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A detailed understanding of the material properties that affect the splitting between the two low-lying valley states in Si/SiGe heterostructures will be increasingly important as the number of spin qubits is increased. Scanning gate microscopy has been proposed as a method to measure the spatial variation of the valley splitting as a tip-induced dot is moved around in the plane of the Si quantum well. We develop a simulation using an electrostatic model of the scanning gate microscope tip and the overlapping gate structure combined with an approximate solution to the three-dimensional Schr\"odinger-Poisson equation in the device stack. Using this simulation, we show that a tip-induced quantum dot formed near source and drain electrodes can be adiabatically moved to a region far from the gate electrodes. We argue that by spatially translating the tip-induced dot across a defect in the Si/SiGe interface, changes in valley splitting can be detected.

We theoretically propose a method to perform in situ measurements of charge noise during logical operations in silicon quantum dot spin qubits. Our method does not require ancillary spectator qubits but makes use of the valley degree of freedom in silicon. Sharp interface steps or alloy disorder in the well provide a valley transition dipole element that couples to the field of an on-chip microwave resonator, allowing rapid reflectometry of valley splitting fluctuations caused by charge noise. We derive analytic expressions for the signal-to-noise ratio that can be expected and use tight binding simulations to extract the key parameters (valley splitting and valley dipole elements) under realistic disorder. We find that unity signal-to-noise ratio can often be obtained with measurement times below 1ms, faster than typical decoherence times, opening the potential for closed-loop control, real-time recalibration, and feedforward circuits, Comment: 12 pages and 7 figures

Increasing the number of electrons in electrostatically confined quantum dots can enable faster qubit gates. Although this has been experimentally demonstrated, a detailed quantitative understanding has been missing. Here we study one- and three-electron quantum dots in silicon/silicon-germanium heterostructures within the context of electrically-driven spin resonance (EDSR) using full configuration interaction and tight binding approaches. Our calculations show that anharmonicity of the confinement potential plays an important role: while the EDSR Rabi frequency of electrons in a harmonic potential is indifferent to the electron number, soft anharmonic confinements lead to larger and hard anharmonic confinements lead to smaller Rabi frequencies. We also confirm that double dots allow fast Rabi oscillations, and further suggest that purposefully engineered confinements can also yield similarly fast Rabi oscillations in a single dot. Finally, we discuss the role of interface steps. These findings have important implications for the design of multielectron Si/SiGe quantum dot qubits.

Conventional quantum transport methods can provide quantitative information on spin, orbital, and valley states in quantum dots, but often lack spatial resolution. Scanning tunneling microscopy, on the other hand, provides exquisite spatial resolution of the local electronic density of states, but often at the expense of speed. Working to combine the spatial resolution and energy sensitivity of scanning probe microscopy with the speed of microwave measurements, we couple a metallic probe tip to a Si/SiGe double quantum dot that is integrated with a local charge detector. We first demonstrate that a dc-biased tip can be used to change the charge occupancy of the double dot. We then apply microwave excitation through the scanning tip to drive photon-assisted tunneling transitions in the double dot. We infer the double dot energy level diagram from the frequency and detuning dependence of the photon-assisted tunneling resonance condition. These measurements allow us to resolve $\sim$65 $\mu$eV excited states, an energy scale consistent with typical valley splittings in Si/SiGe. Future extensions of this approach may allow spatial mapping of the valley splitting in Si devices, which is of fundamental importance for spin-based quantum processors.

In this paper we present a computational procedure that utilizes real-space grids to obtain high precision approximations of electrostatically confined few-electron states such as those that arise in gated semiconductor quantum dots. We use the Full Configuration Interaction (FCI) method with a continuously adapted orthonormal orbital basis to approximate the ground and excited states of such systems. We also introduce a benchmark problem based on a realistic analytical electrostatic potential for quantum dot devices. We show that our approach leads to highly precise computed energies and energy differences over a wide range of model parameters. The analytic definition of the benchmark allows for a collection of tests that are easily replicated, thus facilitating comparisons with other computational approaches., Comment: 8 pages, 4 figures

