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The fidelity of gate operations on neutral atom qubits is often limited by fluctuations of the laser drive. Here, we quantify the sensitivity of quantum gate fidelities to laser phase and intensity noise. We first develop models to identify features observed in laser self-heterodyne noise spectra, focusing on the effects of white noise and servo bumps. In the weak-noise regime, characteristic of well-stabilized lasers, we show that an analytical theory based on a perturbative solution of a master equation agrees very well with numerical simulations that incorporate phase noise. We compute quantum gate fidelities for one- and two-photon Rabi oscillations and show that they can be enhanced by an appropriate choice of Rabi frequency relative to spectral noise peaks. We also analyze the influence of intensity noise with spectral support smaller than the Rabi frequency. Our results establish requirements on laser noise levels needed to achieve desired gate fidelities., Comment: v3: added analysis of the Lambda configuration

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 π-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.

This paper investigates the concept of perceived price fairness and its dynamic alteration along the customer buying cycle. Today, variable pricing is widespread in many service industries. Besides the current sales price, customers are extensively exposed to varying external reference prices (for example, advertised prices). Thus, this pricing practice risks being perceived as unfair at some stage along the purchasing process, and negative consumer reactions cannot be ruled out. However, previous research has adopted a quite static approach, which only offered an incomplete picture of fairness perceptions with a specific service offer. To better capture the dynamics, this study conducted a scenario-based experiment with 459 airline customers encompassing repeated measures. The results provide evidence that the perception of distributive and procedural fairness significantly varies with the exposure to changing external reference prices along the buying cycle. Therefore, marketers should be cautious regarding price variations and advertised prices.

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., Main text and supplemental information, 11 pages, 7 figures

Implementing two-qubit gates via strong coupling between quantum-dot qubits and a superconducting microwave cavity requires achieving coupling rates that are much faster than decoherence rates. Typically, this involves tuning the qubit either to a sweet spot, where it is relatively insensitive to charge noise, or to a point where it is resonant with the microwave cavity. Unfortunately, such operating points seldom coincide. Here, we theoretically investigate several schemes for performing gates between two quantum-dot hybrid qubits, mediated by a microwave cavity. The rich physics of the quantum dot hybrid qubit gives rise to two types of sweet spots, which can occur at operating points with strong charge dipole moments. Such strong interactions provide new opportunities for off-resonant gating, thereby removing one of the main obstacles for long-distance two-qubit gates. Our results suggest that the numerous tuning knobs of quantum dot hybrid qubits make them good candidates for strong coupling. In particular, we show that off-resonant red-sideband-mediated two-qubit gates can exhibit fidelities $>$95\% for realistic operating parameters, and we describe improvements that could potentially yield gate fidelities $>$99\%., 15 pages, 5 figures

The valley degree of freedom presents challenges and opportunities for silicon spin qubits. An important consideration for singlet-triplet states is the presence of two distinct triplets, comprised of valley vs. orbital excitations. Here we show that both of these triplets are present in the typical operating regime, but that only the valley-excited triplet offers intrinsic protection against charge noise. We further show that this protection arises naturally in dots with stronger confinement. These results reveal an inherent advantage for silicon-based multi-electron qubits., Comment: 6 pages, 5 figures

Spin qubits and superconducting qubits are among the promising candidates for realizing a solid state quantum computer. For the implementation of a hybrid architecture which can profit from the advantages of either approach, a coherent link is necessary that integrates and controllably couples both qubit types on the same chip over a distance that is several orders of magnitude longer than the physical size of the spin qubit. We realize such a link with a frequency-tunable high impedance SQUID array resonator. The spin qubit is a resonant exchange qubit hosted in a GaAs triple quantum dot. It can be operated at zero magnetic field, allowing it to coexist with superconducting qubits on the same chip. We spectroscopically observe coherent interaction between the resonant exchange qubit and a transmon qubit in both resonant and dispersive regimes, where the interaction is mediated either by real or virtual resonator photons., Nature Communications, 10 (1), ISSN:2041-1723

