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The challenges of operating qubits in a cryogenic environment point to a looming bottleneck for large-scale quantum processors, limited by the number of input-output connections. Classical processors solve this problem via multiplexing; however, on-chip multiplexing circuits have not been shown to have similar benefits for cryogenic quantum devices. In this work we integrate classical circuitry and Si/SiGe quantum devices on the same chip, providing a test bed for qubit scale-up. Our method uses on-chip field-effect transistors (FETs) to multiplex a grid of work zones, achieving a nearly tenfold reduction in control wiring. We leverage this set-up to probe device properties across a 6x6mm$^2$ array of 16 Hall bars. We successfully operate the array at cryogenic temperatures and high magnetic fields where the quantum Hall effect is observed. Building upon these results, we propose a vision for readout in a large-scale silicon quantum processor with a limited number of control connections.

Latching techniques are widely used to enhance readout of qubits. These methods require precise tuning of multiple tunnel rates, which can be challenging to achieve under realistic experimental conditions, such as when a qubit is coupled to a single reservoir. Here, we present a method for single-shot measurement of a quantum dot qubit with a single reservoir using a latched-readout scheme. Our approach involves pulsing a barrier gate to dynamically control qubit-to-reservoir tunnel rates, a method that is readily applicable to the latched readout of various spin-based qubits. We use this method to enable qubit state latching and to reduce the qubit reset time in measurements of coherent Larmor oscillations of a Si/SiGe quantum dot hybrid qubit., Comment: 6 pages, including supplemental materials

We perform readout of a quantum-dot hybrid qubit coupled to a superconducting resonator through a parametric, longitudinal interaction mechanism. Our experiments are performed with the qubit and resonator frequencies detuned by $\sim$10 GHz, demonstrating that longitudinal coupling can facilitate semiconductor qubit operation in the 'ultra-dispersive' regime of circuit quantum electrodynamics., Comment: Main text and Supplementary Information; 12 pages, 7 figures

We estimate the equilibration rate of a nearly homogeneous Higgs field, displaced from its ground state during the onset of an electroweak phase transition. The computation is carried out with Hard Thermal Loop resummed perturbation theory, and a significant part of the result originates from Bose-enhanced $t$-channel $2\leftrightarrow 2$ scatterings. The expression is shown to be IR finite and gauge independent. Possible applications to Langevin simulations of bubble nucleation are mentioned, and we also contrast with the friction affecting bubble growth., Comment: 30 pages. v2: clarifications added

The rapid development of quantum dot (QD) devices for quantum computing has necessitated more efficient and automated methods for device characterization and tuning. Many of the measurements acquired during the tuning process come in the form of images that need to be properly analyzed to guide the subsequent tuning steps. By design, features present in such images capture certain behaviors or states of the measured QD devices. When considered carefully, such features can aid the control and calibration of QD devices. An important example of such images are so-called \textit{triangle plots}, which visually represent current flow and reveal characteristics important for QD device calibration. While image-based classification tools, such as convolutional neural networks (CNNs), can be used to verify whether a given measurement is \textit{good} and thus warrants the initiation of the next phase of tuning, they do not provide any insights into how the device should be adjusted in the case of \textit{bad} images. This is because CNNs sacrifice prediction and model intelligibility for high accuracy. To ameliorate this trade-off, a recent study introduced an image vectorization approach that relies on the Gabor wavelet transform [1]. Here we propose an alternative vectorization method that involves mathematical modeling of synthetic triangles to mimic the experimental data. Using explainable boosting machines, we show that this new method offers superior explainability of model prediction without sacrificing accuracy. This work demonstrates the feasibility and advantages of applying explainable machine learning techniques to the analysis of quantum dot measurements, paving the way for further advances in automated and transparent QD device tuning., Comment: 17 pages, 4 figures, abbreviated version published in Proceedings of the XAI4Sci: Explainable machine learning for sciences workshop at AAAI 2024, (Vancouver, Canada)

