Charge-Noise Resilience of Two-Electron Quantum Dots in Si/SiGe Heterostructures

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, composed 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 multielectron qubits.

How Valley-Orbit States in Silicon Quantum Dots Probe Quantum Well Interfaces

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.

Corrigendum: Identifying single electron charge sensor events using wavelet edge detection (2015Nanotechnology215201)

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/fnoise.

Coherent Control and Spectroscopy of a Semiconductor Quantum Dot Wigner Molecule

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.

Fabrication process and failure analysis for robust quantum dots in silicon

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.

Autotuning of double dot devices in situ with machine learning

The current practice of manually tuning quantum dots (QDs) for qubit operation is a relatively time-consuming procedure that is inherently impractical for scaling up and applications. In this work, we report on the in situ implementation of a recently proposed autotuning protocol that combines machine learning (ML) with an optimization routine to navigate the parameter space. In particular, we show that a ML algorithm trained using exclusively simulated data to quantitatively classify the state of a double-QD device can be used to replace human heuristics in the tuning of gate voltages in real devices. We demonstrate active feedback of a functional double-dot device operated at millikelvin temperatures and discuss success rates as a function of the initial conditions and the device performance. Modifications to the training network, fitness function, and optimizer are discussed as a path toward further improvement in the success rate when starting both near and far detuned from the target double-dot range.

A programmable two-qubit quantum processor in silicon

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 computing. 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 platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, 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.

A decoherence-free subspace in a charge quadrupole qubit

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.

Characterization of a gate-defined double quantum dot in a Si/SiGe nanomembrane

We report the fabrication and characterization of a gate-defined double quantum dot formed in a Si/SiGe nanomembrane. In the past, all gate-defined quantum dots in Si/SiGe heterostructures were formed on top of strain-graded virtual substrates. The strain grading process necessarily introduces misfit dislocations into a heterostructure, and these defects introduce lateral strain inhomogeneities, mosaic tilt, and threading dislocations. The use of a SiGe nanomembrane as the virtual substrate enables the strain relaxation to be entirely elastic, eliminating the need for misfit dislocations. However, in this approach the formation of the heterostructure is more complicated, involving two separate epitaxial growth procedures separated by a wet-transfer process that results in a buried non-epitaxial interface 625 nm from the quantum dot. We demonstrate that in spite of this buried interface in close proximity to the device, a double quantum dot can be formed that is controllable enough to enable tuning of the inter-dot tunnel coupling, the identification of spin states, and the measurement of a singlet-to-triplet transition as a function of an applied magnetic field.

Second-Harmonic Coherent Driving of a Spin Qubit in a Si/SiGe Quantum Dot

We demonstrate coherent driving of a single electron spin using second-harmonic excitation in a Si/SiGe quantum dot. Our estimates suggest that the anharmonic dot confining potential combined with a gradient in the transverse magnetic field dominates the second-harmonic response. As expected, the Rabi frequency depends quadratically on the driving amplitude, and the periodicity with respect to the phase of the drive is twice that of the fundamental harmonic. The maximum Rabi frequency observed for the second harmonic is just a factor of 2 lower than that achieved for the first harmonic when driving at the same power. Combined with the lower demands on microwave circuitry when operating at half the qubit frequency, these observations indicate that second-harmonic driving can be a useful technique for future quantum computation architectures.

Identifying single electron charge sensor events using wavelet edge detection

The operation of solid-state qubits often relies on single-shot readout using a nanoelectronic charge sensor, and the detection of events in a noisy sensor signal is crucial for high fidelity readout of such qubits. The most common detection scheme, comparing the signal to a threshold value, is accurate at low noise levels but is not robust to low-frequency noise and signal drift. We describe an alternative method for identifying charge sensor events using wavelet edge detection. The technique is convenient to use and we show that, with realistic signals and a single tunable parameter, wavelet detection can outperform thresholding and is significantly more tolerant to 1/f and low-frequency noise.

