The scalability and power of quantum computing architectures depend critically on high-fidelity operations and robust and flexible qubit connectivity^{1, 2–3}. In this respect, mobile qubits are particularly attractive as they enable dynamic and reconfigurable qubit arrays. This approach allows quantum processors to adapt their connectivity patterns during operation, implement different quantum error correction codes on the same hardware and optimize resource use through dedicated functional zones for specific operations such as measurement or entanglement generation^{4, 5, 6–7}. Such flexibility also relieves architectural constraints, as recently demonstrated in atomic systems based on trapped ions^4,5 and neutral atoms manipulated with optical tweezers^6,7. In solid-state platforms, highly coherent shuttling of electron spins was recently reported^8,9. A key outstanding question is whether it may be possible to perform quantum gates directly on the mobile spins. Here we demonstrate two-qubit operations between two electron spins carried towards each other in separate travelling potential minima in a semiconductor device. We find that the interaction strength is highly tunable by their spatial separation. When we shuttle the two spins towards the centre by 120 nm each for a total displacement of 240 nm, we achieve an average two-qubit gate fidelity of about 99%. Furthermore, we implement conditional post-selected quantum state teleportation between qubits separated by 320 nm with an average gate fidelity of 87%, showcasing the potential of mobile spin qubits for non-local quantum information processing. We expect that operations on mobile qubits will become a universal feature of future large-scale semiconductor quantum processors.

The large-scale integration of semiconductor spin qubits into quantum processors will require the characterization of quantum components at scale. However, such characterization is challenging and typically requires radio-frequency measurements at millikelvin temperatures and the presence of magnetic fields. Here we report a scalable architecture for characterizing spin qubits using a quantum dot crossbar array. The approach, which we term as the qubit-array research platform for engineering and testing, uses a crossbar array comprising tightly pitched spin-qubit tiles and is implemented in planar germanium, with the potential to host 1,058 single-hole spin qubits. We measure a subset of 40 tiles and demonstrate key device functionality at millikelvin temperatures, including tile addressability, threshold voltage and charge noise statistics, as well as the characterization of hole spin qubits and their coherence times in a single tile.

Evaluation of the quantum lifetime in two-dimensional hole systems, together with band-structure parameters such as the effective mass and g factor, becomes challenging when competing energy scales shape Shubnnikov–de Haas oscillations in a magnetic field. Here, we overcome this challenge for holes with pseudospin J_z = ± ₂ ³, confined in low-disorder strained germanium quantum wells. We extract self-consistently the effective mass, g factor, and quantum lifetime, and estimate a maximum quantum mobility of 133(3) × 10³ cm²/V s, setting a benchmark for holes in group IV semiconductors. The high quality of the hole gas if further highlighted by observing clean fractional quantum Hall states at low magnetic field and density.

Quantum simulators enable studies of many-body phenomena, which are intractable with classical hardware. The manipulation of electronic spin states in devices based on semiconductor quantum dots promises precise electrical control and scalability advantages, but accessing many-body phenomena has so far been restricted by challenges in nanofabrication and simultaneous control of multiple interactions. in this study, we performed spectroscopy of up to eight interacting spins using a 2-×-4 array of gate-defined germanium quantum dots. The spectroscopy protocol is based on ramsey interferometry and adiabatic mapping of many-body eigenstates to single-spin eigenstates, enabling complete energy spectrum reconstruction. As the interaction strength exceeds magnetic disorder, we observed signatures of the crossover from localization to a chaotic phase marking a step toward the observation of many-body phenomena in quantum dot systems.

Understanding scattering mechanisms in semiconductor heterostructures is crucial to reducing sources of disorder and ensuring high yield and uniformity in large spin qubit arrays. Disorder of the parent two-dimensional electron or hole gas is commonly estimated by the critical, percolation-driven density associated with the metal–insulator transition. However, a reliable estimation of the critical density within percolation theory is hindered by the need to measure conductivity with high precision at low carrier densities, where experiments are most difficult. Here, we connect experimentally percolation density and quantum Hall plateau width, in line with an earlier heuristic intuition, and offer an alternative method for characterizing semiconductor heterostructure disorder.

