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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., QCD/Veldhorst Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Veldhorst Lab

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., BUS/TNO STAFF, QCD/Scappucci Lab

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., QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Veldhorst Lab, QCD/Scappucci Lab, QN/Veldhorst Lab, QN/Vandersypen Lab

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., Aerospace Engineering, BUS/TNO STAFF, QCD/Scappucci Lab

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 double quantum dot in a strained germanium double quantum well, where both quantum dots are tunnel coupled to both reservoirs and parallel transport occurs. We analyze the capacitive coupling to nearby gates and find both quantum dots to be accumulated under the central plunger gate. We extract their position and size, from which we conclude that the double quantum dots are vertically stacked in the two quantum wells. We discuss the challenges and opportunities of multilayer devices and outline some potential applications in quantum computing and quantum simulation., QCD/Veldhorst Lab, QCD/Scappucci Lab, BUS/TNO STAFF, QN/Veldhorst Lab

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., QCD/Vandersypen Lab, QID/Dobrovitski Group, Business Development, BUS/TNO STAFF, BUS/Quantum Delft, QCD/Scappucci Lab, QN/Vandersypen Lab

A clear understanding of the spectral components of an irradiated beam, or captured optical emission, is essential to optimize an optical system and increase its performance. Logically, for this purpose a grating-based spectrometer could be the first choice. However, in the case of a wide range spectrum, and for radiation with one dominant wavelength, this option may not work well. In this paper, we present a technique based on an array of bandpass detectors to measure accurately the power of a number of beam-specific spectral components in a wide spectrum range: from soft X-ray to infrared. The main unique features of this technique are: customization for specific wavelengths of interest; vacuum compatibility; and high sensitivity to low-energy spectral components in the presence of one or more dominant highpower spectral components., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Electronic Instrumentation, EKL Processing, BUS/TNO STAFF

Simulations using highly tunable quantum systems may enable investigations of condensed matter systems beyond the capabilities of classical computers. Quantum dots and donors in semiconductor technology define a natural approach to implement quantum simulation. Several material platforms have been used to study interacting charge states, while gallium arsenide has also been used to investigate spin evolution. However, decoherence remains a key challenge in simulating coherent quantum dynamics. Here, we introduce quantum simulation using hole spins in germanium quantum dots. We demonstrate extensive and coherent control enabling the tuning of multi-spin states in isolated, paired, and fully coupled quantum dots. We then focus on the simulation of resonating valence bonds and measure the evolution between singlet product states which remains coherent over many periods. Finally, we realize four-spin states with s-wave and d-wave symmetry. These results provide means to perform non-trivial and coherent simulations of correlated electron systems., QCD/Veldhorst Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Veldhorst Lab

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., QCD/Veldhorst Lab, QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Veldhorst Lab

Micromagnet-based electric dipole spin resonance offers an attractive path for the near-term scaling of dense arrays of silicon spin qubits in gate-defined quantum dots while maintaining long coherence times and high control fidelities. However, accurately controlling dense arrays of qubits using a multiplexed drive will require an understanding of the cross-talk mechanisms that may reduce operational fidelity. We identify an unexpected cross-talk mechanism whereby the Rabi frequency of a driven qubit is drastically changed when the drive of an adjacent qubit is turned on. These observations raise important considerations for scaling single-qubit control., QCD/Vandersypen Lab, QID/Dobrovitski Group, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Vandersypen Lab

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., QCD/Scappucci Lab, QN/Veldhorst Lab, BUS/TNO STAFF

The efficient control of a large number of qubits is one of the most challenging aspects for practical quantum computing. Current approaches in solid-state quantum technology are based on brute-force methods, where each and every qubit requires at least one unique control line—an approach that will become unsustainable when scaling to the required millions of qubits. Here, inspired by random-access architectures in classical electronics, we introduce the shared control of semiconductor quantum dots to efficiently operate a two-dimensional crossbar array in planar germanium. We tune the entire array, comprising 16 quantum dots, to the few-hole regime. We then confine an odd number of holes in each site to isolate an unpaired spin per dot. Moving forward, we demonstrate on a vertical and a horizontal double quantum dot a method for the selective control of the interdot coupling and achieve a tunnel coupling tunability over more than 10 GHz. The operation of a quantum electronic device with fewer control terminals than tunable experimental parameters represents a compelling step forward in the construction of scalable quantum technology., QCD/Veldhorst Lab, BUS/TNO STAFF, QCD/Vandersypen Lab, QCD/Scappucci Lab, QN/Veldhorst Lab

