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.

Corrigendum: Identifying single electron charge sensor events using wavelet edge detection (2015Nanotechnology26215201).

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.

Quantum control and process tomography of a semiconductor quantum dot hybrid qubit.

The similarities between gated quantum dots and the transistors in modern microelectronics--in fabrication methods, physical structure and voltage scales for manipulation--have led to great interest in the development of quantum bits (qubits) in semiconductor quantum dots. Although quantum dot spin qubits have demonstrated long coherence times, their manipulation is often slower than desired for important future applications, such as factoring. Furthermore, scalability and manufacturability are enhanced when qubits are as simple as possible. Previous work has increased the speed of spin qubit rotations by making use of integrated micromagnets, dynamic pumping of nuclear spins or the addition of a third quantum dot. Here we demonstrate a qubit that is a hybrid of spin and charge. It is simple, requiring neither nuclear-state preparation nor micromagnets. Unlike previous double-dot qubits, the hybrid qubit enables fast rotations about two axes of the Bloch sphere. We demonstrate full control on the Bloch sphere with π-rotation times of less than 100 picoseconds in two orthogonal directions, which is more than an order of magnitude faster than any other double-dot qubit. The speed arises from the qubit's charge-like characteristics, and its spin-like features result in resistance to decoherence over a wide range of gate voltages. We achieve full process tomography in our electrically controlled semiconductor quantum dot qubit, extracting high fidelities of 85 per cent for X rotations (transitions between qubit states) and 94 per cent for Z rotations (phase accumulation between qubit states).

Ubiquitous Spin-Orbit Coupling in a Screw Dislocation with High Spin Coherency.

We theoretically demonstrate that screw dislocation (SD), a 1D topological defect widely present in semiconductors, exhibits ubiquitously a new form of spin-orbit coupling (SOC) effect. Differing from the widely known conventional 2D Rashba-Dresselhaus (RD) SOC effect that typically exists at surfaces or interfaces, the deep-level nature of SD-SOC states in semiconductors readily makes it an ideal SOC. Remarkably, the spin texture of 1D SD-SOC, pertaining to the inherent symmetry of SD, exhibits a significantly higher degree of spin coherency than the 2D RD-SOC. Moreover, the 1D SD-SOC can be tuned by ionicity in compound semiconductors to ideally suppress spin relaxation, as demonstrated by comparative first-principles calculations of SDs in Si/Ge, GaAs, and SiC. Our findings therefore open a new door to manipulating spin transport in semiconductors by taking advantage of an otherwise detrimental topological defect.

Synthesis, assembly and applications of semiconductor nanomembranes.

Research in electronic nanomaterials, historically dominated by studies of nanocrystals/fullerenes and nanowires/nanotubes, now incorporates a growing focus on sheets with nanoscale thicknesses, referred to as nanomembranes. Such materials have practical appeal because their two-dimensional geometries facilitate integration into devices, with realistic pathways to manufacturing. Recent advances in synthesis provide access to nanomembranes with extraordinary properties in a variety of configurations, some of which exploit quantum and other size-dependent effects. This progress, together with emerging methods for deterministic assembly, leads to compelling opportunities for research, from basic studies of two-dimensional physics to the development of applications of heterogeneous electronics.

Two-axis control of a singlet-triplet qubit with an integrated micromagnet.

The qubit is the fundamental building block of a quantum computer. We fabricate a qubit in a silicon double-quantum dot with an integrated micromagnet in which the qubit basis states are the singlet state and the spin-zero triplet state of two electrons. Because of the micromagnet, the magnetic field difference ΔB between the two sides of the double dot is large enough to enable the achievement of coherent rotation of the qubit's Bloch vector around two different axes of the Bloch sphere. By measuring the decay of the quantum oscillations, the inhomogeneous spin coherence time T2* is determined. By measuring T2* at many different values of the exchange coupling J and at two different values of ΔB, we provide evidence that the micromagnet does not limit decoherence, with the dominant limits on T2* arising from charge noise and from coupling to nuclear spins.

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.

Thermal Resistance of Transferred-Silicon-Nanomembrane Interfaces.