Optical illumination of quantum-dot qubit devices at cryogenic temperatures, while not well studied, is often used to recover operating conditions after undesired shocking events or charge injection. Here, we demonstrate systematic threshold voltage shifts in a dopant-free, Si/SiGe field effect transistor using a near infrared (780 nm) laser diode. We find that illumination under an applied gate voltage can be used to set a specific, stable, and reproducible threshold voltage that, over a wide range in gate bias, is equal to that gate bias. Outside this range, the threshold voltage can still be tuned, although the resulting threshold voltage is no longer equal to the applied gate bias during illumination. We present a simple and intuitive model that provides a mechanism for the tunability in gate bias. The model presented also explains why cryogenic illumination is successful at resetting quantum dot qubit devices after undesired charging events., Comment: 8 pages, 6 figures

Nanofabricated metal gate electrodes are commonly used to confine and control electrons in electrostatically defined quantum dots. However, these same gates impart a complicated strain geometry that affects the confinement potential and potentially impairs device functionality. Here we investigate strain-induced fluctuations of the potential energy in Si/SiGe heterostructures, caused by (i) lattice mismatch, (ii) materials-dependent thermal contraction, and (iii) deposition stress in the metal gates. By simulating different gate geometries, ranging from simple to realistically complicated, and including features like overlapping metal and oxide layers, we can explain most observed strain features. In particular, we show that strain-induced potential fluctuations can be suppressed by employing overlapping gates that cover the whole active region, when the oxide layers are thin. These results suggest that strain effects should not present a serious challenge to qubit uniformity when following simple design rules., Comment: 13 pages, 9 figures

Engineering conduction-band valley couplings is a key challenge for Si-based spin qubits. Recent work has shown that the most reliable method for enhancing valley couplings entails adding Ge concentration oscillations to the quantum well. However, ultrashort oscillation periods are difficult to grow, while long oscillation periods do not provide useful improvements. Here, we show that the main benefits of short-wavelength oscillations can be achieved in long-wavelength structures through a second-order coupling process involving Brillouin-zone folding induced by shear strain. We finally show that such strain can be achieved through common fabrication techniques, making this an exceptionally promising system for scalable quantum computing., Comment: 13 pages (5 main text), 5 figures. Published version

Silicon/silicon-germanium heterostructures have many important advantages for hosting spin qubits. However, controlling the valley splitting (the energy splitting between the two low-lying conduction-band valleys) remains a critical challenge for ensuring qubit reliability. Broad distributions of valley splittings are commonplace, even among quantum dots formed on the same chip. In this work, we theoretically explore the interplay between quantum-well imperfections that suppress the valley splitting and cause variability, such as broadened interfaces and atomic steps at the interface, while self-consistently accounting for germanium concentration fluctuations. We consider both conventional and unconventional approaches for controlling the valley splitting, and present concrete strategies for implementing them. Our results provide a clear path for achieving qubit uniformity in a scalable silicon quantum computer., Comment: 35 pages, 22 figures

We report an experiment estimating the three parameters of a general rotation. The scheme uses quantum states attaining the ultimate precision dictated by the quantum Cram\'er-Rao bound. We realize the states experimentally using the orbital angular momentum of light and implement the rotations with a multiplane light conversion setup, which allows one to perform arbitrary unitary transformations on a finite set of spatial modes. The observed performance suggests a range of potential applications in the next generation of rotation sensors., Comment: 8 pages, 4 figures. Comments welcome! arXiv admin note: text overlap with arXiv:2012.00590