Highly uniform quantum systems are essential for the practical implementation of scalable quantum processors. While quantum dot spin qubits based on semiconductor technology are a promising platform for large-scale quantum computing, their small size makes them particularly sensitive to their local environment. Here, we present a method to electrically obtain a high degree of uniformity in the intrinsic potential landscape using hysteretic shifts of the gate voltage characteristics. We demonstrate the tuning of pinch-off voltages in quantum dot devices over hundreds of millivolts that then remain stable at least for hours. Applying our method, we homogenize the pinch-off voltages of the plunger gates in a linear array for four quantum dots, reducing the spread in pinch-off voltages by one order of magnitude. This work provides a new tool for the tuning of quantum dot devices and offers new perspectives for the implementation of scalable spin qubit arrays., QCD/Veldhorst Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Veldhorst Lab

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., QCD/Scappucci Lab, QRD/Kouwenhoven Lab, QCD/Veldhorst Lab, BUS/TNO STAFF, QN/Veldhorst Lab

We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy. This ability to probe the Jaynes-Cummings ladder is enabled by improvements in the coupling-to-decoherence ratio, and shows an increase in the maturity of spin circuit QED as an interesting platform for studying quantum phenomena., BUS/Quantum Delft, QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Vandersypen Lab

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., QCD/Veldhorst Lab, QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Vandersypen Lab, QN/Veldhorst Lab

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around gs/2p=40 MHz. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J/2p=20 MHz. In addition, photon-number states are resolved from the shift 2?s/2p=-13 MHz that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip., QCD/Vandersypen Lab, QuTech, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Vandersypen Lab

A hole bilayer in a strained germanium double quantum well is designed, fabricated, and studied. Magnetotransport characterization of double quantum well field-effect transistors as a function of gate voltage reveals the population of two hole channels with a high combined mobility of (Formula presented.) and a low percolation density of (Formula presented.). The individual population of the channels from the interference patterns of the Landau fan diagram was resolved. At a density of (Formula presented.) the system is in resonance and an anti-crossing of the first two bilayer subbands is observed and a symmetric-antisymmetric gap of (Formula presented.) is estimated, in agreement with Schrödinger-Poisson simulations., QCD/Scappucci Lab, QuTech, BUS/TNO STAFF, QN/Veldhorst Lab

As part of the National Agenda for Quantum Technology, QuTech (TU Delft and TNO) has agreed to make quantum technology accessible to society and industry via its full-stack prototype: Quantum Inspire. This system includes two different types of programmable quantum chips: circuits made from superconducting materials (transmons), and circuits made from silicon-based materials that localize and control single-electron spins (spin qubits). Silicon-based spin qubits are a natural match to the semiconductor manufacturing community, and several industrial fabrication facilities are already producing spin-qubit chips. Here, we discuss our latest results in spin-qubit technology and highlight where the semiconducting community has opportunities to drive the field forward. Specifically, developments in the following areas would enable fabrication of more powerful spin-qubit based quantum computing devices: circuit design rules implementing cryogenic device physics models, high-fidelity gate patterning of low resistance or superconducting metals, gate-oxide defect mitigation in relevant materials, silicon-germanium heterostructure optimization, and accurate magnetic field generation from on-chip micromagnets., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., BUS/TNO STAFF

Fault-tolerant quantum computers that can solve hard problems rely on quantum error correction1. One of the most promising error correction codes is the surface code2, which requires universal gate fidelities exceeding an error correction threshold of 99 per cent3. Among the many qubit platforms, only superconducting circuits4, trapped ions5 and nitrogen-vacancy centres in diamond6 have delivered this requirement. Electron spin qubits in silicon7–15 are particularly promising for a large-scale quantum computer owing to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent owing to the slow operation16. Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch–Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate universal gate fidelity beyond the fault-tolerance threshold and may enable scalable silicon quantum computers., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., BUS/TNO STAFF, QCD/Scappucci Lab

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., BUS/Quantum Delft, QCD/Scappucci Lab, QCD/Vandersypen Lab, BUS/TNO STAFF, QN/Vandersypen Lab

Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qubits via coherent spin shuttling, a key technology for linking distant silicon quantum processors. Coherent shuttling of a spin qubit enables efficient switching of the exchange coupling with an on/off ratio exceeding 1000, while preserving the spin coherence by 99.6% for the single shuttling between neighboring dots. With this shuttling-mode exchange control, we demonstrate a two-qubit controlled-phase gate with a fidelity of 93%, assessed via randomized benchmarking. Combination of our technique and a phase coherent shuttling of a qubit across a large quantum dot array will provide feasible path toward a quantum link between distant silicon quantum processors, a key requirement for large-scale quantum computation., Corection DOI 10.1038/s41467-022-34236-2, BUS/TNO STAFF, QCD/Scappucci Lab

