A CMOS silicon spin qubit

Design of high-performance entangling logic in silicon quantum dot systems with Bayesian optimization

Device engineering based on computer-aided simulations is essential to make silicon (Si) quantum bits (qubits) be competitive to commercial platforms based on superconductors and trapped ions. Combining device simulations with the Bayesian optimization (BO), here we propose a systematic design approach that is quite useful to procure fast and precise entangling operations of qubits encoded to electron spins in electrode-driven Si quantum dot (QD) systems. For a target problem of the controlled-X (CNOT) logic operation, we employ BO with the Gaussian process regression to evolve design factors of a Si double QD system to the ones that are optimal in terms of speed and fidelity of a CNOT logic driven by a single microwave pulse. The design framework not only clearly contributes to cost-efficient securing of solutions that enhance performance of the target quantum operation, but can be extended to implement more complicated logics with Si QD structures in experimentally unprecedented ways.

Shared control of a 16 semiconductor quantum dot crossbar array

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.

Excited state spectroscopy and spin splitting in single layer MoS2 quantum dots

Semiconducting transition metal dichalcogenides (TMDCs) are very promising materials for quantum dots and spin-qubit implementation. Reliable operation of spin qubits requires the knowledge of the Landé g-factor, which can be measured by exploiting the discrete energy spectrum on a quantum dot. However, the quantum dots realized in TMDCs are yet to reach the required control and quality for reliable measurement of excited state spectroscopy and the g-factor, particularly in atomically thin layers. Quantum dot sizes reported in TMDCs so far are not small enough to observe discrete energy levels on them. Here, we report on electron transport through discrete energy levels of quantum dots in a single layer MoS2 isolated from its environment using a dual gate geometry. The quantum dot energy levels are separated by a few (5-6) meV such that the ground state and the first excited state transitions are clearly visible, thanks to the low contact resistance of ∼700 Ω and relatively low gate voltages. This well-resolved energy separation allowed us to accurately measure the ground state g-factor of ∼5 in MoS2 quantum dots. We observed a spin-filling sequence in our quantum dots under a perpendicular magnetic field. Such a system offers an excellent testbed to measure the key parameters for evaluation and implementation of spin-valley qubits in TMDCs, thus accelerating the development of quantum systems in two-dimensional semiconducting TMDCs.

Phase-Driving Hole Spin Qubits

The spin-orbit interaction in spin qubits enables spin-flip transitions, resulting in Rabi oscillations when an external microwave field is resonant with the qubit frequency. Here, we introduce an alternative driving mechanism mediated by the strong spin-orbit interactions in hole spin qubits, where a far-detuned oscillating field couples to the qubit phase. Phase-driving at radio frequencies, orders of magnitude slower than the microwave qubit frequency, induces highly nontrivial spin dynamics, violating the Rabi resonance condition. By using a qubit integrated in a silicon fin field-effect transistor, we demonstrate a controllable suppression of resonant Rabi oscillations and their revivals at tunable sidebands. These sidebands enable alternative qubit control schemes using global fields and local far-detuned pulses, facilitating the design of dense large-scale qubit architectures with local qubit addressability. Phase-driving also decouples Rabi oscillations from noise, an effect due to a gapped Floquet spectrum and can enable Floquet engineering high-fidelity gates in future quantum processors.

Hole-Spin Driving by Strain-Induced Spin-Orbit Interactions

Hole spins in semiconductor quantum dots can be efficiently manipulated with radio-frequency electric fields owing to the strong spin-orbit interactions in the valence bands. Here we show that the motion of the dot in inhomogeneous strain fields gives rise to linear Rashba spin-orbit interactions (with spatially dependent spin-orbit lengths) and g-factor modulations that allow for fast Rabi oscillations. Such inhomogeneous strains build up spontaneously in the devices due to process and cool down stress. We discuss spin qubits in Ge/GeSi heterostructures as an illustration. We highlight that Rabi frequencies can be enhanced by 1 order of magnitude by shear strain gradients as small as 3×10^{-6}  nm^{-1} within the dots. This underlines that spins in solids can be very sensitive to strains and opens the way for strain engineering in hole spin devices for quantum information and spintronics.