Strained germanium ((Formula presented.) -Ge) and strained silicon ((Formula presented.) -Si) buried quantum wells have enabled advanced spin-qubit quantum processors. However, in the absence of suitable lattice-matched substrates, (Formula presented.) -Ge and (Formula presented.) -Si are deposited on defective, metamorphic SiGe buffers, which may impact device performance and scaling. Here an alternative platform is introduced based on the heterojunction between bulk unstrained Ge and a lattice-matched strained silicon-germanium ((Formula presented.) -SiGe) barrier, eliminating the need for metamorphic buffers altogether. In a structure with a 52-nm-thick (Formula presented.) -SiGe barrier, a low-disorder two-dimensional hole gas is demonstrated with a high-mobility of (Formula presented.) and a low percolation density of (Formula presented.). Quantum transport shows that holes confined in the buried unstrained Ge channel have a strong density-dependent in-plane effective mass and out-of-plane (Formula presented.) -factor, pointing to a significant heavy-hole–light-hole mixing in agreement with theory. Measurements of Zeeman-split levels in quantum point contacts further highlight this character, showing a two-fold larger in-plane (Formula presented.) -factor in Ge than in (Formula presented.) -Ge. The prospects of strong spin–orbit interaction, isotopic purification, and of hosting superconducting pairing correlations make this platform appealing for fast quantum hardware and hybrid quantum systems.

Constricting transport through a one-dimensional quantum point contact in the quantum Hall regime enables gate-tunable selection of the edge modes propagating between voltage probe electrodes. Here, we investigate the quantum Hall effect in a quantum point contact fabricated on low disorder strained germanium quantum wells. For increasing magnetic field, we observe Zeeman spin-split 1D ballistic hole transport evolving to integer quantum Hall states, with well-defined quantized conductance increasing in multiples of e ² / h down to the first integer filling factor ν = 1. These results establish strained germanium as a viable platform for complex experiments probing many-body states and quantum phase transitions.

The simplicity of encoding a qubit in the state of a single electron spin and the potential for their integration into industry-standard microchips continue to drive the field of semiconductor-based quantum computing. After a series of key first-principles demonstrations validating universal gate operations, initialization and readout, three-qubit algorithms have already been realized with silicon-based quantum dots in past years. Devices containing more qubits have become available since then but experiments have not gone beyond meeting the DiVincenzo criteria. In this work, we fully exploit the capacity of a spin-qubit array and implement a six-qubit quantum circuit, the largest utilizing semiconductor quantum technology. By programming the quantum processor, we execute quantum circuits across all permutations of three, four, five, and six neighboring qubits, demonstrating successful programmable multi-qubit operation throughout the array. Using an error model that incorporates quasi-static noise allows us to qualitatively explain some key trends in our experimental results and highlight the necessity to minimize idling times through simultaneous operations, extending dephasing times, and consistently improving state preparation and measurement fidelities.

We investigate low-frequency noise in a spin-qubit device made in isotopically purified Si/Si-Ge. Observing sizable cross-correlations among energy fluctuations of different qubits, we conclude that these fluctuations are dominated by charge noise. At low frequencies, the noise spectra are not well described by a power law; instead, they reveal the presence of a few individual two-level fluctuators (TLFs). We demonstrate that the noise cross-correlations allow one to get information on the spatial location of such individual TLFs.

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.

Solid-state qubits are sensitive to their microscopic environment, causing the qubit properties to fluctuate on a wide range of timescales. The sub-Hz end of the spectrum is usually dealt with by repeated background calibrations, which bring considerable overhead. It is thus important to characterize and understand the low-frequency variations of the relevant qubit characteristics. In this study, we investigate the stability of spin qubit frequencies in the Si/SiGe quantum dot platform. We find that the calibrated qubit frequencies of a six-qubit device vary by up to ±100 MHz while performing a variety of experiments over a span of 912 days. These variations are sensitive to the precise voltage settings of the gate electrodes, however when these are kept constant to within 15 µV, the qubit frequencies vary by less than ±7 MHz over periods up to 36 days. During overnight scans, the qubit frequencies of ten qubits across two different devices show a standard deviation below 200 kHz within a 1-hour time window. The qubit frequency noise spectral density shows roughly a 1/f trend above 10⁻⁴ Hz and, strikingly, a steeper trend at even lower frequencies.

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 rapidly growing number of qubits in semiconductor quantum computers requires a scalable control interface, including the efficient generation of dc bias voltages for gate electrodes. To avoid unrealistically complex wiring between any room-temperature electronics and the cryogenic qubits, this article presents an integrated cryogenic solution for the bias-voltage generation and distribution for large-scale semiconductor spin-qubit quantum processors. A dedicated cryogenic CMOS (cryo-CMOS) demultiplexer and a cryo-CMOS dc digital-to-analog converter (DAC) have been developed in a 22-nm fin field-effect transistor process to control a codeveloped 2-D array designed with 648 single-hole transistors. Thanks to the dissipation below 120 µ W, the whole system operates at temperatures below 70 mK in a custom-built electrical/mechanical infrastructure embedded in a standard single-pulse-tube dilution refrigerator. The bias voltages generated by the cryo-CMOS DAC are demultiplexed to sample-and-hold structures, allowing to store 96 unique bias voltages over a 3 V range with a voltage drift between 60 µ V / s and 18 mV/s. This work demonstrates a tight integration at mK temperatures of cryo-CMOS bias generation and distribution with a dedicated large-scale quantum device. This showcases how this approach simplifies the wiring to the electronics, thus facilitating the scaling up of quantum processors toward the large number of qubits required for a practical quantum computer.