Interactions between electrons can strongly affect the shape and functionality of multi-electron quantum dots. The resulting charge distributions can be localized, as in the case of Wigner molecules, with consequences for the energy spectrum and tunneling to states outside the dot. The situation is even more complicated for silicon dots, due to the interplay between valley, orbital, and interaction energy scales. Here, we study two-electron wavefunctions in electrostatically confined quantum dots formed in a SiGe/Si/SiGe quantum well at zero magnetic field, using a combination of tight-binding and full-configuration-interaction (FCI) methods, and taking into account atomic-scale disorder at the quantum well interface. We model dots based on recent qubit experiments, which straddle the boundary between strongly interacting and weakly interacting systems, and display a rich and diverse range of behaviors. Our calculations show that strong electron-electron interactions, induced by weak confinement, can significantly suppress the low-lying, singlet-triplet (ST) excitation energy. However, when the valley-orbit interactions caused by interfacial disorder are weak, the ST splitting can approach its noninteracting value, even when the electron-electron interactions are strong and Wigner-molecule behavior is observed. These results have important implications for the rational design and fabrication of quantum dot qubits with predictable properties., 22 pages, 11 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., 11 pages, 7 figures

We theoretically investigate the properties of holes in a Si$_{x}$Ge$_{1-x}$/Ge/ Si$_{x}$Ge$_{1-x}$ quantum well in a perpendicular magnetic field that make them advantageous as qubits, including a large ($>$100~meV) intrinsic splitting between the light and heavy hole bands, a very light ($\sim$0.05$\, m_0$) in-plane effective mass, consistent with higher mobilities and tunnel rates, and larger dot sizes that could ameliorate constraints on device fabrication. Compared to electrons in quantum dots, hole qubits do not suffer from the presence of nearby quantum levels (e.g., valley states) that can compete with spins as qubits. The strong spin-orbit coupling in Ge quantum wells may be harnessed to implement electric-dipole spin resonance, leading to gate times of several nanoseconds for single-qubit rotations. The microscopic mechanism of this spin-orbit coupling is discussed, along with its implications for quantum gates based on electric-dipole spin resonance, stressing the importance of coupling terms that arise from the underlying cubic crystal field. Our results provide a theoretical foundation for recent experimental advances in Ge hole-spin qubits., 1 pages

Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport. We find that the concentration fluctuations of Si and Ge atoms within the 3D landscape of Si/SiGe interfaces can explain the observed large spread of valley splitting from measurements on many quantum dot devices. Against the prevailing belief, we propose to boost these random alloy composition fluctuations by incorporating Ge atoms in the Si quantum well to statistically enhance valley splitting.

Semiconductor quantum dots containing more than one electron 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 transitions 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.

One obstacle that has slowed the development of electrically gated metal-oxide-semiconductor (MOS) singlet-triplet qubits is the frequent lack of observed spin blockade, even in samples with large singlet-triplet energy splittings. We present theoretical and experimental evidence that the cause of this problem in MOS double quantum dots is the stray positive charges in the oxide inducing accidental levels near the device's active region that allow spin blockade lifting. We also present evidence that these effects can be mitigated by device design modifications, such as overlapping gates., Comment: 10 pages, 8 figures

We study spatial noise correlations in a Si/SiGe two-qubit device with integrated micromagnets. Our method relies on the concept of decoherence-free subspaces, whereby we measure the coherence time for two different Bell states, designed to be sensitive only to either correlated or anti-correlated noise respectively. From these measurements, we find weak correlations in low-frequency noise acting on the two qubits, while no correlations could be detected in high-frequency noise. A theoretical model and numerical simulations give further insight into the additive effect of multiple independent (anti-)correlated noise sources with an asymmetric effect on the two qubits. Such a scenario is plausible given the data and our understanding of the physics of this system. This work is highly relevant for the design of optimized quantum error correction codes for spin qubits in quantum dot arrays, as well as for optimizing the design of future quantum dot arrays., Comment: 6+6 pages, 4+3 figures

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.

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field $B$ and Hall density by performing activation energy measurements in the quantum Hall regime over a large range of filling factors. The mobility gap of the valley-split levels increases linearly with $B$ and is strikingly independent of Hall density. The data are consistent with a transport model in which valley splitting depends on the incremental changes in density $eB/h$ across quantum Hall edge strips, rather than the bulk density. Based on these results, we estimate that the valley splitting increases with density at a rate of 116 $\mu$eV/10$^{11}$cm$^{-2}$, consistent with theoretical predictions for near-perfect quantum well top interfaces.

The simulated noise used to benchmark wavelet edge detection in this work was described incorrectly. The correct description is given here, and new results based on noise that matches the original description are provided. The results support our original conclusion, which is that wavelet edge detection outperforms thresholding in the presence of white noise and 1/f noise.