The future transistors

The metal-oxide-semiconductor field-effect transistor (MOSFET), a core element of complementary metal-oxide-semiconductor (CMOS) technology, represents one of the most momentous inventions since the industrial revolution. Driven by the requirements for higher speed, energy efficiency and integration density of integrated-circuit products, in the past six decades the physical gate length of MOSFETs has been scaled to sub-20 nanometres. However, the downscaling of transistors while keeping the power consumption low is increasingly challenging, even for the state-of-the-art fin field-effect transistors. Here we present a comprehensive assessment of the existing and future CMOS technologies, and discuss the challenges and opportunities for the design of FETs with sub-10-nanometre gate length based on a hierarchical framework established for FET scaling. We focus our evaluation on identifying the most promising sub-10-nanometre-gate-length MOSFETs based on the knowledge derived from previous scaling efforts, as well as the research efforts needed to make the transistors relevant to future logic integrated-circuit products. We also detail our vision of beyond-MOSFET future transistors and potential innovation opportunities. We anticipate that innovations in transistor technologies will continue to have a central role in driving future materials, device physics and topology, heterogeneous vertical and lateral integration, and computing technologies.

An efficient quantum partial differential equation solver with chebyshev points

Differential equations are the foundation of mathematical models representing the universe's physics. Hence, it is significant to solve partial and ordinary differential equations, such as Navier-Stokes, heat transfer, convection-diffusion, and wave equations, to model, calculate and simulate the underlying complex physical processes. However, it is challenging to solve coupled nonlinear high dimensional partial differential equations in classical computers because of the vast amount of required resources and time. Quantum computation is one of the most promising methods that enable simulations of more complex problems. One solver developed for quantum computers is the quantum partial differential equation (PDE) solver, which uses the quantum amplitude estimation algorithm (QAEA). This paper proposes an efficient implementation of the QAEA by utilizing Chebyshev points for numerical integration to design robust quantum PDE solvers. A generic ordinary differential equation, a heat equation, and a convection-diffusion equation are solved. The solutions are compared with the available data to demonstrate the effectiveness of the proposed approach. We show that the proposed implementation provides a two-order accuracy increase with a significant reduction in solution time.

Ultrafast and Electrically Tunable Rabi Frequency in a Germanium Hut Wire Hole Spin Qubit

Hole spin qubits based on germanium (Ge) have strong tunable spin-orbit interaction (SOI) and ultrafast qubit operation speed. Here we report that the Rabi frequency (f_Rabi) of a hole spin qubit in a Ge hut wire (HW) double quantum dot (DQD) is electrically tuned through the detuning energy (ϵ) and middle gate voltage (V_M). f_Rabi gradually decreases with increasing ϵ; on the contrary, f_Rabi is positively correlated with V_M. We attribute our results to the change of electric field on SOI and the contribution of the excited state in quantum dots to f_Rabi. We further demonstrate an ultrafast f_Rabi exceeding 1.2 GHz, which indicates the strong SOI in our device. The discovery of an ultrafast and electrically tunable f_Rabi in a hole spin qubit has potential applications in semiconductor quantum computing.

Isotopically Enriched Layers for Quantum Computers Formed by 28Si Implantation and Layer Exchange

²⁸Si enrichment is crucial for production of group IV semiconductor-based quantum computers. Cryogenically cooled, monocrystalline ²⁸Si is a spin-free, vacuum-like environment where qubits are protected from sources of decoherence that cause loss of quantum information. Currently, ²⁸Si enrichment techniques rely on deposition of centrifuged SiF₄ gas, the source of which is not widely available, or bespoke ion implantation methods. Previously, conventional ion implantation into ^naturalSi substrates has produced heavily oxidized ²⁸Si layers. Here we report on a novel enrichment process involving ion implantation of ²⁸Si into Al films deposited on native-oxide free Si substrates followed by layer exchange crystallization. We measured continuous, oxygen-free epitaxial ²⁸Si enriched to 99.7%. Increases in isotopic enrichment are possible, and improvements in crystal quality, aluminum content, and thickness uniformity are required before the process can be considered viable. TRIDYN models, used to model 30 keV ²⁸Si implants into Al to understand the observed post-implant layers and to investigate the implanted layer exchange process window over different energy and vacuum conditions, showed that the implanted layer exchange process is insensitive to implantation energy and would increase in efficiency with oxygen concentrations in the implanter end-station by reducing sputtering. Required implant fluences are an order of magnitude lower than those required for enrichment by direct ²⁸Si implants into Si and can be chosen to control the final thickness of the enriched layer. We show that implanted layer exchange could potentially produce quantum grade ²⁸Si using conventional semiconductor foundry equipment within production-worthy time scales.

Combining n-MOS Charge Sensing with p-MOS Silicon Hole Double Quantum Dots in a CMOS platform

Holes in silicon quantum dots are receiving attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. We address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole double quantum dot. We demonstrate control of the spin state via electric dipole spin resonance. We achieve smooth control of the interdot coupling rate over 1 order of magnitude and use the charge sensor to perform spin-to-charge conversion to measure the hole singlet-triplet relaxation time of 11 μs for a known hole occupation. These results provide a path toward improving the quality and controllability of hole spin-qubits.