Microwave-driven coherent operation of a semiconductor quantum dot charge qubit

An intuitive realization of a qubit is an electron charge at two well-defined positions of a double quantum dot. This qubit is simple and has the potential for high-speed operation because of its strong coupling to electric fields. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at all but one special operating point called the 'sweet spot'. In previous studies d.c. voltage pulses have been used to manipulate semiconductor charge qubits but did not achieve high-fidelity control, because d.c. gating requires excursions away from the sweet spot. Here, by using resonant a.c. microwave driving we achieve fast (greater than gigahertz) and universal single qubit rotations of a semiconductor charge qubit. The Z-axis rotations of the qubit are well protected at the sweet spot, and we demonstrate the same protection for rotations about arbitrary axes in the X-Y plane of the qubit Bloch sphere. We characterize the qubit operation using two tomographic approaches: standard process tomography and gate set tomography. Both methods consistently yield process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.

Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot

Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment. The outstanding challenge is to engineer the environment so that it minimally affects the qubit, but still allows qubit control and scalability. Here, we demonstrate a long-lived single-electron spin qubit in a Si/SiGe quantum dot with all-electrical two-axis control. The spin is driven by resonant microwave electric fields in a transverse magnetic field gradient from a local micromagnet, and the spin state is read out in the single-shot mode. Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, a Ramsey decay timescale of 1 μs is observed, almost two orders of magnitude longer than the intrinsic timescales in GaAs quantum dots, whereas gate operation times are comparable to those reported in GaAs. The spin echo decay time is ~40 μs, both with one and four echo pulses, possibly limited by intervalley scattering. These advances strongly improve the prospects for quantum information processing based on quantum dots.

Pulse-gated quantum-dot hybrid qubit

A quantum-dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to the presence of level crossings where the qubit becomes chargelike. Here, we show how to exploit the level crossings to implement fast pulsed gating. We develop one- and two-qubit dc quantum gates that are simpler than the previously proposed ac gates. We obtain closed-form solutions for the control sequences and show that the gates are fast (subnanosecond) and can achieve high fidelities.

Fast hybrid silicon double-quantum-dot qubit

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers S(2)=3/4 (S=1/2) and S(z)=-1/2, with the two different states being singlet and triplet in the doubly occupied dot. Gate operations can be implemented electrically and the qubit is highly tunable, enabling fast implementation of one- and two-qubit gates in a simpler geometry and with fewer operations than in other proposed quantum dot qubit architectures with fast operations. Moreover, the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

Single-shot measurement of triplet-singlet relaxation in a Si/SiGe double quantum dot

We investigate the lifetime of two-electron spin states in a few-electron Si/SiGe double dot. At the transition between the (1,1) and (0,2) charge occupations, Pauli spin blockade provides a readout mechanism for the spin state. We use the statistics of repeated single-shot measurements to extract the lifetimes of multiple states simultaneously. When the magnetic field is zero, we find that all three triplet states have equal lifetimes, as expected, and this time is ~10 ms. When the field is nonzero, the T(0) lifetime is unchanged, whereas the T- lifetime increases monotonically with the field, reaching 3 sec at 1 T.

Unconventional transport in the "hole" regime of a si double quantum dot

Studies of electronic charge transport through semiconductor double quantum dots rely on a conventional "hole" model of transport in the three-electron regime. We show that experimental measurements of charge transport through a Si double quantum dot in this regime cannot be fully explained using the conventional picture. Using a Hartree-Fock (HF) formalism and relevant HF energy parameters extracted from transport data in the multiple-electron regime, we identify a novel spin-flip cotunneling process that lifts a singlet blockade.

Tunable spin loading and T1 of a silicon spin qubit measured by single-shot readout

We demonstrate single-shot readout of a silicon quantum dot spin qubit, and we measure the spin relaxation time T1. We show that the rate of spin loading can be tuned by an order of magnitude by changing the amplitude of a pulsed-gate voltage, and the fraction of spin-up electrons loaded can also be controlled. This tunability arises because electron spins can be loaded through an orbital excited state. Using a theory that includes excited states of the dot and energy-dependent tunneling, we find that a global fit to the loading rate and spin-up fraction is in good agreement with the data.