Today, dynamic pricing (DP) in most industries is an established form of pricing, and supported by the DP functionality of many revenue management (RM) systems and the general simplification of airline pricing driven by low-cost carriers. The technological changes (NDC, Big data, IoT, etc.) allow further steps for price differentiation culminating in either personalized or personalized dynamic pricing (PDP). PDP as we define it is not to be confused with the traditional DP of today‘s RM practices. Whether appropriate strategies for a 1:1 price setting can be successfully implemented in the market, depends on several factors: (1) technological advances in data mining and the ability to detect customer preferences (2) the ability to accurately determine customer’s willingness-to-pay by predictive analytics; (3) the use of personal data by airlines and its acceptance by consumers as well as (4) the medium-term impact on customer loyalty and the associated risks for the sustainability of the whole airline business model.

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

Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step toward the implementation of quantum error-correcting codes, quantum nondemolition measurements are needed to efficiently detect the state of a logical qubit without destroying it. Here we implement quantum nondemolition measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla. Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla. Repeating this procedure enhances the logical readout fidelity from 75.5±0.3% to 94.5±0.2% after 15 ancilla readouts. In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit. We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance, in the case of readouts with a low signal-to-noise ratio. These results pave the way for the implementation of quantum error correction with spin qubits in silicon. published

Quantum dot hybrid qubits exploit an extended charge-noise sweet spot that suppresses dephasing and has enabled the experimental achievement of high-fidelity single-qubit gates. However, current proposals for two-qubit gates require tuning the qubits away from their sweet spots. Here, we propose a two-hybrid-qubit coupling scheme, based on exchange interactions, that allows the qubits to remain at their sweet spots at all times. The interaction is controlled via the inter-qubit tunnel coupling. By simulating such gates in the presence of realistic quasistatic and $1\!/\!f$ charge noise, we show that our scheme should enable controlled-$Z$ gates of length $\sim$5~ns, and Z-CNOT gates of length $\sim$7~ns, both with fidelities $>$99.9\%., 19 pages

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., 6 pages + supplementary information, 4 figures

Semiconductor double quantum dot hybrid qubits are promising candidates for high-fidelity quantum computing. However, their performance is limited by charge noise, which is ubiquitous in solid-state devices, and phonon-induced dephasing. Here we explore methods for improving the quantum operations of a hybrid qubit, using strong microwave driving to enable gate operations that are much faster than decoherence processes. Using numerical simulations and a theoretical method based on a cumulant expansion, we analyze qubit dynamics in the presence of $1/f$ charge noise, which forms the dominant decoherence mechanism in many solid-state devices. We show that, while strong-driving effects and charge noise both reduce the quantum gate fidelity, simple pulse-shaping techniques effectively suppress the strong-driving effects. Moreover, a broad AC sweet spot emerges when the detuning parameter and the tunneling coupling are driven simultaneously. Taking into account phonon-mediated noise, we find that it should be possible to achieve $X_{\pi}$ gates with fidelities higher than $99.9\%$., Comment: 14 pages, 6 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., 9 pages + 4 pages of SI

The ability to tune qubits to flat points in their energy dispersions ("sweet spots") is an important tool for mitigating the effects of charge noise and dephasing in solid-state devices. However, the number of derivatives that must be simultaneously set to zero grows exponentially with the number of coupled qubits, making the task untenable for as few as two qubits. This is a particular problem for adiabatic gates, due to their slower speeds. Here, we propose an adiabatic two-qubit gate for quantum dot hybrid qubits, based on the tunable, electrostatic coupling between distinct charge configurations. We confirm the absence of a conventional sweet spot, but show that controlled-Z (CZ) gates can nonetheless be optimized to have fidelities of $\sim$99% for a typical level of quasistatic charge noise ($\sigma_\varepsilon$$\simeq$1 $\mu$eV). We then develop the concept of a dynamical sweet spot (DSS), for which the time-averaged energy derivatives are set to zero, and identify a simple pulse sequence that achieves an approximate DSS for a CZ gate, with a 5$\times$ improvement in the fidelity. We observe that the results depend on the number of tunable parameters in the pulse sequence, and speculate that a more elaborate sequence could potentially attain a true DSS., Comment: 14 pages, 9 figures

We develop an engineered microwave environment for coupling high Q superconducting resonators to quantum dots using a multilayer fabrication stack for dot control wiring. Analytical and numerical models are presented, which show that high resonator quality factors can be attained by either minimizing the parasitic coupling capacitance to the leads or creating a low effective environmental impedance at the cavity frequency. We implement the later approach by fabricating low characteristic impedance ( Z g ≈ 10 Ω) microstrips on-chip for the dot bias wiring and show resonator quality factors of 8140 that 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 electrodynamics quantum dot processors.