The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-S−1 gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can preserve the state of the data qubit by applying a refocusing pulse to the ancilla qubit. In addition, we implement a phase flip code on three qubits, making use of a Toffoli-like gate for the final correction step. Both the quality and quantity of the qubits will require significant improvement to achieve fault-tolerance. However, the capability to implement quantum error correction codes enables co-design development of quantum hardware and software, where codes tailored to the properties of spin qubits and advances in fabrication and operation can now come together to advance semiconductor quantum technology., QCD/Veldhorst Lab, QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Terhal Group, Quantum Computing, QCD/Scappucci Lab, QN/Veldhorst Lab

Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably1. However, the requirements of having a large qubit count and operating with high fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise2,3 but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout4-11. Here, we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits, and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will enable testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers., QCD/Vandersypen Lab, BUS/TNO STAFF, BUS/Quantum Delft, QCD/Veldhorst Lab, QCD/Scappucci Lab, QN/Veldhorst Lab, QN/Vandersypen Lab

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around gs/2p=40 MHz. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J/2p=20 MHz. In addition, photon-number states are resolved from the shift 2?s/2p=-13 MHz that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip., QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Vandersypen Lab

A hole bilayer in a strained germanium double quantum well is designed, fabricated, and studied. Magnetotransport characterization of double quantum well field-effect transistors as a function of gate voltage reveals the population of two hole channels with a high combined mobility of (Formula presented.) and a low percolation density of (Formula presented.). The individual population of the channels from the interference patterns of the Landau fan diagram was resolved. At a density of (Formula presented.) the system is in resonance and an anti-crossing of the first two bilayer subbands is observed and a symmetric-antisymmetric gap of (Formula presented.) is estimated, in agreement with Schrödinger-Poisson simulations., QCD/Scappucci Lab, BUS/TNO STAFF, QN/Veldhorst Lab

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance—the ability to correct errors faster than they occur1. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code2,3. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage advanced semiconductor technology4. Here we report a spin-based quantum processor in silicon with single-qubit and two-qubit gate fidelities, all of which are above 99.5%, extracted from gate-set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighbouring qubit. Using this high-fidelity gate set, we execute the demanding task of calculating molecular ground-state energies using a variational quantum eigensolver algorithm5. Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediate-scale quantum devices., QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab, QN/Vandersypen Lab

The most promising quantum algorithms require quantum processors that host millions of quantum bits when targeting practical applications1. A key challenge towards large-scale quantum computation is the interconnect complexity. In current solid-state qubit implementations, an important interconnect bottleneck appears between the quantum chip in a dilution refrigerator and the room-temperature electronics. Advanced lithography supports the fabrication of both control electronics and qubits in silicon using technology compatible with complementary metal oxide semiconductors (CMOS)2. When the electronics are designed to operate at cryogenic temperatures, they can ultimately be integrated with the qubits on the same die or package, overcoming the ‘wiring bottleneck’3–6. Here we report a cryogenic CMOS control chip operating at 3 kelvin, which outputs tailored microwave bursts to drive silicon quantum bits cooled to 20 millikelvin. We first benchmark the control chip and find an electrical performance consistent with qubit operations of 99.99 per cent fidelity, assuming ideal qubits. Next, we use it to coherently control actual qubits encoded in the spin of single electrons confined in silicon quantum dots7–9 and find that the cryogenic control chip achieves the same fidelity as commercial instruments at room temperature. Furthermore, we demonstrate the capabilities of the control chip by programming a number of benchmarking protocols, as well as the Deutsch–Josza algorithm10, on a two-qubit quantum processor. These results open up the way towards a fully integrated, scalable silicon-based quantum computer., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Vandersypen Lab, QuTech, QCD/Sebastiano Lab, Quantum & Computer Engineering, QCD/Scappucci Lab, BUS/TNO STAFF, QCD/Veldhorst Lab, Quantum Circuit Architectures and Technology, Electronics, QN/Vandersypen Lab

