Full-scale quantum computers require the integration of millions of qubits, and the potential of using industrial semiconductor manufacturing to meet this need has driven the development of quantum computing in silicon quantum dots. However, fabrication has so far relied on electron-beam lithography and, with a few exceptions, conventional lift-off processes that suffer from low yield and poor uniformity. Here we report quantum dots that are hosted at a ²⁸Si/²⁸SiO₂ interface and fabricated in a 300 mm semiconductor manufacturing facility using all-optical lithography and fully industrial processing. With this approach, we achieve nanoscale gate patterns with excellent yield. In the multi-electron regime, the quantum dots allow good tunnel barrier control—a crucial feature for fault-tolerant two-qubit gates. Single-spin qubit operation using magnetic resonance in the few-electron regime reveals relaxation times of over 1 s at 1 T and coherence times of over 3 ms.

@en

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around gs/2p=40 MHz. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J/2p=20 MHz. In addition, photon-number states are resolved from the shift 2?s/2p=-13 MHz that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.

@en

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.

@en

Quantum computers (QC) promise to solve certain computational problems exponentially faster than a classical computer due to the superposition and entanglement properties of quantum bits (qubits). Among several qubit technologies, spin qubits are a promising candidate for large-scale QC, since (1) they have a small footprint allowing them to be densely integrated and (2) they can operate at relatively high temperatures (\gt1\mathrm{K}) [1], potentially reducing system cost and complexity.

@en

This dissertation describes a set of experiments with the goal of creating a super-conductor-semiconductor hybrid circuit quantum electrodynamics architecture with single electron spins. Single spins in silicon quantum dots have emerged as attractive qubits for quantum computation. However, how to scale up spin qubit systems remains an open question. The hybrid architecture considered here could provide a route to realizing large networks of quantum dot–based spin qubit registers. The first experiment in this thesis is aimed at achieving strong coupling between a single electron spin and a single microwave photon. The electron is trapped in a gate-defined double quantum dot in a Si/SiGe heterostructure and the photon is stored in an on-chip superconducting high-impedance NbTiN cavity. The photon is coupled directly to the electron charge, and indirectly to the electron spin, mediated through a synthetic spin-orbit field. We observe a vacuum Rabi splitting that depends on the spin-charge hybridization. The ratio of spin-photon coupling strength to decoherence rates of the spin and cavity combined is larger than unity, confirming the strong coupling regime has been reached. In addition, we find an optimal degree of spin-charge hybridization for which this ratio is maximized. The demonstration of strong spin-photon coupling not only opens a new range of physics experiments, but fulfills also a crucial requirement for coupling spin qubits at a distance via a cavity. The second experiment is focused on spin readout with the on-chip cavity. Instead of the direct dispersive readout of a single spin, we use the cavity to detect whether the electron is allowed to tunnel between the two dots or not. We benchmark the charge sensitivity and bandwidth of the detector and find that rapid detection of the electron charge with high SNR is possible. In the two-electron regime, electron tunneling is contingent on the total spin state (Pauli spin blockade). This spin-to-charge conversion scheme enables single-shot detection of singlet states with high-fidelity. The demonstration of single-shot spin readout with a cavity is an essential step towards readout in dense spin qubit arrays, such as the crossbar network, where it is not possible to integrate electrometers and accompanying reservoirs adjacent to the qubit dots. In the third experiment, we develop on-chip microwave filters to suppress microwave photon leakage from the cavity through the gate electrodes that are necessary to form quantum dots. We introduce a new cavity design that is compatible with long-distance connectivity between spins, but is also more susceptible to microwave leakage. We test and compare two low-pass filter variations in terms of performance, footprint and integrability. They use the same nanowire inductor, but different implementations of the capacitor: one with a planar interdigitated capacitor and one novel design with an overlapping thin-film capacitor. We find that both approaches are effective against microwave leakage. However, the large footprint of the interdigitated capacitor makes this solution inconvenient as the number of gate lines increases. The thin-film capacitor, with its much smaller footprint, is better suited for our devices. The final part of this dissertation contains concluding remarks and possible future directions are proposed. @en

Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of their total capacitance over the parasitic port capacitance is smaller, leading to larger microwave leakage than for 50-ω resonators. Here, we introduce an implementation of on-chip filters to suppress the microwave leakage. The filters comprise a high-kinetic-inductance nanowire inductor and a thin-film capacitor. The filter has a small footprint and can be placed close to the resonator, confining microwaves to a small area of the chip. The inductance and capacitance of the filter elements can be varied over a wider range of values than their typical spiral inductor and interdigitated capacitor counterparts. We demonstrate that the total linewidth of a 6.4 GHz and approximately 3-kω resonator can be improved down to 540 kHz using these filters.

@en

In the version of this Letter originally published, the second, third and fourth exponential terms in equation (3) were incorrect; the corrected equation is shown below. (Formula presented.). The correct equation was used for data analysis. The online versions have been amended.

@en

Silicon spin qubits are one of the leading platforms for quantum computation^1,2. As with any qubit implementation, a crucial requirement is the ability to measure individual quantum states rapidly and with high fidelity. Since the signal from a single electron spin is minute, the different spin states are converted to different charge states^3,4. Charge detection, so far, has mostly relied on external electrometers^5–7, which hinders scaling to two-dimensional spin qubit arrays^2,8,9. Alternatively, gate-based dispersive read-out based on off-chip lumped element resonators has been demonstrated^10–13, but integration times of 0.2–2 ms were required to achieve single-shot read-out^14–16. Here, we connect an on-chip superconducting resonant circuit to two of the gates that confine electrons in a double quantum dot. Measurement of the power transmitted through a feedline coupled to the resonator probes the charge susceptibility, distinguishing whether or not an electron can oscillate between the dots in response to the probe power. With this approach, we achieve a signal-to-noise ratio of about six within an integration time of only 1 μs. Using Pauli’s exclusion principle for spin-to-charge conversion, we demonstrate single-shot read-out of a two-electron spin state with an average fidelity of >98% in 6 μs. This result may form the basis of frequency-multiplexed read-out in dense spin qubit systems without external electrometers, therefore simplifying the system architecture.

@en

We demonstrate the strong coupling between a single electron spin in silicon and a single photon in a superconducting microwave cavity. Using the same cavity we perform rapid high-fidelity single-shot readout of two-electron spin states.

@en

Long coherence times of single spins in silicon quantum dots make these systems highly attractive for quantum computation, but how to scale up spin qubit systems remains an open question. As a first step to address this issue, we demonstrate the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot, and the microwave photon is stored in an on-chip high-impedance superconducting resonator. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet. Our results provide a route to realizing large networks of quantum dot–based spin qubit registers.

@en

We present superconducting microwave-frequency resonators based on NbTiN nanowires. The small cross section of the nanowires minimizes vortex generation, making the resonators resilient to magnetic fields. Measured intrinsic quality factors exceed 2×105 in a 6-T in-plane magnetic field and 3×104 in a 350-mT perpendicular magnetic field. Because of their high characteristic impedance, these resonators are expected to develop zero-point voltage fluctuations one order of magnitude larger than in standard coplanar waveguide resonators. These properties make the nanowire resonators well suited for circuit QED experiments needing strong coupling to quantum systems with small electric dipole moments and requiring a magnetic field, such as electrons in single and double quantum dots.

@en