We study a phase-tunable four-terminal Josephson junction formed in an InSbAs two-dimensional electron gas proximitized by aluminum. By embedding the two pairs of junction terminals in asymmetric DC superconducting quantum-interference devices (SQUIDs) we can control the superconducting phase difference across each pair, thereby gaining information about their current-phase relation. Using a current-bias line to locally control the magnetic flux through one SQUID, we measure a nonlocal Josephson effect, whereby the current-phase relation across two terminals in the junction is strongly dependent on the superconducting phase difference across two completely different terminals. In particular, each pair behaves as a φ0 junction with a phase offset tuned by the phase difference across the other junction terminals. Lastly, we demonstrate that the behavior of an array of two-terminal junctions replicates most features of the current-phase relation of different multiterminal junctions. This highlights that these signatures alone are not sufficient evidence of true multiterminal Josephson effects arising from hybridization of Andreev bound states in the junction.

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Quantum interference of electron tunneling occurs in any system where multiple tunneling paths connect states. This unavoidably arises in two-dimensional semiconducting qubit arrays, and must be controlled as a prerequisite for the manipulation and readout of hybrid topological and parity qubits. Studying a loop formed by two quantum dots, we demonstrate a magnetic-flux-tunable hybridization between two electronic levels, an irreducibly simple system where quantum interference is expected to occur. Using radio-frequency reflectometry of the dots’ gate electrodes we extract an interdot coupling exhibiting oscillations with a periodicity of one flux quantum. In different tunneling regimes we benchmark the oscillations’ contrast, and find their amplitude varies with the charge state of the quantum dots. These results establish the feasibility and limitations of parity readout of qubits with tunnel couplings tuned by flux.@en

Hybrid semiconducting-superconducting mesoscopic circuits are the basis of topological and parity quantum bits or 'qubits'. Both qubits are expected to be intrinsically protected from decoherence, making them promising candidates for fault-tolerant quantum computation. As topological phases effectively manifest exotic nonabelian particles which might not exist in nature, these systems are also of fundamental interest. This thesis primarily employs radio-frequency (RF) reflectometry, an important measurement tool for qubit readout, in order to study localized states in hybrid circuits. Since the hybridization of localized quantum dot and Andreev bound states is foundational to the aforementioned qubit implementations, our focus is on using RF tools to characterize such hybridization. We therefore begin by outlining background theory of these states and of RF reflectometry accompanied by simulations. Subsequently, we describe the results of four distinct experiments.

First, in a system comprised of multiple quantum dots, we demonstrate a signal-to-noise ratio of 15 in 1 microsecond for resolving interdot electron tunneling with RF reflectometry of the dot gate electrodes, a proxy for the readout of numerous types of qubits including spin and topological qubits. Additionally, we show RF reflectometry of the device leads is mappable to DC conductance a priori, implying it can completely replace DC measurement techniques for the characterization of semiconducting quantum circuits.

In the next experiment, we probe a superconducting island surrounded on either side by a semiconducting quantum dot with RF gate reflectometry. Therein, we electrically isolate the system from its leads, fixing the system's total charge. Afterwards, we correlate electron tunneling events between dots using frequency multiplexing of different gate resonators, culminating in the controllable splitting of a single Cooper pair into its constituent electrons. We also demonstrate a form of parity sensing using a strongly coupled double quantum dot and gate reflectometry.

Continuing, we present a study of an irregularly shaped double quantum dot arranged in a loop and threaded by a magnetic flux. Employing gate reflectometry to measure the interdot hybridization, we observe that it oscillates as a function of flux with a period of one flux quantum but with unpredictably varying amplitude and contrast. This result is a prerequisite for the readout and manipulation of measurement-based topological qubits and hybrid parity qubits.

As a final experiment, we investigate markers of the hybridization between Andreev bound states in a multiterminal Josephson junction, itself a potential platform for simulating topological Weyl systems. There, we characterize the current-flux relation of a four-terminal junction using two coupled DC superconducting quantum interference loops, observing a 'nonlocal' Josephson effect tuned by the magnetic fluxes through both loops. With a minimal theoretical model, we show that this behavior can be fully described by an array of two-terminal Josephson junctions and is not a unique signature of the hybridization of Andreev bound states in the junction.

