arXiv subjects

N. W. Hendrickx

Publications and source records attributed to N. W. Hendrickx.

At least 19 recordsLinked to original sources

arXiv2026

Simultaneous operation of an 18-qubit modular array in germanium

Utility-scale quantum computing requires the integration and operation of a large-scale qubit register. Semiconductor spin qubits are a primary candidate for this, due to the prospects of building integrated hybrid quantum-classical architectures. However, scaling spin-qubit systems while preserving performance and control has remained a challenge. Here, we demonstrate the operation of an 18-qubit array in germanium based on an extendable 2xN architecture. We achieve simultaneous initialization, control, and readout across the entire array, enabled by parallel operation of modular unit cells. Across the array, we achieve average and median single-qubit gate fidelities of 99.8% and 99.9%, respectively. Finally, we characterize the nearest-neighbor exchange couplings throughout the device and implement high-quality controlled-Z gates to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state. These results demonstrate that spin-qubit arrays can be scaled while maintaining high-fidelity operation and establish a modular, extendable architecture for planar semiconductor quantum processors.

cond-mat.mes-hall↗

arXiv2026

Disentangling orbital and confinement contributions to $g$-factor in Ge/SiGe hole quantum dots

Spin qubits are typically operated in the lowest orbital of a quantum dot to minimize interference from nearby states. In valence-band hole systems, strong spin-orbit coupling links spin and orbital degrees of freedom, strongly influencing the hole $g$-factor, a key parameter for qubit control. We investigate the out-of-plane $g$-factor in Ge quantum dots using excitation (single-particle) and addition (many-body) spectra. Excitation spectra allow us to distinguish the pure Zeeman $g$-factor from orbital contributions to the magnetic field splitting of states despite the strong spin-orbit coupling. This distinction clarifies discrepancies between $g$-factors extracted with the two methods, for different orbital states and different hole numbers. Furthermore, we find gate-tunability of $g$-factors at the level of 15%, highlighting its relevance for all-electric qubit manipulation.

cond-mat.mes-hall↗

arXiv2025

Operating semiconductor qubits without individual barrier gates

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 fanouts. 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.

cond-mat.mes-hall↗

arXiv2023

Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity

Spin qubits defined by valence band hole states comprise an attractive candidate for quantum information processing due to their inherent coupling to electric fields enabling fast and scalable qubit control. In particular, heavy holes in germanium have shown great promise, with recent demonstrations of fast and high-fidelity qubit operations. However, the mechanisms and anisotropies that underlie qubit driving and decoherence are still mostly unclear. Here, we report on the highly anisotropic heavy-hole $g$-tensor and its dependence on electric fields, allowing us to relate both qubit driving and decoherence to an electric modulation of the $g$-tensor. We also confirm the predicted Ising-type hyperfine interaction but show that qubit coherence is ultimately limited by $1/f$ charge noise. Finally, we operate the qubit at low magnetic field and measure a dephasing time of $T_2^*=9.2$ $μ$s, while maintaining a single-qubit gate fidelity of 99.94 %, that remains well above 99 % at an operation temperature T>1 K. This understanding of qubit driving and decoherence mechanisms are key for the design and operation of scalable and highly coherent hole qubit arrays.

cond-mat.mes-hall↗

arXiv2023

Impact of interface traps on charge noise, mobility and percolation density in Ge/SiGe heterostructures

Hole spins in Ge/SiGe heterostructure quantum dots have emerged as promising qubits for quantum computation. The strong spin-orbit coupling (SOC), characteristic of heavy-hole states in Ge, enables fast and all-electrical qubit control. However, SOC also increases the susceptibility of spin qubits to charge noise. While qubit coherence can be significantly improved by operating at sweet spots with reduced hyperfine or charge noise sensitivity, the latter ultimately limits coherence, underlining the importance of understanding and reducing charge noise at its source. In this work, we study the voltage-induced hysteresis commonly observed in SiGe-based quantum devices and show that the dominant charge fluctuators are localized at the semiconductor-oxide interface. By applying increasingly negative gate voltages to Hall bar and quantum dot devices, we investigate how the hysteretic filling of interface traps impacts transport metrics and charge noise. We find that the gate-induced accumulation and trapping of charge at the SiGe-oxide interface leads to an increased electrostatic disorder, as probed by transport measurements, as well as the activation of low-frequency relaxation dynamics, resulting in slow drifts and increased charge noise levels. Our results highlight the importance of a conservative device tuning strategy and reveal the critical role of the semiconductor-oxide interface in SiGe heterostructures for spin qubit applications.