On-demand electrical control of spin qubits

Once called a 'classically non-describable two-valuedness' by Pauli, the electron spin forms a qubit that is naturally robust to electric fluctuations. Paradoxically, a common control strategy is the integration of micromagnets to enhance the coupling between spins and electric fields, which, in turn, hampers noise immunity and adds architectural complexity. Here we exploit a switchable interaction between spins and orbital motion of electrons in silicon quantum dots, without a micromagnet. The weak effects of relativistic spin-orbit interaction in silicon are enhanced, leading to a speed up in Rabi frequency by a factor of up to 650 by controlling the energy quantization of electrons in the nanostructure. Fast electrical control is demonstrated in multiple devices and electronic configurations. Using the electrical drive, we achieve a coherence time T_2,Hahn ≈ 50 μs, fast single-qubit gates with T_π/2 = 3 ns and gate fidelities of 99.93%, probed by randomized benchmarking. High-performance all-electrical control improves the prospects for scalable silicon quantum computing.

Colloquium: Advances in automation of quantum dot devices control

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Charge-Noise-Induced Dephasing in Silicon Hole-Spin Qubits

We investigate, theoretically, charge-noise-induced spin dephasing of a hole confined in a quasi-two-dimensional silicon quantum dot. Central to our treatment is accounting for higher-order corrections to the Luttinger Hamiltonian. Using experimentally reported parameters, we find that the new terms give rise to sweet spots for the hole-spin dephasing, which are sensitive to device details: dot size and asymmetry, growth direction, and applied magnetic and electric fields. Furthermore, we estimate that the dephasing time at the sweet spots is boosted by several orders of magnitude, up to on the order of milliseconds.

A single hole spin with enhanced coherence in natural silicon

Semiconductor spin qubits based on spin-orbit states are responsive to electric field excitations, allowing for practical, fast and potentially scalable qubit control. Spin electric susceptibility, however, renders these qubits generally vulnerable to electrical noise, which limits their coherence time. Here we report on a spin-orbit qubit consisting of a single hole electrostatically confined in a natural silicon metal-oxide-semiconductor device. By varying the magnetic field orientation, we reveal the existence of operation sweet spots where the impact of charge noise is minimized while preserving an efficient electric-dipole spin control. We correspondingly observe an extension of the Hahn-echo coherence time up to 88 μs, exceeding by an order of magnitude existing values reported for hole spin qubits, and approaching the state-of-the-art for electron spin qubits with synthetic spin-orbit coupling in isotopically purified silicon. Our finding enhances the prospects of silicon-based hole spin qubits for scalable quantum information processing.

Anomalous Zero-Field Splitting for Hole Spin Qubits in Si and Ge Quantum Dots

An anomalous energy splitting of spin triplet states at zero magnetic field has recently been measured in germanium quantum dots. This zero-field splitting could crucially alter the coupling between tunnel-coupled quantum dots, the basic building blocks of state-of-the-art spin-based quantum processors, with profound implications for semiconducting quantum computers. We develop an analytical model linking the zero-field splitting to the Rashba spin-orbit interaction that is cubic in momentum. Such interactions naturally emerge in hole nanostructures, where they can also be tuned by external electric fields, and we find them to be particularly large in silicon and germanium, resulting in a significant zero-field splitting in the μeV range. We confirm our analytical theory by numerical simulations of different quantum dots, also including other possible sources of zero-field splitting. Our findings are applicable to a broad range of current architectures encoding spin qubits and provide a deeper understanding of these materials, paving the way toward the next generation of semiconducting quantum processors.

Devitalizing noise-driven instability of entangling logic in silicon devices with bias controls

The quality of quantum bits (qubits) in silicon is highly vulnerable to charge noise that is omnipresent in semiconductor devices and is in principle hard to be suppressed. For a realistically sized quantum dot system based on a silicon-germanium heterostructure whose confinement is manipulated with electrical biases imposed on top electrodes, we computationally explore the noise-robustness of 2-qubit entangling operations with a focus on the controlled-X (CNOT) logic that is essential for designs of gate-based universal quantum logic circuits. With device simulations based on the physics of bulk semiconductors augmented with electronic structure calculations, we not only quantify the degradation in fidelity of single-step CNOT operations with respect to the strength of charge noise, but also discuss a strategy of device engineering that can significantly enhance noise-robustness of CNOT operations with almost no sacrifice of speed compared to the single-step case. Details of device designs and controls that this work presents can establish practical guideline for potential efforts to secure silicon-based quantum processors using an electrode-driven quantum dot platform.