Superconducting cavities have emerged as a key tool for measuring the spin states of quantum dots. So far however, few experiments have explored longitudinal couplings between dots and cavities, and no solid-state qubit experiments have explicitly probed the "adiabatic" regime, where the Purcell decay is strongly suppressed. Here, we report measurements of a double-quantum-dot charge qubit coupled to a high-impedance resonator via a "flip-chip" design geometry. By applying an adiabatic ac drive to the qubit through two different channels, and studying the effects of qubit energy detuning, interdot tunneling, and driving strength, we are able to unequivocally confirm the presence of a longitudinal coupling between the qubit and cavity, while the qubit remains in its ground state. Since this coupling is proportional to the driving amplitude, and is therefore switchable, it has the potential to become a powerful new tool in qubit experiments., Comment: Main text and Supplementary Materials, 16 pages, 10 figures

A primary method of reading out a quantum dot hybrid qubit involves projection of the logical basis onto distinct charge states that are readily detected by an integrated charge sensing dot. However, in the simplest configuration, the excited charge state decays rapidly, making single-shot readout challenging. Here, we demonstrate a readout procedure where the qubit excited state is latched to a metastable charge configuration whose lifetime is tunnel rate limited, persisting here as long as 2.5 ms. Additionally, we show that working in the (4,1)-(3,2) charge configuration enables a latched readout window that is larger and more tunable than typical charge configurations, because the size of the readout window is determined by an orbital splitting rather than a valley splitting.

We show that Ge concentration oscillations within the quantum well region of a Si/SiGe heterostructure can significantly enhance the spin-orbit coupling of the low-energy conduction-band valleys. Specifically, we find that for Ge oscillation wavelengths near $\lambda = 1.57~\text{nm}$ with an average Ge concentration of $\bar{n}_{\text{Ge}} = 5\%$ in the quantum well region, a Dresselhaus spin-orbit coupling is induced, at all physically relevant electric field strengths, which is over an order of magnitude larger than what is found in conventional Si/SiGe heterostructures without Ge concentration oscillations. This enhancement is caused by the Ge concentration oscillations producing wave-function satellite peaks a distance $2 \pi/\lambda$ away in momentum space from each valley, which then couple to the opposite valley through Dresselhaus spin-orbit coupling. Our results indicate that the enhanced spin-orbit coupling can enable fast spin manipulation within Si quantum dots using electric dipole spin resonance in the absence of micromagnets. Indeed, our calculations yield a Rabi frequency $\Omega_{\text{Rabi}}/B > 500~\text{MHz/T}$ near the optimal Ge oscillation wavelength $\lambda = 1.57~\text{nm}$., Comment: 19 pages, 11 figures

Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells require large or tunable energy splittings of the valley states associated with degenerate conduction band minima. Existing proposals to deterministically enhance the valley splitting rely on sharp interfaces or modifications in the quantum well barriers that can be difficult to grow. Here, we propose and demonstrate a new heterostructure, the "Wiggle Well," whose key feature is Ge concentration oscillations inside the quantum well. Experimentally, we show that placing Ge in the quantum well does not significantly impact our ability to form and manipulate single-electron quantum dots. We further observe large and widely tunable valley splittings, from 54 to 239 ueV. Tight-binding calculations, and the tunability of the valley splitting, indicate that these results can mainly be attributed to random concentration fluctuations that are amplified by the presence of Ge alloy in the heterostructure, as opposed to a deterministic enhancement due to the concentration oscillations. Quantitative predictions for several other heterostructures point to the Wiggle Well as a robust method for reliably enhancing the valley splitting in future qubit devices., Comment: Main text and supplemental information, 11 pages, 7 figures

The current autotuning approaches for quantum dot (QD) devices, while showing some success, lack an assessment of data reliability. This leads to unexpected failures when noisy or otherwise low-quality data is processed by an autonomous system. In this work, we propose a framework for robust autotuning of QD devices that combines a machine learning (ML) state classifier with a data quality control module. The data quality control module acts as a "gatekeeper" system, ensuring that only reliable data are processed by the state classifier. Lower data quality results in either device recalibration or termination. To train both ML systems, we enhance the QD simulation by incorporating synthetic noise typical of QD experiments. We confirm that the inclusion of synthetic noise in the training of the state classifier significantly improves the performance, resulting in an accuracy of 95.0(9) % when tested on experimental data. We then validate the functionality of the data quality control module by showing that the state classifier performance deteriorates with decreasing data quality, as expected. Our results establish a robust and flexible ML framework for autonomous tuning of noisy QD devices., Comment: 12 pages, 6 figures