Single-charge pumps are the main candidates for quantum-based standards of the unit ampere because they can generate accurate and quantized electric currents. In order to approach the metrological requirements in terms of both accuracy and speed of operation, in the past decade there has been a focus on semiconductor-based devices. The use of a variety of semiconductor materials enables the universality of charge pump devices to be tested, a highly desirable demonstration for metrology, with GaAs and Si pumps at the forefront of these tests. Here, we show that pumping can be achieved in a yet unexplored semiconductor, i.e. germanium. We realise a single-hole pump with a tunable-barrier quantum dot electrostatically defined at a Ge/SiGe heterostructure interface. We observe quantized current plateaux by driving the system with a single sinusoidal drive up to a frequency of 100 MHz. The operation of the prototype was affected by accidental formation of multiple dots, probably due to disorder potential, and random charge fluctuations. We suggest straightforward refinements of the fabrication process to improve pump characteristics in future experiments 2021 The Author(s). Published by IOP Publishing Ltd., QCD/Veldhorst Lab, QuTech, BUS/TNO STAFF, QN/Veldhorst Lab, QCD/Scappucci Lab

Hole gases in planar germanium can have high mobilities in combination with strong spin-orbit interaction and electrically tunable g factors, and are therefore emerging as a promising platform for creating hybrid superconductor-semiconductor devices. A key challenge towards hybrid Ge-based quantum technologies is the design of high-quality interfaces and superconducting contacts that are robust against magnetic fields. In this work, by combining the assets of aluminum, which provides good contact to the Ge, and niobium, which has a significant superconducting gap, we demonstrate highly transparent low-disordered JoFETs with relatively large ICRN products that are capable of withstanding high magnetic fields. We furthermore demonstrate the ability of phase-biasing individual JoFETs, opening up an avenue to explore topological superconductivity in planar Ge. The persistence of superconductivity in the reported hybrid devices beyond 1.8 T paves the way towards integrating spin qubits and proximity-induced superconductivity on the same chip., BUS/TNO STAFF, QN/Veldhorst Lab, QuTech, QCD/Scappucci Lab

Quantum dots fabricated using methods compatible with semiconductor manufacturing are promising for quantum information processing. In order to fully utilize the potential of this platform, scaling quantum dot arrays along two dimensions is a key step. Here, we demonstrate a two-dimensional quantum dot array where each quantum dot is tuned to single-charge occupancy, verified by simultaneous measurements using two integrated radio frequency charge sensors. We achieve this by using planar germanium quantum dots with low disorder and a small effective mass, allowing the incorporation of dedicated barrier gates to control the coupling of the quantum dots. We measure the hole charge filling spectrum and show that we can tune single-hole quantum dots from isolated quantum dots to strongly exchange coupled quantum dots. These results motivate the use of planar germanium quantum dots as building blocks for quantum simulation and computation., QCD/Veldhorst Lab, QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab

Quantum computers (QC) promise to solve certain computational problems exponentially faster than a classical computer due to the superposition and entanglement properties of quantum bits (qubits). Among several qubit technologies, spin qubits are a promising candidate for large-scale QC, since (1) they have a small footprint allowing them to be densely integrated and (2) they can operate at relatively high temperatures (\gt1\mathrm{K}) [1], potentially reducing system cost and complexity., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Sebastiano Lab, QCD/Vandersypen Lab, Electronics, QCD/Scappucci Lab, Quantum Circuit Architectures and Technology, QN/Vandersypen Lab

The most promising quantum algorithms require quantum processors that host millions of quantum bits when targeting practical applications1. A key challenge towards large-scale quantum computation is the interconnect complexity. In current solid-state qubit implementations, an important interconnect bottleneck appears between the quantum chip in a dilution refrigerator and the room-temperature electronics. Advanced lithography supports the fabrication of both control electronics and qubits in silicon using technology compatible with complementary metal oxide semiconductors (CMOS)2. When the electronics are designed to operate at cryogenic temperatures, they can ultimately be integrated with the qubits on the same die or package, overcoming the ‘wiring bottleneck’3–6. Here we report a cryogenic CMOS control chip operating at 3 kelvin, which outputs tailored microwave bursts to drive silicon quantum bits cooled to 20 millikelvin. We first benchmark the control chip and find an electrical performance consistent with qubit operations of 99.99 per cent fidelity, assuming ideal qubits. Next, we use it to coherently control actual qubits encoded in the spin of single electrons confined in silicon quantum dots7–9 and find that the cryogenic control chip achieves the same fidelity as commercial instruments at room temperature. Furthermore, we demonstrate the capabilities of the control chip by programming a number of benchmarking protocols, as well as the Deutsch–Josza algorithm10, on a two-qubit quantum processor. These results open up the way towards a fully integrated, scalable silicon-based quantum computer., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Vandersypen Lab, QCD/Sebastiano Lab, Quantum & Computer Engineering, QCD/Scappucci Lab, BUS/TNO STAFF, QCD/Veldhorst Lab, Quantum Circuit Architectures and Technology, Electronics, QN/Vandersypen Lab