Fully Tunable Longitudinal Spin-Photon Interactions in Si and Ge Quantum Dots

Spin qubits in silicon and germanium quantum dots are promising platforms for quantum computing, but entangling spin qubits over micrometer distances remains a critical challenge. Current prototypical architectures maximize transversal interactions between qubits and microwave resonators, where the spin state is flipped by nearly resonant photons. However, these interactions cause backaction on the qubit that yields unavoidable residual qubit-qubit couplings and significantly affects the gate fidelity. Strikingly, residual couplings vanish when spin-photon interactions are longitudinal and photons couple to the phase of the qubit. We show that large and tunable spin-photon interactions emerge naturally in state-of-the-art hole spin qubits and that they change from transversal to longitudinal depending on the magnetic field direction. We propose ways to electrically control and measure these interactions, as well as realistic protocols to implement fast high-fidelity two-qubit entangling gates. These protocols work also at high temperatures, paving the way toward the implementation of large-scale quantum processors.

Double gate operation of metal nanodot array based single electron device

Multidot single-electron devices (SEDs) can enable new types of computing technologies, such as those that are reconfigurable and reservoir-computing. A self-assembled metal nanodot array film that is attached to multiple gates is a candidate for use in such SEDs for achieving high functionality. However, the single-electron properties of such a film have not yet been investigated in conjunction with optimally controlled multiple gates because of the structural complexity of incorporating many nanodots. In this study, Fe nanodot-array-based double-gate SEDs were fabricated by vacuum deposition, and their single-electron properties (modulated by the top- and bottom-gate voltages; V_T and V_B, respectively) were investigated. The phase of the Coulomb blockade oscillation systematically shifted with V_T, indicating that the charge state of the single dot was controlled by both the gate voltages despite the metallic random multidot structure. This result demonstrates that the Coulomb blockade oscillation (originating from the dot in the multidot array) can be modulated by the two gates. The top and bottom gates affected the electronic state of the dot unevenly owing to the geometrical effect caused by the following: (1) vertically asymmetric dot shape and (2) variation of the dot size (including the surrounding dots). This is a characteristic feature of a nanodot array that uses self-assembled metal dots; for example, prepared by vacuum deposition. Such variations derived from a randomly distributed nanodot array will be useful in enhancing the functionality of multidot devices.

DFT Analysis of Hole Qubits Spin State in Germanium Thin Layer

Due to the presence of a strong spin–orbit interaction, hole qubits in germanium are increasingly being considered as candidates for quantum computing. These objects make it possible to create electrically controlled logic gates with the basic properties of scalability, a reasonable quantum error correction, and the necessary speed of operation. In this paper, using the methods of quantum-mechanical calculations and considering the non-collinear magnetic interactions, the quantum states of the system 2D structure of Ge in the presence of even and odd numbers of holes were investigated. The spatial localizations of hole states were calculated, favorable quantum states were revealed, and the magnetic structural characteristics of the system were analyzed.

The functions of a reservoir offset voltage applied to physically defined p-channel Si quantum dots

We propose and define a reservoir offset voltage as a voltage commonly applied to both reservoirs of a quantum dot and study the functions in p-channel Si quantum dots. By the reservoir offset voltage, the electrochemical potential of the quantum dot can be modulated. In addition, when quantum dots in different channels are capacitively coupled, the reservoir offset voltage of one of the QDs can work as a gate voltage for the others. Our results show that the technique will lead to reduction of the number of gate electrodes, which is advantageous for future qubit integration.

Dynamics of Hole Singlet-Triplet Qubits with Large g-Factor Differences

The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.

Miniaturizing neural networks for charge state autotuning in quantum dots

A key challenge in scaling quantum computers is the calibration and control of multiple qubits. In solid-state quantum dots (QDs), the gate voltages required to stabilize quantized charges are unique for each individual qubit, resulting in a high-dimensional control parameter space that must be tuned automatically. Machine learning techniques are capable of processing high-dimensional data—provided that an appropriate training set is available—and have been successfully used for autotuning in the past. In this paper, we develop extremely small feed-forward neural networks that can be used to detect charge-state transitions in QD stability diagrams. We demonstrate that these neural networks can be trained on synthetic data produced by computer simulations, and robustly transferred to the task of tuning an experimental device into a desired charge state. The neural networks required for this task are sufficiently small as to enable an implementation in existing memristor crossbar arrays in the near future. This opens up the possibility of miniaturizing powerful control elements on low-power hardware, a significant step towards on-chip autotuning in future QD computers.