Silicon-germanium heterostructures have successfully hosted quantum dot qubits, but the intrinsic near-degeneracy of the two lowest valley states poses an obstacle to high fidelity quantum computing. We present a modification to the Si/SiGe heterostructure by the inclusion of a spike in germanium concentration within the quantum well in order to increase the valley splitting. The heterostructure is grown by chemical vapor deposition and magnetospectroscopy is performed on gate-defined quantum dots to measure the excited state spectrum. We demonstrate a large and widely tunable valley splitting as a function of applied vertical electric field and lateral dot confinement. We further investigate the role of the germanium spike by means of tight-binding simulations in single-electron dots and show a robust doubling of the valley splitting when the spike is present, as compared to a standard (spike-free) heterostructure. This doubling effect is nearly independent of the electric field, germanium content of the spike, and spike location. This experimental evidence of a stable, tunable quantum dot, despite a drastic change to the heterostructure, provides a foundation for future heterostructure modifications., Comment: 11 pages, 7 figures

The energies of valley-orbit states in silicon quantum dots are determined by an as yet poorly understood interplay between interface roughness, orbital confinement, and electron interactions. Here, we report measurements of one- and two-electron valley-orbit state energies as the dot potential is modified by changing gate voltages, and we calculate these same energies using full configuration interaction calculations. The results enable an understanding of the interplay between the physical contributions and enable a new probe of the quantum well interface., Comment: 9 pages, 5 figures

Spins in SiGe quantum dots are promising candidates for quantum bits but are also challenging due to the valley degeneracy which could potentially cause spin decoherence and weak spin-orbital coupling. In this work we demonstrate that valley states can serve as an asset that enables two-axis control of a singlet-triplet qubit formed in a double quantum dot without the application of a magnetic field gradient. We measure the valley spectrum in each dot using magnetic field spectroscopy of Zeeman split triplet states. The interdot transition between ground states requires an electron to flip between valleys, which in turn provides a g-factor difference $\Delta g$ between two dots. This $\Delta g$ serves as an effective magnetic field gradient and allows for qubit rotations with a rate that increases linearly with an external magnetic field. We measured several interdot transitions and found that this valley introduced $\Delta g$ is universal and electrically tunable. This could potentially simplify scaling up quantum information processing in the SiGe platform by removing the requirement for magnetic field gradients which are difficult to engineer., Comment: 4 figures

RF reflectometry offers a fast and sensitive method for charge sensing and spin readout in gated quantum dots. We focus in this work on the implementation of RF readout in accumulation-mode gate-defined quantum dots, where the large parasitic capacitance poses a challenge. We describe and test two methods for mitigating the effect of the parasitic capacitance, one by on-chip modifications and a second by off-chip changes. We demonstrate that these methods enable high-performance charge readout in Si/SiGe quantum dots, achieving a fidelity of 99.9% for a measurement time of 1 $\mu$s., Comment: 6 pages, 4 figures

Spins in semiconductor quantum dots are a candidate for cryogenic quantum processors due to their exceptionally long coherence times. One major challenge to scaling quantum dot spin qubits is the dense wiring requirements, making it difficult to envision fabricating large arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to solve this problem by spacing the qubits out using high-impedance superconducting resonators with a 2D grid unit cell area of $0.16~\text{mm}^2$ using 3D integration. To prove the viability of this approach, we demonstrate 3D integration of a high-impedance TiN resonator coupled to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36 limited by the resonator-dot capacitance. Characterization of the dot and resonator systems shows such integration can be done while maintaining low charge noise metrics for the quantum dots and with improved loaded quality factors for the superconducting resonator ($Q_L = 2.14 \times 10^4$), allowing for high-sensitivity charge detection and the potential for high fidelity 2-qubit gates. This work paves the way for 2D quantum dot qubit arrays with cavity mediated interactions., Comment: 12 pages, 7 figures