Hole gases in planar germanium can have high mobilities in combination with strong spin-orbit interaction and electrically tunable g factors, and are therefore emerging as a promising platform for creating hybrid superconductor-semiconductor devices. A key challenge towards hybrid Ge-based quantum technologies is the design of high-quality interfaces and superconducting contacts that are robust against magnetic fields. In this work, by combining the assets of aluminum, which provides good contact to the Ge, and niobium, which has a significant superconducting gap, we demonstrate highly transparent low-disordered JoFETs with relatively large ICRN products that are capable of withstanding high magnetic fields. We furthermore demonstrate the ability of phase-biasing individual JoFETs, opening up an avenue to explore topological superconductivity in planar Ge. The persistence of superconductivity in the reported hybrid devices beyond 1.8 T paves the way towards integrating spin qubits and proximity-induced superconductivity on the same chip., BUS/TNO STAFF, QN/Veldhorst Lab, QCD/Scappucci Lab

Single-charge pumps are the main candidates for quantum-based standards of the unit ampere because they can generate accurate and quantized electric currents. In order to approach the metrological requirements in terms of both accuracy and speed of operation, in the past decade there has been a focus on semiconductor-based devices. The use of a variety of semiconductor materials enables the universality of charge pump devices to be tested, a highly desirable demonstration for metrology, with GaAs and Si pumps at the forefront of these tests. Here, we show that pumping can be achieved in a yet unexplored semiconductor, i.e. germanium. We realise a single-hole pump with a tunable-barrier quantum dot electrostatically defined at a Ge/SiGe heterostructure interface. We observe quantized current plateaux by driving the system with a single sinusoidal drive up to a frequency of 100 MHz. The operation of the prototype was affected by accidental formation of multiple dots, probably due to disorder potential, and random charge fluctuations. We suggest straightforward refinements of the fabrication process to improve pump characteristics in future experiments 2021 The Author(s). Published by IOP Publishing Ltd., QCD/Veldhorst Lab, BUS/TNO STAFF, QN/Veldhorst Lab, QCD/Scappucci Lab

Quantum dots fabricated using methods compatible with semiconductor manufacturing are promising for quantum information processing. In order to fully utilize the potential of this platform, scaling quantum dot arrays along two dimensions is a key step. Here, we demonstrate a two-dimensional quantum dot array where each quantum dot is tuned to single-charge occupancy, verified by simultaneous measurements using two integrated radio frequency charge sensors. We achieve this by using planar germanium quantum dots with low disorder and a small effective mass, allowing the incorporation of dedicated barrier gates to control the coupling of the quantum dots. We measure the hole charge filling spectrum and show that we can tune single-hole quantum dots from isolated quantum dots to strongly exchange coupled quantum dots. These results motivate the use of planar germanium quantum dots as building blocks for quantum simulation and computation., QCD/Veldhorst Lab, QCD/Vandersypen Lab, BUS/TNO STAFF, QCD/Scappucci Lab

Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of their total capacitance over the parasitic port capacitance is smaller, leading to larger microwave leakage than for 50-ω resonators. Here, we introduce an implementation of on-chip filters to suppress the microwave leakage. The filters comprise a high-kinetic-inductance nanowire inductor and a thin-film capacitor. The filter has a small footprint and can be placed close to the resonator, confining microwaves to a small area of the chip. The inductance and capacitance of the filter elements can be varied over a wider range of values than their typical spiral inductor and interdigitated capacitor counterparts. We demonstrate that the total linewidth of a 6.4 GHz and approximately 3-kω resonator can be improved down to 540 kHz using these filters., QCD/Vandersypen Lab, QuTech, Business Development, QCD/Scappucci Lab, QN/Vandersypen Lab

Quantum computers (QC), comprising qubits and a classical controller, can provide exponential speed-up in solving certain problems. Among solid-state qubits, transmons and spin-qubits are the most promising, operating « 1K. A qubit can be implemented in a physical system with two distinct energy levels representing the |0) and |1) states, e.g. the up and down spin states of an electron. The qubit states can be manipulated with microwave pulses, whose frequency f matches the energy level spacing E = hf (Fig. 19.1.1). For transmons, f 6GHz, for spin qubits f20GHz, with the desire to lower it in the future. Qubit operations can be represented as rotations in the Bloch sphere. The rotation axis is set by the phase of the microwave signal relative to the qubit phase, which must be tracked for coherent operations. The pulse amplitude and duration determine the rotation angle. A π-rotation is typically obtained using a 50ns Gaussian pulse for transmons and a 500ns rectangular pulse for spin qubits with powers of -60dBm and -45dBm, respectively., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., OLD QCD/Charbon Lab, QCD/Vandersypen Lab, QCD/Scappucci Lab, QCD/Veldhorst Lab, QN/Vandersypen Lab, Electronics, (OLD)Applied Quantum Architectures

