal, Montréal, Case Postale 6079, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3A7 4QuTech and Netherlands Organisation for Applied Scientific Research (TNO), Delft, The Netherlands. 5University of New South Wales, Sydney, Australia (Dated: December 20, 2021)

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field B and Hall density by performing activation energy measurements in the quantum Hall regime over a large range of filling factors. The mobility gap of the valley-split levels increases linearly with B and is strikingly independent of Hall density. The data are consistent with a transport model in which valley splitting depends on the incremental changes in density eB/h across quantum Hall edge strips, rather than the bulk density. Based on these results, we estimate that the valley splitting increases with density at a rate of 116  μeV/10^{11} cm^{-2}, which is consistent with theoretical predictions for near-perfect quantum well top interfaces.