A strained Ge quantum well, grown on a SiGe/Si virtual substrate and hosting two electrostatically defined hole spin qubits, is nondestructively investigated by synchrotron-based scanning X-ray diffraction microscopy to determine all its Bravais lattice parameters. This allows rendering the three-dimensional spatial dependence of the six strain tensor components with a lateral resolution of approximately 50 nm. Two different spatial scales governing the strain field fluctuations in proximity of the qubits are observed at <100 nm and >1 μm, respectively. The short-ranged fluctuations have a typical bandwidth of 2 × 10-4 and can be quantitatively linked to the compressive stressing action of the metal electrodes defining the qubits. By finite element mechanical simulations, it is estimated that this strain fluctuation is increased up to 6 × 10-4 at cryogenic temperature. The longer-ranged fluctuations are of the 10-3 order and are associated with misfit dislocations in the plastically relaxed virtual substrate. From this, energy variations of the light and heavy-hole energy maxima of the order of several 100 μeV and 1 meV are calculated for electrodes and dislocations, respectively. These insights over material-related inhomogeneities may feed into further modeling for optimization and design of large-scale quantum processors manufactured using the mainstream Si-based microelectronics technology.

One of the main bottlenecks in the pursuit of a large-scale-chip-based quantum computer is the large number of control signals needed to operate qubit systems. As system sizes scale up, the number of terminals required to connect to off-chip control electronics quickly becomes unmanageable. Here, we discuss a quantum-dot spin-qubit architecture that integrates on-chip control electronics, allowing for a significant reduction in the number of signal connections at the chip boundary. By arranging the qubits in a two-dimensional array with about 12μm pitch, we create space to implement locally integrated sample-and-hold circuits. This allows us to offset the inhomogeneities in the potential landscape across the array and to globally share the majority of the control signals for qubit operations. We make use of advanced circuit modeling software to go beyond conceptual drawings of the component layout, to assess the feasibility of the scheme through a concrete floor plan, including estimates of footprints for quantum and classical electronics, as well as routing of signal lines across the chip using different interconnect layers. We make use of local demultiplexing circuits to achieve an efficient signal-connection scaling, leading to a Rent's exponent as low as p=0.43. Furthermore, we use available data from state-of-the-art spin qubit and microelectronics technology development, as well as circuit models and simulations, to estimate the operation frequencies and power consumption of a million-qubit array. This work presents a complementary approach to previously proposed architectures, focusing on a feasible scheme to integrating quantum and classical hardware, and identifying remaining challenges for achieving full fault-tolerant quantum computation. It thereby significantly closes the gap towards a fully CMOS-compatible quantum computer implementation.

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.

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.

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.

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.

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 (0.09m_e), 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.

Extremely long coherence times, excellent single-qubit gate fidelities, and two-qubit logic have been demonstrated with silicon metal-oxide-semiconductor spin qubits, making it one of the leading platforms for quantum information processing. Despite this, a long-standing challenge in this system has been the demonstration of tunable tunnel coupling between single electrons. Here we overcome this hurdle with gate-defined quantum dots and show couplings that can be tuned on and off for quantum operations. We use charge sensing to discriminate between the (2,0) and (1,1) charge states of a double quantum dot and show excellent charge sensitivity. We demonstrate tunable coupling up to 13 GHz, obtained by fitting charge polarization lines, and tunable tunnel rates down to <1 Hz, deduced from the random telegraph signal. The demonstration of tunable coupling between single electrons in a silicon metal-oxide-semiconductor device provides significant scope for high-fidelity two-qubit logic toward quantum information processing with standard manufacturing.

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so-called crossbar architectures. Recently we made a proposal for a large-scale quantum processor (Li et al arXiv:1711.03807 (2017)) to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single-qubit control, but allows the scheme to overcome control scaling issues that form a major hurdle to large-scale quantum computing systems. In this work, we develop a language that makes it possible to easily map quantum circuits to crossbar systems, taking into account their architecture and control limitations. Using this language we show how to map well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. We analyze the logical error behavior of this surface code mapping for estimated experimental parameters of the crossbar system and conclude that logical error suppression to a level useful for real quantum computation is feasible.