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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., Comment: 9 pages, 4 figures

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., Comment: 11 pages, 4 figures

Achieving controllable coupling of dopants in silicon is crucial for operating donor-based qubit devices, but it is difficult because of the small size of donor-bound electron wavefunctions. Here we report the characterization of a quantum dot coupled to a localized electronic state, and we present evidence of controllable coupling between the quantum dot and the localized state. A set of measurements of transport through this device enable the determination of the most likely location of the localized state, consistent with an electronically active impurity in the quantum well near the edge of the quantum dot. The experiments we report are consistent with a gate-voltage controllable tunnel coupling, which is an important building block for hybrid donor and gate-defined quantum dot devices., Comment: 5 pages, 3 figures

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 two 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., Comment: 9 pages, 9 figures

We propose an optimal set of quantum gates for a singlet-triplet qubit in a double quantum dot with two electrons utilizing the $S$-$T_-$ subspace. Qubit rotations are driven by the applied magnetic field and an orthogonal field gradient provided by a micromagnet. We optimize the fidelity of this qubit as a function of magnetic fields, taking advantage of "sweet spots" where the rotation frequencies are independent of the energy level detuning, providing protection against charge noise. We simulate gate operations and qubit rotations in the presence of quasistatic noise from charge and nuclear spins as well as leakage to nonqubit states, and predict that in silicon quantum dots gate fidelities greater than $99\%$ can be achieved for two nearly-orthogonal rotation axes.

Note: This preprint has been superseded by arXiv:1806.04318. Recent advances in nanotechnology have enabled researchers to control individual quantum mechanical objects with unprecedented accuracy, opening the door for both quantum and extreme-scale conventional computing applications. As these devices become larger and more complex, the ability to design them such that they can be simply controlled becomes a daunting and computationally infeasible task. Here, motivated by ideas from compressed sensing, we introduce a protocol for the Compressed Optimization of Device Architectures (CODA). It leads naturally to a metric for benchmarking device performance and optimizing device designs, and provides a scheme for automating the control of gate operations and reducing their complexity. Because CODA is computationally efficient, it is readily extensible to large systems. We demonstrate the CODA benchmarking and optimization protocols through simulations of up to eight quantum dots in devices that are currently being developed experimentally for quantum computation., Comment: Note: This preprint has been superseded by arXiv:1806.04318

A most intuitive realization of a qubit is a single electron charge sitting at two well-defined positions, such as the left and right sides of a double quantum dot. This qubit is not just simple but also has the potential for high-speed operation, because of the strong coupling of electric fields to the electron. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at nearly all operating points, with the exception of one special 'sweet spot'. Fast dc voltage pulses have been used to manipulate semiconductor charge qubits, but these previous experiments did not achieve high-fidelity control, because dc gating requires excursions away from the sweet spot. Here, by using resonant ac microwave driving, we achieve coherent manipulation of a semiconductor charge qubit, demonstrating a Rabi frequency of up to 2GHz, a value approaching the intrinsic qubit frequency of 4.5GHz. Z-axis rotations of the qubit are well-protected at the sweet spot, and by using ac gating, we demonstrate the same protection for rotations about arbitrary axes in the X-Y plane of the qubit Bloch sphere. We characterize operations on the qubit using two independent tomographic approaches: standard process tomography and a newly developed method known as gate set tomography. Both approaches show that this qubit can be operated with process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations., Comment: 9 pages, 5 figures including supplementary information

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 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, Ramsey and Hahn echo decay timescales of 1us and 40us, respectively, are observed. This is almost two orders of magnitude longer than the intrinsic timescales in III-V quantum dots, while gate operation times are comparable to those achieved in GaAs. This places the single-qubit rotations in the fault-tolerant regime and strongly raises the prospects of quantum information processing based on quantum dots., Comment: submitted 26th February 2014

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 micro magnet, the magnetic field difference $\Delta B$ between the two sides of the double dot is large enough to enable the achievement of coherent rotation of the qubit's Bloch vector about two different axes of the Bloch sphere. By measuring the decay of the quantum oscillations, the inhomogeneous spin coherence time $T_{2}^{*}$ is determined. By measuring $T_{2}^{*}$ at many different values of the exchange coupling $J$ and at two different values of $\Delta B$, we provide evidence that the micromagnet does not limit decoherence, with the dominant limits on $T_{2}^{*}$ arising from charge noise and from coupling to nuclear spins., Comment: 10 pages, 9 figures

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. While quantum dot spin qubits have demonstrated long coherence times, their manipulation is often slower than desired for important future applications, such as factoring. Further, 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 new qubit that offers both simplicity - it requires no special preparation and lives in a double quantum dot with no added complexity - and is very fast: we demonstrate full control on the Bloch sphere with $\pi$-rotation times less than 100 ps in two orthogonal directions. We report full process tomography, extracting high fidelities equal to or greater than 85% for X-rotations and 94% for Z-rotations. We discuss a path forward to fidelities better than the threshold for quantum error correction., Comment: 6 pages, excluding Appendix