Atomic Layer Deposition of Ultrathin La2O3/Al2O3 Nanolaminates on MoS2 with Ultraviolet Ozone Treatment

Due to the chemically inert surface of MoS2, uniform deposition of ultrathin high-κ dielectric using atomic layer deposition (ALD) is difficult. However, this is crucial for the fabrication of field-effect transistors (FETs). In this work, the atomic layer deposition growth of sub-5 nm La2O3/Al2O3 nanolaminates on MoS2 using different oxidants (H2O and O3) was investigated. To improve the deposition, the effects of ultraviolet ozone treatment on MoS2 surface are also evaluated. It is found that the physical properties and electrical characteristics of La2O3/Al2O3 nanolaminates change greatly for different oxidants and treatment processes. These changes are found to be associated with the residual of metal carbide caused by the insufficient interface reactions. Ultraviolet ozone pretreatment can substantially improve the initial growth of sub-5 nm H2O-based or O3-based La2O3/Al2O3 nanolaminates, resulting in a reduction of residual metal carbide. All results indicate that O3-based La2O3/Al2O3 nanolaminates on MoS2 with ultraviolet ozone treatment yielded good electrical performance with low leakage current and no leakage dot, revealing a straightforward approach for realizing sub-5 nm uniform La2O3/Al2O3 nanolaminates on MoS2.

A Flexible Design Platform for Si/SiGe Exchange-Only Qubits with Low Disorder

Spin-based silicon quantum dots are an attractive qubit technology for quantum information processing with respect to coherence time, control, and engineering. Here we present an exchange-only Si qubit device platform that combines the throughput of CMOS-like wafer processing with the versatility of direct-write lithography. The technology, which we coin "SLEDGE", features dot-shaped gates that are patterned simultaneously on one topographical plane and subsequently connected by vias to interconnect metal lines. The process design enables nontrivial layouts as well as flexibility in gate dimensions, material selection, and additional device features such as for rf qubit control. We show that the SLEDGE process has reduced electrostatic disorder with respect to traditional overlapping gate devices with lift-off metallization, and we present spin coherent exchange oscillations and single qubit blind randomized benchmarking data.

Ultrafast coherent control of a hole spin qubit in a germanium quantum dot

Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the strong SOI of heavy holes (HHs) in our GHW, characterized by a very short spin-orbit length of 1.5 nm, enables the rapid gate operations we accomplish. Our results demonstrate the potential of ultrafast coherent control of hole spin qubits to meet the requirement of DiVincenzo’s criteria for a scalable quantum information processor.

Hole-spin qubits in germanium are promising candidates for rapid, all-electrical qubit control. Here the authors report Rabi oscillations with the record frequency of 540 MHz in a hole-based double quantum dot in a germanium hut wire, which is attributed to strong spin-orbit interaction of heavy holes.

Fully Tunable Hyperfine Interactions of Hole Spin Qubits in Si and Ge Quantum Dots

Hole spin qubits are frontrunner platforms for scalable quantum computers, but state-of-the-art devices suffer from noise originating from the hyperfine interactions with nuclear defects. We show that these interactions have a highly tunable anisotropy that is controlled by device design and external electric fields. This tunability enables sweet spots where the hyperfine noise is suppressed by an order of magnitude and is comparable to isotopically purified materials. We identify surprisingly simple designs where the qubits are highly coherent and are largely unaffected by both charge and hyperfine noise. We find that the large spin-orbit interaction typical of elongated quantum dots not only speeds up qubit operations, but also dramatically renormalizes the hyperfine noise, altering qualitatively the dynamics of driven qubits and enhancing the fidelity of qubit gates. Our findings serve as guidelines to design high performance qubits for scaling up quantum computers.

Germanium Quantum-Dot Array with Self-Aligned Electrodes for Quantum Electronic Devices

Semiconductor-based quantum registers require scalable quantum-dots (QDs) to be accurately located in close proximity to and independently addressable by external electrodes. Si-based QD qubits have been realized in various lithographically-defined Si/SiGe heterostructures and validated only for milli-Kelvin temperature operation. QD qubits have recently been explored in germanium (Ge) materials systems that are envisaged to operate at higher temperatures, relax lithographic-fabrication requirements, and scale up to large quantum systems. We report the unique scalability and tunability of Ge spherical-shaped QDs that are controllably located, closely coupled between each another, and self-aligned with control electrodes, using a coordinated combination of lithographic patterning and self-assembled growth. The core experimental design is based on the thermal oxidation of poly-SiGe spacer islands located at each sidewall corner or included-angle location of Si₃N₄/Si-ridges with specially designed fanout structures. Multiple Ge QDs with good tunability in QD sizes and self-aligned electrodes were controllably achieved. Spherical-shaped Ge QDs are closely coupled to each other via coupling barriers of Si₃N₄ spacer layers/c-Si that are electrically tunable via self-aligned poly-Si or polycide electrodes. Our ability to place size-tunable spherical Ge QDs at any desired location, therefore, offers a large parameter space within which to design novel quantum electronic devices.