cond-mat.mes-hall↗

arXiv2023

Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold

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 neighbour pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

cond-mat.mes-hall↗

arXiv2022

Phase flip code with semiconductor spin qubits

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-$\text{S}^{-1}$ 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 scale semiconductor quantum technology toward universal quantum computers.

quant-ph↗

arXiv2021

Single-Hole Pump in Germanium

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.

cond-mat.mes-hall↗

arXiv2020

A four-qubit germanium quantum processor

The prospect of building quantum circuits using advanced semiconductor manufacturing positions quantum dots as an attractive platform for quantum information processing. Extensive studies on various materials have led to demonstrations of two-qubit logic in gallium arsenide, silicon, and germanium. However, interconnecting larger numbers of qubits in semiconductor devices has remained an outstanding challenge. Here, we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable coupling along both directions. Qubit logic is implemented all-electrically and the exchange interaction can be pulsed to freely program one-qubit, two-qubit, three-qubit, and four-qubit operations, resulting in a compact and high-connectivity circuit. We execute a quantum logic circuit that generates a four-qubit Greenberger-Horne-Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are an important step towards quantum error correction and quantum simulation with quantum dots.

cond-mat.mes-hall↗

arXiv2020

A two-dimensional array of single-hole quantum dots

Quantum dots fabricated using techniques and materials that are compatible with semiconductor manufacturing are promising for quantum information processing. While great progress has been made toward high-fidelity control of quantum dots positioned in a linear arrangement, scalability along two dimensions is a key step toward practical quantum information processing. Here we demonstrate a two-dimensional quantum dot array where each quantum dot is tuned to single-charge occupancy, verified by simultaneous measuring with two integrated radio frequency charge sensors. We achieve this by using planar germanium quantum dots with low disorder and small effective mass, allowing the incorporation of dedicated barrier gates to control the coupling of the quantum dots. We demonstrate hole charge filling consistent with a Fock-Darwin 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.

cond-mat.mes-hall↗

arXiv2020

Low percolation density and charge noise with holes in germanium

We engineer planar Ge/SiGe heterostructures for low disorder and quiet hole quantum dot operation by positioning the strained Ge channel 55~nm below the semiconductor/dielectric interface. In heterostructure field effect transistors, we measure a percolation density for two-dimensional hole transport of $2.1\times10^{10}~\text{cm}^{-2}$, indicative of a very low disorder potential landscape experienced by holes in the buried Ge channel. These Ge heterostructures support quiet operation of hole quantum dots and we measure charge noise levels that are below the detection limit $\sqrt{S_\text{E}}=0.2~μ\text{eV}/\sqrt{\text{Hz}}$ at 1 Hz. These results establish planar Ge as a promising platform for scaled two-dimensional spin qubit arrays.

cond-mat.mes-hall↗

arXiv2020

Spin relaxation benchmarks and individual qubit addressability for holes in quantum dots

We investigate hole spin relaxation in the single- and multi-hole regime in a 2x2 germanium quantum dot array. We use radiofrequency (rf) charge sensing and observe Pauli Spin-Blockade (PSB) for every second interdot transition up to the (1,5)-(0,6) anticrossing, consistent with a standard Fock-Darwin spectrum. We find spin relaxation times $T_1$ as high as 32 ms for a quantum dot with single-hole occupation and 1.2 ms for a quantum dot occupied by five-holes, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate the qubit addressability and sensitivity to electric fields by measuring the resonance frequency dependence of each qubit on gate voltages. We are able to tune the resonance frequency over a large range for both the single and multi-hole qubit. Simultaneously, we find that the resonance frequencies are only weakly dependent on neighbouring gates, and in particular the five-hole qubit resonance frequency is more than twenty times as sensitive to its corresponding plunger gate. The 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.

cond-mat.mes-hall↗

arXiv2019

A single-hole spin qubit

Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their inherent compatibility with standard semiconductor manufacturing. While early on it was recognized that holes may offer a multitude of favourable properties for fast and scalable quantum control, research thus far has remained almost exclusively restricted to the simpler electron system. However, recent developments with holes have led to separate demonstrations of single-shot readout and fast quantum logic, albeit only in the multi-hole regime. Here, we establish a single-hole spin qubit in germanium and demonstrate the integration of single-shot readout and quantum control. Moreover, we make use of Pauli spin blockade, allowing to arbitrarily set the qubit resonance frequency, while providing large readout windows. We deplete a planar germanium double quantum dot to the last hole, confirmed by radio-frequency reflectrometry charge sensing, and achieve single-shot spin readout. To demonstrate the integration of the readout and qubit operation, we show Rabi driving on both qubits and find remarkable electric control over their resonance frequencies. Finally, we analyse the spin relaxation time, which we find to exceed one millisecond, setting the benchmark for hole-based spin 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 novel quantum hardware.