Theoretical treatments of tunneling in electronic devices are often based on one-dimensional (1D) approximations. Here we show that for many nanoscale devices, such as widely studied semiconductor gate-defined quantum dots, 1D approximations yield an incorrect functional dependence on the tunneling parameters (e.g., lead width and barrier length) and an incorrect magnitude for the transport conductance. Remarkably, the physics of tunneling in 2D or 3D also yields transport behavior that appears classical (like Ohm's law), even deep in the quantum regime., Comment: 9 pages

A fundamental goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T2*[1]. Most manipulations of electron spins in quantum dots have focused on the construction and control of two-state quantum systems, or qubits, in which each quantum dot is occupied by a single electron[2-7]. Here we perform quantum manipulations on a system with more electrons per quantum dot, in a double dot with three electrons. We demonstrate that tailored pulse sequences can be used to induce coherent rotations between 3-electron quantum states. Certain pulse sequences yield coherent oscillations with a very high figure of merit (the ratio of coherence time to rotation time) of >100. The presence of the third electron enables very fast rotations to all possible states, in contrast to the case when only two electrons are used, in which some rotations are slow. The minimum oscillation frequency we observe is >5 GHz., Comment: 5 pages, 2 figures, submitted for publication

Measurement of multiple quantum devices on a single chip increases characterization throughput and enables testing of device repeatability, process yield, and systematic variations in device design. We present a method that uses on-chip field-effect transistor switches to enable multiplexed cryogenic measurements of double quantum dot Si/SiGe devices. Multiplexing makes it feasible to characterize a number of devices that scales exponentially with the number of external wires, a key capability given the significant constraints on cryostat wiring currently in common use. We use this approach to characterize three nominally identical quantum-point contact channels, enabling comparison of their threshold voltages for accumulation and their pinch-off voltages during a single cool-down of a dilution refrigerator.

Quantum dots in silicon are promising candidates for implementation of solid-state quantum information processing. It is important to understand the effects of the multiple conduction band valleys of silicon on the properties of these devices. Here we introduce a novel, systematic effective mass theory of valley-orbit coupling in disordered silicon systems. This theory reveals valley-orbit hybridization effects that are detrimental for storing quantum information in the valley degree of freedom, including non-vanishing dipole matrix elements between valley states and altered intervalley tunneling., Comment: 7 pages, 3 figures

We report transport measurements on a Si/SiGe quantum dot subject to microwave excitation via an on-chip antenna. The response shows signatures of photon-assisted tunneling and only a small effect on charge stability. We also explore the use of a d.c. current applied to the antenna for generating tunable, local magnetic field gradients and put bounds on the achievable field gradients, limited by heating of the reservoirs.

We report measurements consistent with the valley Kondo effect in Si/SiGe quantum dots, evidenced by peaks in the conductance versus source-drain voltage that show strong temperature dependence. The Kondo peaks show unusual behavior in a magnetic field that we interpret as arising from the valley degree of freedom. The interplay of valley and Zeeman splittings is suggested by the presence of side peaks, revealing a zero-field valley splitting between 0.28 to 0.34 meV. A zero-bias conductance peak for non-zero magnetic field, a phenomenon consistent with valley non- conservation in tunneling, is observed in two samples., Comment: 16 pages, 7 figures

Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2* ranges from 127ps to ~2.1ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise(charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T2*, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127ps to 760ps, demonstrating that low-frequency noise processes are an important dephasing mechanism., Comment: 5 pages plus 3 page supplemental (8 pages total)

A quantum dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to presence of level crossings where the qubit becomes charge-like. Here, we show how to take full advantage of the level crossings in a pulsed gating scheme, which decomposes the spin qubit into a series of charge transitions. 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 these sub-nanosecond gates can achieve high fidelities., Comment: ~5 pages, 3 figures, includes supplemental information

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 $S^2=3/4$ ($S=\half$) and $S_z = -\half$, with the two different states being singlet and triplet in the doubly occupied dot. The architecture is relatively simple to fabricate, a universal set of fast operations can be implemented electrically, and the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices., Comment: Includes text and supplemental material, 12 pages, 9 figures

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. At zero magnetic field, we find that all three triplet states have equal lifetimes, as expected, and this time is ~10 ms. At non-zero field, the T0 lifetime is unchanged, whereas the T- lifetime increases monotonically with field, reaching 3 seconds at 1 T., Comment: 4 pages, 3 figures, supplemental information. Typos fixed; updated to submitted version