Multi-electron semiconductor quantum dots have found wide application in qubits, where they enable readout and enhance polarizability. However, coherent control in such dots has typically been restricted to only the lowest two levels, and such control in the strongly interacting regime has not been realized. Here we report quantum control of eight different resonances in a silicon-based quantum dot. We use qubit readout to perform spectroscopy, revealing a dense set of energy levels with characteristic spacing far smaller than the single-particle energy. By comparing with full configuration interaction calculations, we argue that the dense set of levels arises from Wigner-molecule physics.

We develop an engineered microwave environment for coupling high Q superconducting resonators to quantum dots using a multilayer fabrication stack for the dot control wiring. Analytic and numerical models are presented to understand how parasitic capacitive coupling to the dot bias leads can result in microwave energy leakage and low resonator quality factors. We show that by controlling the characteristic impedance of the dot bias wiring, on-chip quality factors of 8140 can be attained without the addition of explicit filtering. Using this approach we demonstrate single electron occupation in double and triple dots detected via dipole or quadrupole coupling to a superconducting resonator. Additionally, by using multilayer fabrication we are able to improve ground plane integrity and keep microwave crosstalk below -20 dB out to 18 GHz while maintaining high wire density which will be necessary for future circuit quantum electrodyanmics (cQED) quantum dot processors., Comment: 5 pages, 3 figures

We present an improved fabrication process for overlapping aluminum gate quantum dot devices on Si/SiGe heterostructures that incorporates low-temperature inter-gate oxidation, thermal annealing of gate oxide, on-chip electrostatic discharge (ESD) protection, and an optimized interconnect process for thermal budget considerations. This process reduces gate-to-gate leakage, damage from ESD, dewetting of aluminum, and formation of undesired alloys in device interconnects. Additionally, cross-sectional scanning transmission electron microscopy (STEM) images elucidate gate electrode morphology in the active region as device geometry is varied. We show that overlapping aluminum gate layers homogeneously conform to the topology beneath them, independent of gate geometry, and identify critical dimensions in the gate geometry where pattern transfer becomes non-ideal, causing device failure., Comment: 5 figures, 9 pages

Fast operations, an easily tunable Hamiltonian, and a straightforward two-qubit interaction make charge qubits a useful tool for benchmarking device performance and exploring two-qubit dynamics. Here, we tune a linear chain of four Si/SiGe quantum dots to host two double dot charge qubits. Using the capacitance between the double dots to mediate a strong two-qubit interaction, we simultaneously drive coherent transitions to generate correlations between the qubits. We then sequentially pulse the qubits to drive one qubit conditionally on the state of the other. We find that a conditional $\pi$-rotation can be driven in just 74 ps with a modest fidelity demonstrating the possibility of two-qubit operations with a 13.5 GHz clockspeed., Comment: Main text plus supplemental information, 24 pages, 13 figures total)

We study how the shape of a periodic magnetic field affects the presence of Majorana bound states (MBS) in a nanowire-superconductor system. Motivated by the field configurations that can be produced by an array of nanomagnets, we consider spiral fields with an elliptic cross-section and fields with two sinusoidal components. We show that MBS are robust to imperfect helical magnetic fields. In particular, if the amplitude of one component is tuned to the value determined by the superconducting order parameter in the wire, the MBS can exist even if the second component has a much smaller amplitude. We also explore the effect of the chemical potential on the phase diagram. Our analysis is both numerical and analytical, with good agreement between the two methods.