Electron-spin qubits in Si/SiGe quantum wells are limited by the small and variable energy separation of the conduction-band valleys. While sharp quantum-well interfaces are pursued to increase the valley-splitting energy deterministically, here we explore an alternative approach to enhancing the valley splitting on average. We grow increasingly thinner quantum wells with broad interfaces to controllably increase the electron wave function overlap with Ge atoms. Quantum Hall measurements of two-dimensional electron gases reveal a linear correlation between valley splitting and disorder-induced single-particle energy-level broadening, driven by increasing alloy scattering at the Si/SiGe interface. We demonstrate enhanced valley splitting while maintaining respectable electron mobility, indicating a low-disorder electrostatic potential environment. Simulations using experimental Ge concentration profiles predict an average valley splitting in quantum dots that matches the enhancement observed in two-dimensional systems. Our results motivate the experimental realization of quantum-dot spin qubits in these heterostructures.

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.

Coupled spins in semiconductor quantum dots are a versatile platform for quantum computing and simulations of complex many-body phenomena. However, on the path of scale-up, crosstalk from densely packed electrodes poses a severe challenge. While crosstalk onto the quantum dot potentials is nowadays routinely compensated for, crosstalk on the exchange interaction is much more difficult to tackle because it is not always directly measurable. Here we propose and implement a way of characterizing and compensating crosstalk on adjacent exchange interactions by following the singlet-triplet avoided crossing in Ge. We show that we can easily identify the barrier-to-barrier crosstalk element without knowledge of the particular exchange value in a 2×4 quantum dot array. We uncover striking differences among these crosstalk elements that can be linked to the geometry of the device and the barrier gate fan-out. We validate the method by tuning up four-spin Heisenberg chains. The same method should be applicable to longer chains of spins and to other semiconductor platforms in which mixing of the singlet and the lowest-energy triplet is present or can be engineered. Additionally, this procedure is well-suited for automated tuning routines as we obtain a standout feature that can be easily tracked and directly returns the magnitude of the crosstalk.

Semiconductor spin qubits have emerged as a promising platform for quantum computing, following a significant improvement in their control fidelities over recent years. Increasing the qubit count remains challenging, beginning with the fabrication of small features and complex fan-outs. A particular challenge has been formed by the need for individual barrier gates to control the exchange interaction between adjacent spin qubits. Here, we propose a method to vary two-qubit interactions without applying pulses on individual barrier gates while also remaining insensitive to detuning noise in first order. Experimentally we find that changing plunger gate voltages over 300 mV can tune the exchange energy J from 100 kHz to 60 MHz. This allows us to perform two-qubit operations without changing the barrier gate voltage. Based on these findings we conceptualize a spin qubit architecture without individual barrier gates, simplifying the fabrication while maintaining the control necessary for universal quantum computation.

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.

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.

(Scanning) transmission electron microscopy ((S)TEM) has significantly advanced materials science but faces challenges in correlating precise atomic structure information with the functional properties of devices due to its time-intensive nature. To address this, an analytical workflow is introduced for the holistic characterization, modelling, and simulation of device heterostructures. This workflow automates the experimental (S)TEM data analysis, providing an in-depth characterization of crystallographic information, 3D orientation, elemental composition, and strain distribution. It reduces a process that typically takes days for a trained human into an automatic routine solved in minutes. Utilizing a physics-guided artificial intelligence model, it generates representative descriptions of materials and samples. The workflow culminates in creating digital twins of systems limited with at least one axis of translational invariance –3D finite element and atomic models of millions of atoms–enabling simulations that provide crucial insights into device behavior in practical applications. Demonstrated with SiGe planar heterostructures for scalable spin qubits, the workflow links digital twins to theoretical properties, revealing how atomic structure impacts materials and functional properties such as spatially-resolved phononic or electronic characteristics, or (inverse) spin orbit lengths. The versatility of the workflow is demonstrated through its application to a wide array of materials systems, device configurations, and sample morphologies.