Building a large-scale quantum computer requires the co-optimization of both the quantum bits (qubits) and their control electronics. By operating the CMOS control circuits at cryogenic temperatures (cryo-CMOS), and hence in close proximity to the cryogenic solid-state qubits, a compact quantum-computing system can be achieved, thus promising scalability to the large number of qubits required in a practical application. This work presents a cryo-CMOS microwave signal generator for frequency-multiplexed control of 4\times 32 qubits (32 qubits per RF output). A digitally intensive architecture offering full programmability of phase, amplitude, and frequency of the output microwave pulses and a wideband RF front end operating from 2 to 20 GHz allow targeting both spin qubits and transmons. The controller comprises a qubit-phase-tracking direct digital synthesis (DDS) back end for coherent qubit control and a single-sideband (SSB) RF front end optimized for minimum leakage between the qubit channels. Fabricated in Intel 22-nm FinFET technology, it achieves a 48-dB SNR and 45-dB spurious-free dynamic range (SFDR) in a 1-GHz data bandwidth when operating at 3 K, thus enabling high-fidelity qubit control. By exploiting the on-chip 4096-instruction memory, the capability to translate quantum algorithms to microwave signals has been demonstrated by coherently controlling a spin qubit at both 14 and 18 GHz., OLD QCD/Charbon Lab, QuTech, QCD/Vandersypen Lab, Business Development, QCD/Scappucci Lab, QCD/Veldhorst Lab, QN/Vandersypen Lab, Electronics, (OLD)Applied Quantum Architectures

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/1011 cm-2, which is consistent with theoretical predictions for near-perfect quantum well top interfaces., QCD/Scappucci Lab, QuTech, Business Development, QCD/Veldhorst Lab

Building a large-scale quantum computer requires the co-optimization of both the quantum bits (qubits) and their control electronics. By operating the CMOS control circuits at cryogenic temperatures (cryo-CMOS), and hence in close proximity to the cryogenic solid-state qubits, a compact quantum-computing system can be achieved, thus promising scalability to the large number of qubits required in a practical application. This work presents a cryo-CMOS microwave signal generator for frequency-multiplexed control of 4\times 32 qubits (32 qubits per RF output). A digitally intensive architecture offering full programmability of phase, amplitude, and frequency of the output microwave pulses and a wideband RF front end operating from 2 to 20 GHz allow targeting both spin qubits and transmons. The controller comprises a qubit-phase-tracking direct digital synthesis (DDS) back end for coherent qubit control and a single-sideband (SSB) RF front end optimized for minimum leakage between the qubit channels. Fabricated in Intel 22-nm FinFET technology, it achieves a 48-dB SNR and 45-dB spurious-free dynamic range (SFDR) in a 1-GHz data bandwidth when operating at 3 K, thus enabling high-fidelity qubit control. By exploiting the on-chip 4096-instruction memory, the capability to translate quantum algorithms to microwave signals has been demonstrated by coherently controlling a spin qubit at both 14 and 18 GHz., OLD QCD/Charbon Lab, QuTech, QCD/Vandersypen Lab, Business Development, QCD/Scappucci Lab, QCD/Veldhorst Lab, QN/Vandersypen Lab, Electronics, (OLD)Applied Quantum Architectures

Solid-state qubits integrated on semiconductor substrates currently require at least one wire from every qubit to the control electronics, leading to a so-called wiring bottleneck for scaling. Demultiplexing via on-chip circuitry offers an effective strategy to overcome this bottleneck. In the case of gate-defined quantum dot arrays, specific static voltages need to be applied to many gates simultaneously to realize electron confinement. When a charge-locking structure is placed between the quantum device and the demultiplexer, the voltage can be maintained locally. In this study, we implement a switched-capacitor circuit for charge-locking and use it to float the plunger gate of a single quantum dot. Parallel plate capacitors, transistors, and quantum dot devices are monolithically fabricated on a Si/SiGe-based substrate to avoid complex off-chip routing. We experimentally study the effects of the capacitor and transistor size on the voltage accuracy of the floating node. Furthermore, we demonstrate that the electrochemical potential of the quantum dot can follow a 100 Hz pulse signal while the dot is partially floating, which is essential for applying this strategy in qubit experiments., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Vandersypen Lab, QuTech, Business Development, QCD/Veldhorst Lab, QCD/Scappucci Lab, QID/Ishihara Lab, (OLD)Quantum Integration Technology, QN/Vandersypen Lab