4.2 K sensitivity-tunable radio frequency reflectometry of a physically defined p-channel silicon quantum dot

We demonstrate the measurement of p-channel silicon-on-insulator quantum dots at liquid helium temperatures by using a radio frequency (rf) reflectometry circuit comprising of two independently tunable GaAs varactors. This arrangement allows observing Coulomb diamonds at 4.2 K under nearly best matching condition and optimal signal-to-noise ratio. We also discuss the rf leakage induced by the presence of the large top gate in MOS nanostructures and its consequence on the efficiency of rf-reflectometry. These results open the way to fast and sensitive readout in multi-gate architectures, including multi qubit platforms.

Isotropic and Anisotropic g-Factor Corrections in GaAs Quantum Dots

We experimentally determine isotropic and anisotropic g-factor corrections in lateral GaAs single-electron quantum dots. We extract the Zeeman splitting by measuring the tunnel rates into the individual spin states of an empty quantum dot for an in-plane magnetic field with various strengths and directions. We quantify the Zeeman energy and find a linear dependence on the magnetic field strength that allows us to extract the g factor. The measured g factor is understood in terms of spin-orbit interaction induced isotropic and anisotropic corrections to the GaAs bulk g factor. Experimental detection and identification of minute band-structure effects in the g factor is of significance for spin qubits in GaAs quantum dots.

Sub-bandgap absorption and photo-response of molybdenum heavily doped black silicon fabricated by a femtosecond laser

Molybdenum (Mo)-doped black silicon (Si) is obtained by using femtosecond laser irradiation. The concentration of Mo atoms at the depth from 10 to 200 nm has exceeded 10¹⁹cm^-3. In contrast, the carrier concentration in the Mo-doped layer is lower than 10¹⁵cm^-3. The surface morphologies with ripple and conical spike microstructures are formed by changing the pulsed laser fluences. The Mo-doped Si samples exhibit a sub-bandgap (1100∼2500nm) absorptance of more than 60% at a wavelength of 1310 nm. A Mo-doped Si photodetector is made, and the responsivity of the device for 1310 nm is up to 76 mA/W at a -10V bias.

Anisotropic g-Factor and Spin-Orbit Field in a Germanium Hut Wire Double Quantum Dot

Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inversion asymmetry in Ge hut wires. We also demonstrate two different spin relaxation mechanisms for the holes in the Ge hut wire double dot: spin-flip co-tunneling to the leads, and spin-orbit interaction within the double dot. These results help establish feasibility of a Ge-based quantum processor.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Probing hole spin transport of disorder quantum dots via Pauli spin-blockade in standard silicon transistors

Single hole transport and spin detection is achievable in standard p-type silicon transistors owing to the strong orbital quantization of disorder based quantum dots. Through the use of the well acting as a pseudo-gate, we discover the formation of a double-quantum dot system exhibiting Pauli spin-blockade and investigate the magnetic field dependence of the leakage current. This enables attributes that are key to hole spin state control to be determined, where we calculate a tunnel couplingt_cof 57μeV and a short spin-orbit lengthl_SOof 250 nm. The demonstrated strong spin-orbit interaction at the interface when using disorder based quantum dots supports electric-field mediated control. These results provide further motivation that a readily scalable platform such as industry standard silicon technology can be used to investigate interactions which are useful for quantum information processing.

A four-qubit germanium quantum processor

The prospect of building quantum circuits^1,2 using advanced semiconductor manufacturing makes quantum dots an attractive platform for quantum information processing^3,4. Extensive studies of various materials have led to demonstrations of two-qubit logic in gallium arsenide⁵, silicon^6-12 and germanium¹³. 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.

Ultrafast hole spin qubit with gate-tunable spin-orbit switch functionality

Quantum computers promise to execute complex tasks exponentially faster than any possible classical computer, and thus spur breakthroughs in quantum chemistry, material science and machine learning. However, quantum computers require fast and selective control of large numbers of individual qubits while maintaining coherence. Qubits based on hole spins in one-dimensional germanium/silicon nanostructures are predicted to experience an exceptionally strong yet electrically tunable spin-orbit interaction, which allows us to optimize qubit performance by switching between distinct modes of ultrafast manipulation, long coherence and individual addressability. Here we used millivolt gate voltage changes to tune the Rabi frequency of a hole spin qubit in a germanium/silicon nanowire from 31 to 219 MHz, its driven coherence time between 7 and 59 ns, and its Landé g-factor from 0.83 to 1.27. We thus demonstrated spin-orbit switch functionality, with on/off ratios of roughly seven, which could be further increased through improved gate design. Finally, we used this control to optimize our qubit further and approach the strong driving regime, with spin-flipping times as short as ~1 ns.