Motivated by potential transformative applications of nanoelectronic circuits that incorporate superconducting elements, and by the advantages of integrating these elements in a silicon materials platform, we investigate the properties of the superconductivity of silicon ion-implanted with gallium. Here we measure 40 different samples and explore both a variety of preparation methods (yielding both superconducting and non-superconducting samples), and the reproducibility of one of the preparation methods yielding superconducting samples. While we find agreement with the existing literature that superconducting effects are visible in this system, we also find that this superconductivity is not influenced by voltages applied to a top gate. The superconductivity in this materials system is not gateable for applied electric fields as large as 8 MV/cm. We also present results of scanning transmission electron microscopy imaging of some of the same samples for which we report electronic characterization. In agreement with the existing literature, we find that the presence of Ga precipitates is essential to the presence of a superconducting transition in these samples. However, we also find evidence for large inhomogeneities in this system, which we discuss in connection with the lack of gateability we report here., Comment: 22 pages, 6 figures

We present measurements of the capacitive coupling energy and the inter-dot capacitances in a linear quadruple quantum dot array in undoped Si/SiGe. With the device tuned to a regime of strong ($>$1 GHz) intra-double dot tunnel coupling, as is typical for double dot qubits, we measure a capacitive coupling energy of $20.9 \pm 0.3$ GHz. In this regime, we demonstrate a fitting procedure to extract all the parameters in the 4D Hamiltonian for two capacitively coupled charge qubits from a 2D slice through the quadruple dot charge stability diagram. We also investigate the tunability of the capacitive coupling energy, using inter-dot barrier gate voltages to tune the inter- and intra-double dot capacitances, and change the capacitive coupling energy of the double dots over a range of 15-32 GHz. We provide a model for the capacitive coupling energy based on the electrostatics of a network of charge nodes joined by capacitors, which shows how the coupling energy should depend on inter-double dot and intra-double dot capacitances in the network, and find that the expected trends agree well with the measurements of coupling energy., Comment: 6 pages + supplementary information, 4 figures

A fundamental design challenge for quantum dot spin qubits is to extend the strength and range of qubit interactions while suppressing their coupling to the environment, since both effects have electrical origins. Key tools include the ability to retune the qubits, to take advantage of physical resources in different operating regimes, and to access optimal working points, or "sweet spots," where dephasing is minimized. Here, we explore an important, new resource for singlet-triplet qubits: a transverse sweet spot (TSS) that enables (i) direct transitions between qubit states, (ii) a strong, charge-like qubit coupling, and (iii) leading-order protection from electrical fluctuations. Of particular interest is the possibility of transitioning between the TSS and symmetric operating points while remaining continuously protected. This arrangement is ideal for coupling qubits to a microwave cavity, because it combines maximal tunability of the coupling strength with leading-order noise suppression. We perform simulations with $1/f$-type electrical noise, demonstrating that two-qubit gates mediated by a resonator can achieve fidelities $>99$\% under realistic conditions. These results greatly expand the toolbox for singlet-triplet qubits., Comment: 9 pages + 4 pages of SI

We report the first complete characterization of single-qubit and two-qubit gate fidelities in silicon-based spin qubits, including cross-talk and error correlations between the two qubits. To do so, we use a combination of standard randomized benchmarking and a recently introduced method called character randomized benchmarking, which allows for more reliable estimates of the two-qubit fidelity in this system. Interestingly, with character randomized benchmarking, the two-qubit CPhase gate fidelity can be obtained by studying the additional decay induced by interleaving the CPhase gate in a reference sequence of single-qubit gates only. This work sets the stage for further improvements in all the relevant gate fidelities in silicon spin qubits beyond the error threshold for fault-tolerant quantum computation., Comment: 6+5 pages, 6 figures