We report measurements of the interfacial thermal resistance between mechanically joined single crystals of silicon, the results of which are up to a factor of 5 times lower than any previously reported thermal resistances of mechanically created interfaces. Detailed characterization of the interfaces is presented, as well as a theoretical model incorporating the critical properties determining the interfacial thermal resistance in the experiments. The results demonstrate that van der Waals interfaces can have very low thermal resistance, with important implications for membrane-based micro- and nanoelectronics.

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.

Tensilely strained germanium nanomembranes as infrared optical gain media.

The use of tensilely strained Ge nanomembranes as mid-infrared optical gain media is investigated. Biaxial tensile strain in Ge has the effect of lowering the direct energy bandgap relative to the fundamental indirect one, thereby increasing the internal quantum efficiency for light emission and allowing for the formation of population inversion, until at a strain of about 1.9% Ge is even converted into a direct-bandgap material. Gain calculations are presented showing that, already at strain levels of about 1.4% and above, Ge films can provide optical gain in the technologically important 2.1-2.5 µm spectral region, with transparency carrier densities that can be readily achieved under realistic pumping conditions. Mechanically stressed Ge nanomembranes capable of accommodating the required strain levels are developed and used to demonstrate strong strain-enhanced photoluminescence. A detailed analysis of the high-strain emission spectra also demonstrates that the nanomembranes can be pumped above transparency, and confirms the prediction that biaxial-strain levels in excess of only 1.4% are required to obtain significant population inversion.

Long-term reduction in poly(dimethylsiloxane) surface hydrophobicity via cold-plasma treatments.

Poly(dimethylsiloxane), PDMS, a versatile elastomer, is the polymer of choice for microfluidic systems. It is inexpensive, relatively easy to pattern, and permeable to oxygen. Unmodified PDMS is highly hydrophobic. It is typically exposed to an oxygen plasma to reduce this hydrophobicity. Unfortunately, the PDMS surface soon returns to its original hydrophobic state. We present two alternative plasma treatments that yield long-term modification of the wetting properties of a PDMS surface. An oxygen plasma pretreatment followed by exposure to a SiCl4 plasma and an oxygen-CCl4 mixture plasma both cause a permanent reduction in the hydrophobicity of the PDMS surface. We investigate the properties of the plasma-treated surfaces with X-ray photoelectron spectroscopy (XPS) and contact angle measurements. We propose that the plasma treated PDMS surface is a dynamic mosaic of high- and low-contact-angle functionalities. The SiCl4 and CCl4 plasmas attach polar groups that block coverage of the surface by low-molecular-weight groups that exist in PDMS. We describe an application that benefits from these new plasma treatments, the use of a PDMS stencil to form dense arrays of DNA on a surface.

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.

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.

SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits.

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 µeV. 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.

Stabilizing graphitic thin films of wurtzite materials by epitaxial strain.

Recent theory [Phys. Rev. Lett. 96, 066102 (2006)] and experiment [Phys. Rev. Lett. 99, 026102 (2007)] show that (0001) ultrathin films of wurtzite (WZ) materials surprisingly transform into a stable graphitelike structure, but the stability is limited to thicknesses of only a few atomic layers. Using first-principles calculations of both freestanding and substrate-supported thin films, we predict that the thickness range of stable graphitic films depends sensitively on strain and can be substantially extended to much thicker films by epitaxial tensile strain. Moreover, the band gap of the stable strained graphitic films can be tuned over a wide range either above or below that of the bulk WZ phase.

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.

Quantitative determination of contributions to the thermoelectric power factor in Si nanostructures.

We report thermoelectric measurements on a silicon nanoribbon in which an integrated gate provides strong carrier confinement and enables tunability of the carrier density over a wide range. We find a significantly enhanced thermoelectric power factor that can be understood by considering its behavior as a function of carrier density. We identify the underlying mechanisms for the power factor in the nanoribbon, which include quantum confinement, low scattering due to the absence of dopants, and, at low temperatures, a significant phonon-drag contribution. The measurements set a target for what may be achievable in ultrathin nanowires.

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.

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.