Electrons and holes confined in quantum dots define excellent building blocks for quantum emergence, simulation, and computation. Silicon and germanium are compatible with standard semiconductor manufacturing and contain stable isotopes with zero nuclear spin, thereby serving as excellent hosts for spins with long quantum coherence. Here, we demonstrate quantum dot arrays in a silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe), and strained germanium (Ge/SiGe). We fabricate using a multi-layer technique to achieve tightly confined quantum dots and compare integration processes. While SiMOS can benefit from a larger temperature budget and Ge/SiGe can make an Ohmic contact to metals, the overlapping gate structure to define the quantum dots can be based on a nearly identical integration. We realize charge sensing in each platform, for the first time in Ge/SiGe, and demonstrate fully functional linear and two-dimensional arrays where all quantum dots can be depleted to the last charge state. In Si/SiGe, we tune a quintuple quantum dot using the N + 1 method to simultaneously reach the few electron regime for each quantum dot. We compare capacitive crosstalk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. We put these results into perspective for quantum technology and identify industrial qubits, hybrid technology, automated tuning, and two-dimensional qubit arrays as four key trajectories that, when combined, enable fault-tolerant quantum computation., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Veldhorst Lab, QuTech, QCD/Vandersypen Lab, QCD/Scappucci Lab, BUS/Quantum Delft, QN/Vandersypen Lab

A clear signature of Zeeman split states crossing is observed in a Landau fan diagram of strained germanium two-dimensional hole gas. The underlying mechanisms are discussed based on a perturbative model yielding a closed formula for the critical magnetic fields. These fields depend strongly on the energy difference between the topmost and neighboring valence bands and are sensitive to the quantum well thickness, strain, and spin-orbit interaction. The latter is a necessary feature for the crossing to occur. This framework enables a straightforward quantification of the hole-state parameters from simple measurements, thus paving the way for its use in design and modeling of hole-based quantum devices., QCD/Scappucci Lab, QuTech, Business Development

We investigate hole spin relaxation in the single- and multihole regime in a 2 × 2 germanium quantum dot array. We find spin relaxation times T1 as high as 32 and 1.2 ms for quantum dots with single- and five-hole occupations, respectively, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate qubit addressability and electric field sensitivity by measuring resonance frequency dependence of each qubit on gate voltages. We can tune the resonance frequency over a large range for both single and multihole qubits, while simultaneously finding that the resonance frequencies are only weakly dependent on neighboring gates. In particular, the five-hole qubit resonance frequency is more than 20 times as sensitive to its corresponding plunger gate. Excellent individual qubit tunability and long spin relaxation times make holes in germanium promising for addressable and high-fidelity spin qubits in dense two-dimensional quantum dot arrays for large-scale quantum information., QCD/Veldhorst Lab, QuTech, QCD/Vandersypen Lab, Business Development, QCD/Scappucci Lab

Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their compatibility with standard semiconductor manufacturing. While early research focused on the simpler electron system, recent demonstrations using multi-hole quantum dots illustrated the favourable properties holes can offer for fast and scalable quantum control. Here, we establish a single-hole spin qubit in germanium and demonstrate the integration of single-shot readout and quantum control. We deplete a planar germanium double quantum dot to the last hole, confirmed by radio-frequency reflectrometry charge sensing. To demonstrate the integration of single-shot readout and qubit operation, we show Rabi driving on both qubits. We find remarkable electric control over the qubit resonance frequencies, providing great qubit addressability. Finally, we analyse the spin relaxation time, which we find to exceed one millisecond, setting the benchmark for hole quantum dot qubits. The ability to coherently manipulate a single hole spin underpins the quality of strained germanium and defines an excellent starting point for the construction of quantum hardware., QCD/Veldhorst Lab, Business Development, QCD/Scappucci Lab