Recent advances in nanotechnology have enabled researchers to manipulate small collections of quantum mechanical objects with unprecedented accuracy. In semiconductor quantum dot qubits, this manipulation requires controlling the dot orbital energies, tunnel couplings, and the electron occupations. These properties all depend on the voltages placed on the metallic electrodes that define the device, whose positions are fixed once the device is fabricated. While there has been much success with small numbers of dots, as the number of dots grows, it will be increasingly useful to control these systems with as few electrode voltage changes as possible. Here, we introduce a protocol, which we call the Compressed Optimization of Device Architectures (CODA), in order to both efficiently identify sparse sets of voltage changes that control quantum systems, and to introduce a metric which can be used to compare device designs. As an example of the former, we apply this method to simulated devices with up to 100 quantum dots and show that CODA automatically tunes devices more efficiently than other common nonlinear optimizers. To demonstrate the latter, we determine the optimal lateral scale for a triple quantum dot, yielding a simulated device that can be tuned with small voltage changes on a limited number of electrodes., Comment: 10 pages, 4 figures

We report anomalous behavior in the energy dispersion of a three-electron double-quantum-dot hybrid qubit and argue that it is caused by atomic-scale disorder at the quantum-well interface. By employing tight-binding simulations, we identify potential disorder profiles that induce behavior consistent with the experiments. The results indicate that disorder can give rise to "sweet spots" where the decoherence caused by charge noise is suppressed, even in a parameter regime where true sweet spots are unexpected. Conversely, "hot spots" where the decoherence is enhanced can also occur. Our results suggest that, under appropriate conditions, interfacial atomic structure can be used as a tool to enhance the fidelity of Si double-dot qubits., Comment: 7 pages

Motivated by theoretical predictions that spatially complex concentration modulations of Si and Ge can increase the valley splitting in quantum wells, we grow and characterize Si/SiGe heterostructures with a thin, pure Ge layer at the top of the quantum well using chemical vapor deposition. We show that these heterostructures remain hosts for high-mobility electron gases. We measure two quantum wells with approximately five monolayers of pure Ge at the upper barrier, finding mobilities as high as 70,000 cm$^2$/Vs, compared to 100,000 cm$^2$/Vs measured in samples with no Ge layer. Activation energy measurements in quantum Hall states corresponding to Fermi levels in the gap between different valley states reveal energy gaps ranging from 30 to over 200 $\mu$eV, and we extract a surprisingly strong dependence of the energy gap on electron density. We interpret our results using tight binding theory and argue that our results are evidence that atomic scale disorder at the quantum well interface dominates the behavior of the valley splittings of these modified heterostructures., Comment: 7 pages

With qubit measurement and control fidelities above the threshold of fault-tolerance, much attention is moving towards the daunting task of scaling up the number of physical qubits to the large numbers needed for fault tolerant quantum computing. Here, quantum dot based spin qubits may offer significant advantages due to their potential for high densities, all-electrical operation, and integration onto an industrial platform. In this system, the initialisation, readout, single- and two-qubit gates have been demonstrated in various qubit representations. However, as seen with other small scale quantum computer demonstrations, combining these elements leads to new challenges involving qubit crosstalk, state leakage, calibration, and control hardware which provide invaluable insight towards scaling up. Here we address these challenges and demonstrate a programmable two-qubit quantum processor in silicon by performing both the Deutsch-Josza and the Grover search algorithms. In addition, we characterise the entanglement in our processor through quantum state tomography of Bell states measuring state fidelities between 85-89% and concurrences between 73-80%. These results pave the way for larger scale quantum computers using spins confined to quantum dots.

We study the dynamics of a pulse-gated semiconductor double quantum dot qubit. In our experiments, the qubit coherence times are relatively long, but the visibility of the quantum oscillations is low. We show that these observations are consistent with a theory that incorporates decoherence arising from charge noise that gives rise to detuning fluctuations of the double dot. Because effects from charge noise are largest near the singlet-triplet avoided level crossing, the visibility of the oscillations are low when the singlet-triplet avoided level crossing occurs in the vicinity of the charge degeneracy point crossed during the manipulation, but there is only modest dephasing at the large detuning value at which the quantum phase accumulates. This theory agrees well with experimental data and predicts that the visibility can be increased greatly by appropriate tuning of the interdot tunneling rate.

