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.

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.

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.

An electron confined by a semiconductor quantum dot (QD) can be displaced by changes in electron occupations of surrounding QDs owing to the Coulomb interaction. For a single-spin qubit in an inhomogeneous magnetic field, such a positional displacement of the host electron results in a qubit energy shift, which must be handled carefully for high-fidelity operations. Here, we spectroscopically investigate the qubit energy shift induced by changes in charge occupations of nearby QDs for a silicon single-spin qubit in a magnetic field gradient. Between two different charge configurations of an adjacent double QD, a spin qubit shows an energy shift of about 4 MHz, which necessitates strict management of electron positions over a QD array. We confirm a correlation between the qubit frequency and the charge configuration by using a postselection analysis.

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.

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.

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.

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.

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.

Quantum links can interconnect qubit registers and are therefore essential in networked quantum computing. Semiconductor quantum dot qubits have seen significant progress in the high-fidelity operation of small qubit registers but establishing a compelling quantum link remains a challenge. Here, we show that a spin qubit can be shuttled through multiple quantum dots while preserving its quantum information. Remarkably, we achieve these results using hole spin qubits in germanium, despite the presence of strong spin-orbit interaction. In a minimal quantum dot chain, we accomplish the shuttling of spin basis states over effective lengths beyond 300 microns and demonstrate the coherent shuttling of superposition states over effective lengths corresponding to 9 microns, which we can extend to 49 microns by incorporating dynamical decoupling. These findings indicate qubit shuttling as an effective approach to route qubits within registers and to establish quantum links between registers.

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.

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.

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.

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.

Continuous rounds of quantum error correction (QEC) are essential to achieve faulttolerant quantum computers (QCs). In each QEC cycle, thousands of ancilla quantum bits (qubits) must be read out faster than the qubits' decoherence time (<<T2∗~120μs for spin qubits). To address this urgent need, several CMOS receivers operating at cryogenic temperatures (cryo-CMOS RXs) have recently been introduced for gate-based [1] and RF reflectometry [2] readout of spin qubits, as well as transmons' dispersive readout [3]. However, they have a few shortcomings. First, due to the temperatureindependent shot noise of transistors in nanometer CMOS technology [4], their measured noise temperature (TN) is limited to 40K, thus degrading qubit readout fidelity. Second, due to their large TN, prior art showed either only the electrical performance of their chips by applying a relatively large (i.e., -85dBm [2]) modulated signal directly to the RX input [2,3] or offered limited qubit measurements by exploiting a HEMT amplifier prior to the RX [1]. Those issues hinder future monolithic integration between solid-state qubits and readout electronics. This work advances the prior art by (1) introducing a wideband passive amplification circuit at the RX front-end to minimize the shot noise contribution of the active devices, lowering prior art TN by ~2.7x; (2) demonstrating the RX performance in an RF-reflectometry qubit readout scheme without using off-the-shelf LNA prior to the RX.

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.

Hole-based spin qubits in strained planar germanium quantum wells have received considerable attention due to their favorable properties and remarkable experimental progress. The sizeable spin-orbit interaction in this structure allows for efficient qubit operations with electric fields. However, it also couples the qubit to electrical noise. In this work, we perform simulations of a heterostructure hosting these hole spin qubits. We solve the effective mass equations for a realistic heterostructure, provide a set of analytical basis wavefunctions, and compute the effective g-factor of the heavy-hole ground state. Our investigations reveal a strong impact of highly excited light-hole states located outside the quantum well on the g-factor. We find that sweet spots, points of operations that are least susceptible to charge noise, for out-of-plane magnetic fields are shifted to impractically large electric fields. However, for magnetic fields close to in-plane alignment, partial sweet spots at low electric fields are recovered. Furthermore, sweet spots with respect to multiple fluctuating charge traps can be found under certain circumstances for different magnetic field alignments. This work will be helpful in understanding and improving the coherence of germanium hole spin qubits.

The coherent control of interacting spins in semiconductor quantum dots is of strong interest for quantum information processing and for studying quantum magnetism from the bottom up. Here we present a 2 × 4 germanium quantum dot array with full and controllable interactions between nearest-neighbour spins. As a demonstration of the level of control, we define four singlet–triplet qubits in this system and show two-axis single-qubit control of each qubit and SWAP-style two-qubit gates between all neighbouring qubit pairs, yielding average single-qubit gate fidelities of 99.49(8)–99.84(1)% and Bell state fidelities of 73(1)–90(1)%. Combining these operations, we experimentally implement a circuit designed to generate and distribute entanglement across the array. A remote Bell state with a fidelity of 75(2)% and concurrence of 22(4)% is achieved. These results highlight the potential of singlet–triplet qubits as a competing platform for quantum computing and indicate that scaling up the control of quantum dot spins in extended bilinear arrays can be feasible.

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.