Continuing advancements in quantum information processing have caused a paradigm shift from research mainly focused on testing the reality of quantum mechanics to engineering qubit devices with numbers required for practical quantum computation. One of the major challenges in scaling toward large-scale solid-state systems is the limited input/output (I/O) connectors present in cryostats operating at sub-kelvin temperatures required to execute quantum logic with high fidelity. This interconnect bottleneck is equally present in the device fabrication-measurement cycle, which requires high-throughput and cryogenic characterization to develop quantum processors. Here we multiplex quantum transport of two-dimensional electron gases at sub-kelvin temperatures. We use commercial off-the-shelf CMOS multiplexers to achieve an order of magnitude increase in the number of wires. Exploiting this technology, we accelerate the development of 300 mm epitaxial wafers manufactured in an industrial CMOS fab and report a remarkable electron mobility of (3.9 ± 0.6) × 105 cm2/Vs and percolation density of (6.9 ± 0.4) × 1010 cm−2, representing a key step toward large silicon qubit arrays. We envision that the demonstration will inspire the development of cryogenic electronics for quantum information, and because of the simplicity of assembly and versatility, we foresee widespread use of similar cryo-CMOS circuits for high-throughput quantum measurements and control of quantum engineered systems., QCD/Scappucci Lab, QuTech, General, EMSD EEMCS Project engineers, Business Development, Computer Engineering, (OLD)Applied Quantum Architectures, QCD/Veldhorst Lab

Solid-state qubits integrated on semiconductor substrates currently require at least one wire from every qubit to the control electronics, leading to a so-called wiring bottleneck for scaling. Demultiplexing via on-chip circuitry offers an effective strategy to overcome this bottleneck. In the case of gate-defined quantum dot arrays, specific static voltages need to be applied to many gates simultaneously to realize electron confinement. When a charge-locking structure is placed between the quantum device and the demultiplexer, the voltage can be maintained locally. In this study, we implement a switched-capacitor circuit for charge-locking and use it to float the plunger gate of a single quantum dot. Parallel plate capacitors, transistors, and quantum dot devices are monolithically fabricated on a Si/SiGe-based substrate to avoid complex off-chip routing. We experimentally study the effects of the capacitor and transistor size on the voltage accuracy of the floating node. Furthermore, we demonstrate that the electrochemical potential of the quantum dot can follow a 100 Hz pulse signal while the dot is partially floating, which is essential for applying this strategy in qubit experiments., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Vandersypen Lab, Business Development, QCD/Veldhorst Lab, QCD/Scappucci Lab, QID/Ishihara Lab, Quantum Integration Technology, QN/Vandersypen Lab

We investigate hole spin relaxation in the single- and multihole regime in a 2 × 2 germanium quantum dot array. We find spin relaxation times T1 as high as 32 and 1.2 ms for quantum dots with single- and five-hole occupations, respectively, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate qubit addressability and electric field sensitivity by measuring resonance frequency dependence of each qubit on gate voltages. We can tune the resonance frequency over a large range for both single and multihole qubits, while simultaneously finding that the resonance frequencies are only weakly dependent on neighboring gates. In particular, the five-hole qubit resonance frequency is more than 20 times as sensitive to its corresponding plunger gate. Excellent individual qubit tunability and long spin relaxation times make holes in germanium promising for addressable and high-fidelity spin qubits in dense two-dimensional quantum dot arrays for large-scale quantum information., QCD/Veldhorst Lab, QCD/Vandersypen Lab, Business Development, QCD/Scappucci Lab

Electrons and holes confined in quantum dots define excellent building blocks for quantum emergence, simulation, and computation. Silicon and germanium are compatible with standard semiconductor manufacturing and contain stable isotopes with zero nuclear spin, thereby serving as excellent hosts for spins with long quantum coherence. Here, we demonstrate quantum dot arrays in a silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe), and strained germanium (Ge/SiGe). We fabricate using a multi-layer technique to achieve tightly confined quantum dots and compare integration processes. While SiMOS can benefit from a larger temperature budget and Ge/SiGe can make an Ohmic contact to metals, the overlapping gate structure to define the quantum dots can be based on a nearly identical integration. We realize charge sensing in each platform, for the first time in Ge/SiGe, and demonstrate fully functional linear and two-dimensional arrays where all quantum dots can be depleted to the last charge state. In Si/SiGe, we tune a quintuple quantum dot using the N + 1 method to simultaneously reach the few electron regime for each quantum dot. We compare capacitive crosstalk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. We put these results into perspective for quantum technology and identify industrial qubits, hybrid technology, automated tuning, and two-dimensional qubit arrays as four key trajectories that, when combined, enable fault-tolerant quantum computation., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Veldhorst Lab, QCD/Vandersypen Lab, QCD/Scappucci Lab, BUS/Quantum Delft, QN/Vandersypen Lab