Both Revenue Management (RM) and Dynamic Pricing (DP) are common practices in many industries&mdash, e.g., airlines and hotels&mdash, but they are still relatively unknown in the parking sector. In Europe, with the exception of for airport parking and in some pilot tests, DP is rarely used by private parking operators or local authorities. The main objective of this conceptual paper is to set an agenda for introducing DP in the private parking sector at a larger scale. After a short review of the existing academic and gray literature, we describe the requirements and instruments that parking companies need to make use of RM. Next, we shortly report on the major existing and/or planned DP parking schemes in Europe. We continue by providing a comprehensive reality check discussing the major challenges the sector faces to apply DP. We conclude by suggesting a road map for private parking operators to successfully implement RM and DP. Finally, we give some indications for future research.

Charge qubits formed in double quantum dots represent quintessential two-level systems that enjoy both ease of control and efficient readout. Unfortunately, charge noise can cause rapid decoherence, with typical single-qubit gate fidelities falling below $90\%$. Here, we develop analytical methods to study the evolution of strongly driven charge qubits, for general and $1\!/\!f$ charge-noise spectra. We show that special pulsing techniques can simultaneously suppress errors due to strong driving and charge noise, yielding single-qubit gates with fidelities above $99.9\%$. These results demonstrate that quantum dot charge qubits provide a potential route to high-fidelity quantum computation., 19 pages, 4 figures

A two-qubit quantum processor in a silicon device is demonstrated, which can perform the Deutsch–Josza algorithm and the Grover search algorithm. The development of platforms for spin-based quantum computing continues apace. The individual components of such a system have been the subject of much investigation, and they have been assembled to implement specific quantum-computational algorithms. Thomas Watson and colleagues have now taken such component integration and control to the next level. Using two single-electron-spin qubits in a silicon-based double quantum dot, they realize a system that can be simply programmed to perform different quantum algorithms on demand. Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing1,2. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform3,4,5. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations6,7,8,9. However, as seen with small-scale demonstrations of quantum computers using other types of qubit10,11,12,13, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch–Josza algorithm and the Grover search algorithm—canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85–89 per cent and concurrences of 73–82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

The performance of quantum-error-correction schemes depends sensitively on the physical realizations of the qubits and the implementations of various operations. For example, in quantum-dot spin qubits, readout is typically much slower than gate operations, and conventional surface-code implementations that rely heavily on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum-dot qubits, without readout, can be achieved via tunneling to a reservoir. Here we propose small-scale surface-code implementations for which syndrome measurements are replaced by a combination of Toffoli gates and qubit reset. For quantum-dot qubits, this enables much faster error correction than measurement-based schemes, but requires additional ancilla qubits and non-nearest-neighbor interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of ${10}^{\ensuremath{-}2}$ for a one-dimensional architecture that only corrects bit-flip errors and ${10}^{\ensuremath{-}4}$ for a two-dimensional architecture that corrects bit- and phase-flip errors.

Many quantum dot qubits operate in regimes where the energy splittings between qubit states are large and phonons can be the dominant source of decoherence. The recently proposed charge quadrupole qubit, based on one electron in a triple quantum dot, employs a highly symmetric charge distribution to suppress the influence of charge noise. To study the effects of phonons on the charge quadrupole qubit, we consider Larmor and Ramsey pulse sequences to identify favorable operating parameters. We show that it is possible to implement typical gates with $>99.99\%$ fidelity in the presence of phonons and charge noise.

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

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

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 is 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.

Goals for improving the quality of care for all Veterans and eliminating health disparities are outlined in the Veterans Health Administration Blueprint for Excellence, but the degree to which disparities in utilization, health outcomes, and quality of care affect Veterans is not well understood.To characterize the research on health care disparities in the Veterans Health Administration by means of a map of the evidence.We conducted a systematic search for research studies published from 2006 to February 2016 in MEDLINE and other data sources. We included studies of Veteran populations that examined disparities in 3 outcome categories: utilization, quality of health care, and patient health.We abstracted data on study design, setting, population, clinical area, outcomes, mediators, and presence of disparity for each outcome category. We grouped the data by population characteristics including race, disability status, mental illness, demographics (age, era of service, rural location, and distance from care), sex identity, socioeconomic status, and homelessness, and created maps illustrating the evidence.We reviewed 4249 citations and abstracted data from 351 studies which met inclusion criteria. Studies examining disparities by race/ethnicity comprised by far the vast majority of the literature, followed by studies examining disparities by sex, and mental health condition. Very few studies examined disparities related to lesbian, gay, bisexual, or transgender identity or homelessness. Disparities findings vary widely by population and outcome.Our evidence maps provide a "lay of the land" and identify important gaps in knowledge about health disparities experienced by different Veteran populations.