Triple quantum dots (TQDs) are promising semiconductor spin qubits because of their all-electrical control via fast, tunable exchange interactions and immunity to global magnetic fluctuations. These qubits can experience strong transverse interaction with photons in the resonant exchange (RX) regime, when exchange is simultaneously active on both qubit axes. However, most theoretical work has been based on phenomenological Fermi-Hubbard models, which may not fully capture the complexity of the qubit spin-charge states in this regime. Here we investigate exchange in Si/SiGe and GaAs TQDs using full configuration interaction (FCI) calculations which better describe practical device operation. We show that high exchange operation in general, and the RX regime in particular, can differ significantly from simple models, presenting new challenges and opportunities for spin-photon coupling. We highlight the impact of device electrostatics and effective mass on exchange and identify a new operating point (XRX) where strong spin-photon coupling is most likely to occur in Si/SiGe TQDs. Based on our numerical results, we analyze the feasibility of a remote entanglement cavity iSWAP protocol and discuss design pathways for improving fidelity. Our analysis provides insight into the requirements for TQD spin-photon transduction and demonstrates more generally the necessity of accurate modeling of exchange in spin qubits., Comment: Published version: 25 pages, 9 figures

We design and analyze a logical qubit composed of a linear array of electron spins in semiconductor quantum dots. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a one-dimensional line of silicon quantum dots. Control speed and efficiency are maintained via a scheme in which electron spin states are controlled globally using broadband microwave pulses for magnetic resonance while two-qubit gates are provided by local electrical control of the exchange interaction between neighboring dots. Error correction with two-, three-, and four-qubit codes is adapted to a linear chain of qubits with nearest-neighbor gates. We estimate an error correction threshold of 1e-4. Furthermore, we describe a sequence of experiments to validate the methods on near-term devices starting from four coupled dots., Comment: 29 pages, 27 figures, 170 references

We report on a quantum dot device design that combines the low disorder properties of undoped SiGe heterostructure materials with an overlapping gate stack in which each electrostatic gate has a dominant and unique function -- control of individual quantum dot occupancies and of lateral tunneling into and between dots. Control of the tunneling rate between a dot and an electron bath is demonstrated over more than nine orders of magnitude and independently confirmed by direct measurement within the bandwidth of our amplifiers. The inter-dot tunnel coupling at the (0,2)<-->(1,1) charge configuration anti-crossing is directly measured to quantify the control of a single inter-dot tunnel barrier gate. A simple exponential dependence is sufficient to describe each of these tunneling processes as a function of the controlling gate voltage., Comment: 4 pages, 5 figures

We demonstrate double quantum dots fabricated in undoped Si/SiGe heterostructures relying on a double top-gated design. Charge sensing shows that we can reliably deplete these devices to zero charge occupancy. Measurements and simulations confirm that the energetics are determined by the gate-induced electrostatic potentials. Pauli spin blockade has been observed via transport through the double dot in the two electron configuration, a critical step in performing coherent spin manipulations in Si., Comment: 4 pages, 4 figures

Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of magnitude improvement in the fidelities of a universal set of quantum gates, relative to unprotected evolution, is achieved over a broad range of system-environment coupling strengths, using recursively constructed (concatenated) dynamical decoupling pulse sequences., Comment: Slightly expanded form of the journal version. Also includes the supplementary material as an appendix

We have demonstrated few-electron quantum dots in Si/SiGe and InGaAs, with occupation number controllable from N = 0. These display a high degree of spatial symmetry and identifiable shell structure. Magnetospectroscopy measurements show that two Si-based devices possess a singlet N =2 ground state at low magnetic field and therefore the two-fold valley degeneracy is lifted. The valley splittings in these two devices were 120 and 270 {\mu}eV, suggesting the presence of atomically sharp interfaces in our heterostructures., Comment: 3 pages, 3 figures

We have observed the Zeeman-split excited state of a spin-1/2 multi-electron Si/SiGe depletion quantum dot and measured its spin relaxation time T1 in magnetic fields up to 2 T. Using a new step-and-reach technique, we have experimentally verified the g-value of 2.0 +/- 0.1 for the observed Zeeman doublet. We have also measured T1 of single- and multi-electron spins in InGaAs quantum dots. The lifetimes of the Si/SiGe system are appreciably longer than those for InGaAs dots for comparable magnetic field strengths, but both approach one second at sufficiently low fields (< 1 T for Si, and < 0.2 T for InGaAs)., Comment: 5 pages, 5 figures