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The prospect of building quantum circuits.sup.1,2 using advanced semiconductor manufacturing makes quantum dots an attractive platform for quantum information processing.sup.3,4. Extensive studies of various materials have led to demonstrations of two-qubit logic in gallium arsenide.sup.5, silicon.sup.6-12 and germanium.sup.13. However, interconnecting larger numbers of qubits in semiconductor devices has remained a 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 highly connected 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 a step towards quantum error correction and quantum simulation using quantum dots. Using germanium quantum dots, a four-qubit processor capable of single-, two-, three-, and four-qubit gates, demonstrated by the creation of four-qubit Greenberger-Horne-Zeilinger states, is the largest yet realized with solid-state electron spins., Author(s): Nico W. Hendrickx [sup.1] , William I. L. Lawrie [sup.1] , Maximilian Russ [sup.1] , Floor van Riggelen [sup.1] , Sander L. de Snoo [sup.1] , Raymond N. Schouten [...]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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

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 3.34×105cm2V−1s−1$3.34\times 10^{5}\ {{\rm cm}^2\nobreakspace {\rm V}^{-1}\nobreakspace {\rm s}^{-1}}$ and a low percolation density of 2.38×1010cm−2$2.38 \times 10^{10}\ {{\rm cm}^{-2}}$. The individual population of the channels from the interference patterns of the Landau fan diagram was resolved. At a density of 2.0×1011cm−2$2.0\times 10^{11}\ {{\rm cm}^{-2}}$ the system is in resonance and an anti‐crossing of the first two bilayer subbands is observed and a symmetric‐antisymmetric gap of ≈0.69meV$\approx {0.69}\ {\rm meV}$ is estimated, in agreement with Schrödinger‐Poisson simulations. [ABSTRACT FROM AUTHOR]

We grow 28Si/SiGe heterostructures by reduced-pressure chemical vapor deposition and terminate the stack without an epitaxial Si cap but with an amorphous Si-rich layer obtained by exposing the SiGe barrier to dichlorosilane at 500 °C. As a result, 28Si/SiGe heterostructure field-effect transistors feature a sharp semiconductor/dielectric interface and support a two-dimensional electron gas with enhanced and more uniform transport properties across a 100 mm wafer. At T = 1.7 K, we measure a high mean mobility of (1.8 ± 0.5) × 10 5 cm2/V s and a low mean percolation density of (9 ± 1) × 10 10 cm−2. From the analysis of Shubnikov–de Haas oscillations at T = 190 mK, we obtain a long mean single particle relaxation time of (8.1 ± 0.5) ps, corresponding to a mean quantum mobility and quantum level broadening of (7.5 ± 0.6) × 10 4 cm2/V s and (40 ± 3) μ eV , respectively, and a small mean Dingle ratio of (2.3 ± 0.2) , indicating reduced scattering from long range impurities and a low-disorder environment for hosting high-performance spin-qubits. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study plasmonic nanoantennas for molecular sensing in the mid-infrared made of heavily doped germanium, epitaxially grown with a bottom-up doping process and featuring free carrier density in excess of 1020 cm-3. The dielectric function of the 250 nm thick germanium film is determined, and bow-tie antennas are designed, fabricated, and embedded in a polymer. By using a near-field photoexpansion mapping technique at λ = 5.8 µm, we demonstrate the existence in the antenna gap of an electromagnetic energy density hotspot of diameter below 100nm and confinement volume 105 times smaller than λ³. [ABSTRACT FROM AUTHOR]

Front Cover: A High-Mobility Hole Bilayer in a Germanium Double Quantum Well (Adv. The cover is an artistic impression of a germanium double quantum well (red) embedded in silicon-germanium (magenta). Progress in single planar quantum wells has positioned germanium as a promising material for quantum information processing. [Extracted from the article]

Buried‐channel semiconductor heterostructures are an archetype material platform for the fabrication of 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. Here, a 2D hole gas of high mobility (5 × 105 cm2 V−1 s−1) is demonstrated in a very shallow strained germanium (Ge) channel, which is located only 22 nm below the surface. The top‐gate of a dopant‐less field effect transistor controls the channel carrier density confined in an undoped Ge/SiGe heterostructure with reduced background contamination, sharp interfaces, and high uniformity. The high mobility leads to mean free paths ≈ 6 µm, setting new benchmarks for holes in shallow field effect transistors. The high mobility, along with a percolation density of 1.2 × 1011cm−2, light effective mass (0.09me), and high effective g‐factor (up to 9.2) highlight the potential of undoped Ge/SiGe as a low‐disorder material platform for hybrid quantum technologies. A two‐dimensional hole gas is demonstrated in a strained and shallow germanium quantum well, located 22 nm below the surface. The buried and undoped channel is populated via top‐gating. The high mobility of half a million cm2V−1s−1, light effective mass (0.09me), and high effective g‐factor (9.2) highlight the potential of germanium for spin and hybrid quantum technologies. [ABSTRACT FROM AUTHOR]