Charge sensing and controllable tunnel coupling in a Si/SiGe double quantum dot

We report integrated charge sensing measurements on a Si/SiGe double quantum dot. The quantum dot is shown to be tunable from a single, large dot to a well-isolated double dot. Charge sensing measurements enable the extraction of the tunnel coupling t between the quantum dots as a function of the voltage on the top gates defining the device. Control of the voltage on a single such gate tunes the barrier separating the two dots. The measured tunnel coupling is an exponential function of the gate voltage. The ability to control t is an important step toward controlling spin qubits in silicon quantum dots.

Complexity of the predecessor problem in Kauffman networks

Kauffman nets, also known as N-K models, have been studied extensively because their dynamics can be used to model a variety of interesting dynamical processes. This paper investigates the properties of the problem of determining whether or not a given configuration of a Kauffman net has a predecessor. Here it is shown that when the parameter K that governs the number of connections grows as ln(N) , where N is the number of elements, the problem of finding a solution is extremely sensitive to small changes in the problem statement. This result has implications for studies of the physics of random systems and also may have applications for questions in computational complexity theory.

Performance limitations of flat-histogram methods

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/-J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.

Entangled quantum state of magnetic dipoles

Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors and certain rare-earth intermetallics, the 1/T law is replaced by a power law T(-alpha) with alpha < 1. Here we show that a much simpler material system-namely, the insulating magnetic salt LiHo(x)Y(1-x)F(4)-can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects-entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom-becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.

Scalar model of inhomogeneous elastic and granular media

We investigate theoretically how the stress propagation characteristics of granular materials evolve as they are subjected to increasing pressures, comparing the results of a two-dimensional scalar lattice model to those of a molecular dynamics simulation of slightly polydisperse disks. We characterize the statistical properties of the forces using the force histogram and a two-point spatial correlation function of the forces. For the lattice model, in the granular limit the force histogram has an exponential tail at large forces, while in the elastic regime the force histogram is much narrower, and has a form that depends on the realization of disorder in the model. The behavior of the force histogram in the molecular dynamics simulations as the pressure is increased is very similar to that displayed by the lattice model. In contrast, the spatial correlations evolve qualitatively differently in the lattice model and in the molecular dynamics simulations. For the lattice model, in the granular limit there are no in-plane stress-stress correlations, whereas in the molecular dynamics simulation significant in-plane correlations persist to the lowest pressures studied.

Noise stabilization of self-organized memories

We investigate a nonlinear dynamical system which "remembers" preselected values of a system parameter. The deterministic version of the system can encode many parameter values during a transient period, but in the limit of long times, almost all of them are forgotten. Here we show that a certain type of stochastic noise can stabilize multiple memories, enabling many parameter values to be encoded permanently. We present analytic results that provide insight both into the memory formation and into the noise-induced memory stabilization. The relevance of our results to experiments on the charge-density wave material NbSe3 is discussed.

Properties of layer-by-layer vector stochastic models of force fluctuations in granular materials

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and nontensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model of Liu et al. [Science 269, 513 (1995)] and Coppersmith et al. [Phys. Rev. E 53, 4673 (1996)] while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.

Evidence for Glass and Spin-Glass Phase Transitions From the Dynamic Susceptibility

We present evidence that there is a phase transition, with a diverging static susceptibility, underlying the transformation of a liquid into a glass. The dielectric susceptibility, at frequencies above its characteristic value, shows a power-law tail extending over many decades to higher frequencies. An extrapolation of this behavior to the temperature where the dynamics becomes arrested indicates a diverging susceptibility. We present evidence for analogous behavior in the magnetic susceptibility of a paramagnet approaching the spin-glass transition. The similarity of the response in these two glassy systems suggests that some conventional lore, such as that the spin glass shows evidence for a diverging correlation length only in a nonlinear but not in the linear susceptibility, may be invalid.

Force Fluctuations in Bead Packs

Experimental observations and numerical simulations of the large force inhomogeneities present in stationary bead packs are presented. Forces much larger than the mean occurred but were exponentially rare. An exactly soluble model reproduced many aspects of the experiments and simulations. In this model, the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead in the pile.