cond-mat.mes-hall↗

arXiv2019

Universal quantum logic in hot silicon qubits

Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 mK, where cooling power is extremely limited, and this severely impacts the perspective for practical quantum computation. Recent works on spins in silicon have shown steps towards a platform that can be operated at higher temperatures by demonstrating long spin lifetimes, gate-based spin readout, and coherent single-spin control, but the crucial two-qubit logic gate has been missing. Here we demonstrate that silicon quantum dots can have sufficient thermal robustness to enable the execution of a universal gate set above one Kelvin. We obtain single-qubit control via electron-spin-resonance (ESR) and readout using Pauli spin blockade. We show individual coherent control of two qubits and measure single-qubit fidelities up to 99.3 %. We demonstrate tunability of the exchange interaction between the two spins from 0.5 up to 18 MHz and use this to execute coherent two-qubit controlled rotations (CROT). The demonstration of `hot' and universal quantum logic in a semiconductor platform paves the way for quantum integrated circuits hosting the quantum hardware and their control circuitry all on the same chip, providing a scalable approach towards practical quantum information.

cond-mat.mes-hall↗

arXiv2019

Quantum Dot Arrays in Silicon and Germanium

Electrons and holes confined in quantum dots define an excellent building block for quantum emergence, simulation, and computation. In order for quantum electronics to become practical, large numbers of quantum dots will be required, necessitating the fabrication of scaled structures such as linear and 2D arrays. Group IV semiconductors contain stable isotopes with zero nuclear spin and can thereby serve as excellent host for spins with long quantum coherence. Here we demonstrate group IV quantum dot arrays in 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 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 cross talk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. These results constitute an excellent base for quantum computation with quantum dots and provide opportunities for each platform to be integrated with standard semiconductor manufacturing.

cond-mat.mes-hall↗

arXiv2019

Fast two-qubit logic with holes in germanium

The promise of quantum computation with quantum dots has stimulated widespread research. Still, a platform that can combine excellent control with fast and high-fidelity operation is absent. Here, we show single and two-qubit operations based on holes in germanium. A high degree of control over the tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder and by working in a virtual gate space. Spin-orbit coupling obviates the need for microscopic elements and enables rapid qubit control with Rabi frequencies exceeding 100 MHz and a single-qubit fidelity of 99.3 %. We demonstrate fast two-qubit CX gates executed within 75 ns and minimize decoherence by operating at the charge symmetry point. Planar germanium thus matured within one year from a material that can host quantum dots to a platform enabling two-qubit logic, positioning itself as a unique material to scale up spin qubits for quantum information.

cond-mat.mes-hall↗

arXiv2018

Low disordered, stable, and shallow germanium quantum wells: a playground for spin and hybrid quantum technology

Buried-channel semiconductor heterostructures are an archetype material platform to fabricate gated semiconductor quantum devices. Sharp confinement potential is obtained by positioning the channel near the surface, however nearby surface states degrade the electrical properties of the starting material. In this paper we demonstrate a two-dimensional hole gas of high mobility ($5\times 10^{5}$ cm$^2$/Vs) in a very shallow strained germanium channel, which is located only 22 nm below the surface. This high mobility leads to mean free paths $\approx6 μm$, setting new benchmarks for holes in shallow FET devices. Carriers are confined in an undoped Ge/SiGe heterostructure with reduced background contamination, sharp interfaces, and high uniformity. The top-gate of a dopant-less field effect transistor controls the carrier density in the channel. The high mobility, along with a percolation density of $1.2\times 10^{11}\text{ cm}^{-2}$, light effective mass (0.09 m$_e$), and high g-factor (up to $7$) highlight the potential of undoped Ge/SiGe as a low-disorder material platform for hybrid quantum technologies.

cond-mat.mes-hall↗

arXiv2018

Ballistic supercurrent discretization and micrometer-long Josephson coupling in germanium

We fabricate Josephson field-effect-transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a transparent interface, confirmed by analyzing the excess current. These demonstrations of ballistic superconducting transport are promising for hybrid quantum technology in germanium.

cond-mat.supr-con↗