Cryogenic Transport Characteristics of P-Type Gate-All-Around Silicon Nanowire MOSFETs

A 16-nm-L_g p-type Gate-all-around (GAA) silicon nanowire (Si NW) metal oxide semiconductor field effect transistor (MOSFET) was fabricated based on the mainstream bulk fin field-effect transistor (FinFET) technology. The temperature dependence of electrical characteristics for normal MOSFET as well as the quantum transport at cryogenic has been investigated systematically. We demonstrate a good gate-control ability and body effect immunity at cryogenic for the GAA Si NW MOSFETs and observe the transport of two-fold degenerate hole sub-bands in the nanowire (110) channel direction sub-band structure experimentally. In addition, the pronounced ballistic transport characteristics were demonstrated in the GAA Si NW MOSFET. Due to the existence of spacers for the typical MOSFET, the quantum interference was also successfully achieved at lower bias.

Exploring the behaviors of electrode-driven Si quantum dot systems: from charge control to qubit operations

Charge stabilities and spin-based quantum bit (qubit) operations in Si double quantum dot (DQD) systems, whose confinement potentials are controlled with multiple gate electrodes, are theoretically studied with a multi-scale modeling approach that combines electronic structure simulations and the Thomas-Fermi method. Taking Si/SiGe heterostructures as the target of modeling, this work presents an in-depth discussion on the designs of electron reservoirs, electrostatic controls of quantum dot (QD) shapes and their corresponding charge confinements, and spin qubit manipulations. The effects of unintentional inaccuracies in DC control biases and geometric symmetries on the Rabi cycle of spin qubits are investigated to examine the robustness of logic operations. Solid connections to the latest experimental results are also established to validate the simulation method. As a rare modeling study that explores the full-stack functionality of Si DQD structures as quantum logic gate devices, this work delivers the knowledge of engineering details that are not uncovered by the latest experimental work and can serve as a basic but practical guideline for potential device designs.

Engineering long spin coherence times of spin-orbit qubits in silicon

Electron-spin qubits have long coherence times suitable for quantum technologies. Spin-orbit coupling promises to greatly improve spin qubit scalability and functionality, allowing qubit coupling via photons, phonons or mutual capacitances, and enabling the realization of engineered hybrid and topological quantum systems. However, despite much recent interest, results to date have yielded short coherence times (from 0.1 to 1 μs). Here we demonstrate ultra-long coherence times of 10 ms for holes where spin-orbit coupling yields quantized total angular momentum. We focus on holes bound to boron acceptors in bulk silicon 28, whose wavefunction symmetry can be controlled through crystal strain, allowing direct control over the longitudinal electric dipole that causes decoherence. The results rival the best electron-spin qubits and are 10⁴ to 10⁵ longer than previous spin-orbit qubits. These results open a pathway to develop new artificial quantum systems and to improve the functionality and scalability of spin-based quantum technologies.

Alternatives to aluminum gates for silicon quantum devices: defects and strain

Gate-defined quantum dots (QD) benefit from the use of small grain size metals for gate materials because it aids in shrinking the device dimensions. However, it is not clear what differences arise with respect to process-induced defect densities and inhomogeneous strain. Here, we present measurements of fixed charge, Q _f , interface trap density, D _it , the intrinsic film stress, σ, and the coefficient of thermal expansion, α as a function of forming gas anneal temperature for Al, Ti/Pd, and Ti/Pt gates. We show D _it is minimal at an anneal temperature of 350 °C for all materials but Ti/Pd and Ti/Pt have higher Q _f and D _it compared to Al. In addition, σ and α increase with anneal temperature for all three metals with α larger than the bulk value. These results indicate that there is a tradeoff between minimizing defects and minimizing the impact of strain in quantum device fabrication.