Identifying and ameliorating dominant sources of decoherence are important steps in understanding and improving quantum systems. Here we show that the free induction decay time ($T_{2}^{*}$) and the Rabi decay rate ($\Gamma_{\mathrm{Rabi}}$) of the quantum dot hybrid qubit can be increased by more than an order of magnitude by appropriate tuning of the qubit parameters and operating points. By operating in the spin-like regime of this qubit, and choosing parameters that increase the qubit's resilience to charge noise (which we show is presently the limiting noise source for this qubit), we achieve a Ramsey decay time $T_{2}^{*}$ of $177~\mathrm{ns}$ and a Rabi decay time, $1/\Gamma_{\mathrm{Rabi}}$, exceeding $1~\mathrm{\mu s}$. We find that the slowest $\Gamma_{\mathrm{Rabi}}$ is limited by fluctuations in the Rabi frequency induced by charge noise and not by fluctuations in the qubit energy itself., Comment: 10 pages, 6 figures. Supplementary material is included as appendices

The valley degree of freedom is intrinsic to spin qubits in Si/SiGe quantum dots. It has been viewed alternately as a hazard, especially when the lowest valley-orbit splitting is small compared to the thermal energy, or as an asset, most prominently in proposals to use the valley degree of freedom itself as a qubit. Here we present experiments in which microwave electric field driving induces transitions between both valley-orbit and spin states. We show that this system is highly nonlinear and can be understood through the use of dressed photon-orbital states, enabling a unified understanding of the six microwave resonance lines we observe. Some of these resonances are inter-valley spin transitions that arise from a non-adiabatic process in which both the valley and the spin degree of freedom are excited simultaneously. For these transitions, involving a change in valley-orbit state, we find a tenfold increase in sensitivity to electric fields and electrical noise compared to pure spin transitions, strongly reducing the phase coherence when changes in valley-orbit index are incurred. In contrast to this non-adiabatic transition, the pure spin transitions, whether arising from harmonic or subharmonic generation, are shown to be adiabatic in the orbital sector. The non-linearity of the system is most strikingly manifest in the observation of a dynamical anti-crossing between a spin-flip, inter-valley transition and a three-photon transition enabled by the strong nonlinearity we find in this seemly simple system., Comment: 23 pages, 11 figures, supplementary material included

Quantum computing promises significant speed-up for certain types of computational problems. However, robust implementations of semiconducting qubits must overcome the effects of charge noise that currently limit coherence during gate operations. Here we describe a scheme for protecting solid-state qubits from uniform electric field fluctuations by generalizing the concept of a decoherence-free subspace for spins, and we propose a specific physical implementation: a quadrupole charge qubit formed in a triple quantum dot. The unique design of the quadrupole qubit enables a particularly simple pulse sequence for suppressing the effects of noise during gate operations. Simulations yield gate fidelities 10-1,000 times better than traditional charge qubits, depending on the magnitude of the environmental noise. Our results suggest that any qubit scheme employing Coulomb interactions (for example, encoded spin qubits or two-qubit gates) could benefit from such a quadrupolar design., Comment: 10 pages, 3 figures, Supplementary Information included as appendices

The gate fidelity and the coherence time of a qubit are important benchmarks for quantum computation. We construct a qubit using a single electron spin in a Si/SiGe quantum dot and control it electrically via an artificial spin-orbit field from a micromagnet. We measure an average single-qubit gate fidelity of $\approx$ 99$\%$ using randomized benchmarking, which is consistent with dephasing from the slowly evolving nuclear spins in substrate. The coherence time measured using dynamical decoupling extends up to $\approx$ 400 $\mu$s for 128 decoupling pulses, with no sign of saturation. We find evidence that the coherence time is limited by noise in the 10 kHz $-$ 1 MHz range, possibly because charge noise affecting the spin via the micromagnet gradient. This work shows that an electron spin in a Si/SiGe quantum dot is a good candidate for quantum information processing as well as for a quantum memory, even without isotopic purification.