We measure the excited-state spectrum of a Si/SiGe quantum dot as a function of in-plane magnetic field, and we identify the spin of the lowest three eigenstates in an effective two-electron regime. The singlet-triplet splitting is an essential parameter describing spin qubits, and we extract this splitting from the data. We find it to be tunable by lateral displacement of the dot, which is realized by changing two gate voltages on opposite sides of the device. We present calculations showing the data are consistent with a spectrum in which the first excited state of the dot is a valley-orbit state., Comment: 4 pages with 3 figures

We report a robust process for fabrication of surface-gated Si/SiGe quantum dots (QDs) with an integrated superconducting single-electron transistor (S-SET) charge sensor. A combination of a deep mesa etch and AlOx backfill is used to reduce gate leakage. After the leakage current is suppressed, Coulomb oscillations of the QD and the current-voltage characteristics of the S-SET are observed at a temperature of 0.3 K. Coupling of the S-SET to the QD is confirmed by using the S-SET to perform sensing of the QD charge state., Comment: 4 pages, 3 figures

We present transport measurements of a tunable silicon metal-oxide-semiconductor double quantum dot device with lateral geometry. Experimentally extracted gate-to-dot capacitances show that the device is largely symmetric under the gate voltages applied. Intriguingly, these gate voltages themselves are not symmetric. Comparison with numerical simulations indicates that the applied gate voltages serve to offset an intrinsic asymmetry in the physical device. We also show a transition from a large single dot to two well isolated coupled dots, where the central gate of the device is used to controllably tune the interdot coupling., Comment: 4 pages, 3 figures, to be published in Applied Physics Letters

The remarkable properties of silicon have made it the central material for the fabrication of current microelectronic devices. Silicon's fundamental properties also make it an attractive option for the development of devices for spintronics and quantum information processing. The ability to manipulate and measure spins of single electrons is crucial for these applications. Here we report the manipulation and measurement of a single spin in a quantum dot fabricated in a silicon/silicon-germanium heterostructure. We demonstrate that the rate of loading of electrons into the device can be tuned over an order of magnitude using a gate voltage, that the spin state of the loaded electron depends systematically on the loading voltage level, and that this tunability arises because electron spins can be loaded through excited orbital states of the quantum dot. The longitudinal spin relaxation time T1 is measured using single-shot pulsed techniques and found to be ~3 seconds at a field of 1.85 Tesla. The demonstration of single spin measurement as well as a long spin relaxation time and tunability of the loading are all favorable properties for spintronics and quantum information processing applications., Comment: 4 pages, 3 figures, Supplemental Information

We investigate the tunnel rates and energies of excited states of small numbers of electrons in a quantum dot fabricated in a Si/SiGe heterostructure. Tunnel rates for loading and unloading electrons are found to be strongly energy dependent, and they vary significantly between different excited states. We show that this phenomenon enables charge sensing measurements of the average electron occupation that are analogous to Coulomb diamonds. Excited-state energies can be read directly from the plot, and we develop a rate model that enables a quantitative understanding of the relative sizes of different electron tunnel rates., Comment: 9 pages

We analyze electron transport data through a Si/SiGe double quantum dot in terms of spin blockade and lifetime-enhanced transport (LET), which is transport through excited states that is enabled by long spin relaxation times. We present a series of low-bias voltage measurements showing the sudden appearance of a strong tail of current that we argue is an unambiguous signature of LET appearing when the bias voltage becomes greater than the singlet-triplet splitting for the (2,0) electron state. We present eight independent data sets, four in the forward bias (spin-blockade) regime and four in the reverse bias (lifetime-enhanced transport) regime, and show that all eight data sets can be fit to one consistent set of parameters. We also perform a detailed analysis of the reverse bias (LET) regime, using transport rate equations that include both singlet and triplet transport channels. The model also includes the energy dependent tunneling of electrons across the quantum barriers, and resonant and inelastic tunneling effects. In this way, we obtain excellent fits to the experimental data, and we obtain quantitative estimates for the tunneling rates and transport currents throughout the reverse bias regime. We provide a physical understanding of the different blockade regimes and present detailed predictions for the conditions under which LET may be observed., Comment: published version, 18 pages

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., Comment: Supplemental material included as an appendix

We report the fabrication and measurement of one-electron single and double quantum dots with fast tunnel rates in a Si/SiGe heterostructure. Achieving fast tunnel rates in few-electron dots can be challenging, in part due to the large electron effective mass in Si. Using charge sensing, we identify signatures of tunnel rates in and out of the dot that are fast or slow compared to the measurement rate. Such signatures provide a means to calibrate the absolute electron number and verify single electron occupation. Pulsed gate voltage measurements are used to validate the approach., Comment: 4 pages, double column, 3 figures