Single-electron operations in a foundry-fabricated array of quantum dots

Silicon quantum dots are attractive for the implementation of large spin-based quantum processors in part due to prospects of industrial foundry fabrication. However, the large effective mass associated with electrons in silicon traditionally limits single-electron operations to devices fabricated in customized academic clean rooms. Here, we demonstrate single-electron occupations in all four quantum dots of a 2 x 2 split-gate silicon device fabricated entirely by 300-mm-wafer foundry processes. By applying gate-voltage pulses while performing high-frequency reflectometry off one gate electrode, we perform single-electron operations within the array that demonstrate single-shot detection of electron tunneling and an overall adjustability of tunneling times by a global top gate electrode. Lastly, we use the two-dimensional aspect of the quantum dot array to exchange two electrons by spatial permutation, which may find applications in permutation-based quantum algorithms.

Single-Electron Operation of a Silicon-CMOS 2 × 2 Quantum Dot Array with Integrated Charge Sensing

The advanced nanoscale integration available in CMOS technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multigate designs. We show that quantum dots formed in a CMOS nanowire device can be measured with a remote single electron transistor (SET) formed in an adjacent nanowire, via floating coupling gates. By biasing the SET nanowire with respect to the nanowire hosting the quantum dots, we controllably form ancillary quantum dots under the floating gates, thus enabling control of all quantum dots in a 2 × 2 array, and charge sensing down to the last electron in each dot. We use effective mass theory to investigate the ideal geometrical parameters in order to achieve interdot tunnel rates required for spin-based quantum computation.

Full-band quantum transport simulation in the presence of hole-phonon interactions using a mode-space k·p approach

Fabrication techniques at the nanometer scale offer potential opportunities to access single-dopant features in nanoscale transistors. Here, we report full-band quantum transport simulations with hole-phonon interactions through a device consisting of two gates-all-around in series and a p-type Si nanowire channel with a single dopant within each gated region. For this purpose, we have developed and implemented a mode-space-based full-band quantum transport simulator with phonon scattering using the six-band k · p method. Based on the non-equilibrium Green's function formalism and self-consistent Born's approximation, an expression for the hole-phonon interaction self-energy within the mode-space representation is introduced.

Remote Capacitive Sensing in Two-Dimensional Quantum-Dot Arrays

We investigate gate-induced quantum dots in silicon nanowire field-effect transistors fabricated using a foundry-compatible fully depleted silicon-on-insulator (FD-SOI) process. A series of split gates wrapped over the silicon nanowire naturally produces a 2 × n bilinear array of quantum dots along a single nanowire. We begin by studying the capacitive coupling of quantum dots within such a 2 × 2 array and then show how such couplings can be extended across two parallel silicon nanowires coupled together by shared, electrically isolated, "floating" electrodes. With one quantum dot operating as a single-electron-box sensor, the floating gate serves to enhance the charge sensitivity range, enabling it to detect charge state transitions in a separate silicon nanowire. By comparing measurements from multiple devices, we illustrate the impact of the floating gate by quantifying both the charge sensitivity decay as a function of dot-sensor separation and configuration within the dual-nanowire structure.

Spin Relaxation Benchmarks and Individual Qubit Addressability for Holes in Quantum Dots

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.

Network theory of the bacterial ribosome

In the past two decades, research into the biochemical, biophysical and structural properties of the ribosome have revealed many different steps of protein translation. Nevertheless, a complete understanding of how they lead to a rapid and accurate protein synthesis still remains a challenge. Here we consider a coarse network analysis in the bacterial ribosome formed by the connectivity between ribosomal (r) proteins and RNAs at different stages in the elongation cycle. The ribosomal networks are found to be dis-assortative and small world, implying that the structure allows for an efficient exchange of information between distant locations. An analysis of centrality shows that the second and fifth domains of 23S rRNA are the most important elements in all of the networks. Ribosomal protein hubs connect to much fewer nodes but are shown to provide important connectivity within the network (high closeness centrality). A modularity analysis reveals some of the different functional communities, indicating some known and some new possible communication pathways Our mathematical results confirm important communication pathways that have been discussed in previous research, thus verifying the use of this technique for representing the ribosome, and also reveal new insights into the collective function of ribosomal elements.

A single-hole spin qubit

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.

While most results so far in semiconductor spin-based quantum computation use electron spins, devices based on hole spins may have more favourable properties for quantum applications. Here, the authors demonstrate single-shot readout and coherent control of a qubit made from a single hole spin.

Zero Field Splitting of Heavy-Hole States in Quantum Dots

Using inelastic cotunneling spectroscopy we observe a zero field splitting within the spin triplet manifold of Ge hut wire quantum dots. The states with spin ±1 in the confinement direction are energetically favored by up to 55 μeV compared to the spin 0 triplet state because of the strong spin-orbit coupling. The reported effect should be observable in a broad class of strongly confined hole quantum-dot systems and might need to be considered when operating hole spin qubits.