To conclude, we summarize our experimental results and discuss potential future work. Namely, we emphasize the importance of understanding quasiparticle poisoning for the performance of topological and parity qubits, and consider further applications of RF measurement tools in studying hybrid systems. The results of this dissertation establish RF sensing as a complete characterization tool for hybrid quantum circuits, display its utility in studying floating systems to probe the movement of single electrons and Cooper pairs, and demonstrate the flux-control of interdot tunnel couplings required for hybrid parity qubits. Lastly, we highlight the indistinguishability of hybridized Andreev states from trivial multiterminal Josephson effects in a multiterminal junction's current-phase relation.
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Cooper pair splitters hold utility as a platform for investigating the entanglement of electrons in Cooper pairs, but probing splitters with voltage-biased Ohmic contacts prevents the retention of electrons from split pairs since they can escape to the drain reservoirs. We report the ability to controllably split and retain single Cooper pairs in a multi-quantum-dot device isolated from lead reservoirs, and separately demonstrate a technique for detecting the electrons emerging from a split pair. First, we identify a coherent Cooper pair splitting charge transition using dispersive gate sensing at GHz frequencies. Second, we utilize a double quantum dot as an electron parity sensor to detect parity changes resulting from electrons emerging from a superconducting island.

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Utilizing dispersive gate sensing (DGS), we investigate the spin-orbit field (BSO) orientation in a many-electron double quantum dot (DQD) defined in an InSb nanowire. While characterizing the interdot tunnel couplings, we find the measured dispersive signal depends on the electron-charge occupancy, as well as on the amplitude and orientation of the external magnetic field. The dispersive signal is mostly insensitive to the external field orientation when a DQD is occupied by a total odd number of electrons. For a DQD occupied by a total even number of electrons, the dispersive signal is reduced when the finite external magnetic field aligns with the effective BSO orientation. This fact enables the identification of BSO orientations for different DQD electron occupancies. The BSO orientation varies drastically between charge transitions, and is generally neither perpendicular to the nanowire nor in the chip plane. Moreover, BSO is similar for pairs of transitions involving the same valence orbital, and varies between such pairs. Our work demonstrates the practicality of DGS in characterizing spin-orbit interactions in quantum dot systems, without requiring any current flow through the device.

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We demonstrate the use of radio-frequency (rf) resonators to measure the capacitance of nanoscale semiconducting devices in field-effect transistor configurations. The rf resonator is attached to the gate or the lead of the device. Consequently, tuning the carrier density in the conducting channel of the device affects the resonance frequency, quantitatively reflecting its capacitance. We test the measurement method on InSb and InAs nanowires at dilution-refrigerator temperatures. The measured capacitances are consistent with those inferred from the periodicity of the Coulomb blockade of quantum dots realized in the same devices. In an implementation of the resonator using an off-chip superconducting spiral inductor we find the measurement sensitivity values reaching down to 75zF/Hz at 1 kHz measurement bandwidth, and noise down to 0.45 aF at 1 Hz bandwidth. We estimate the sensitivity of the method for a number of other implementations. In particular, we predict a typical sensitivity of about 40zF/Hz at room temperature with a resonator composed of off-the-shelf components. Of several proposed applications, we demonstrate two: the capacitance measurement of several identical 80-nm-wide gates with a single resonator, and the field-effect mobility measurement of an individual nanowire with the gate capacitance measured in situ.

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Superconducting resonators enable fast characterization and readout of mesoscopic quantum devices. Finding ways to perform measurements of interest on such devices using resonators only is therefore of great practical relevance. We report an experimental investigation of an InAs nanowire multiquantum dot device by probing gigahertz resonators connected to the device. First, we demonstrate accurate extraction of the dc conductance from measurements of the high-frequency admittance. Because our technique does not rely on dc calibration, it could potentially obviate the need for dc measurements in semiconductor qubit devices. Second, we demonstrate multiplexed gate sensing and the detection of charge tunneling on microsecond timescales. The gigahertz detection of dispersive resonator shifts allows rapid acquisition of charge stability diagrams, as well as resolving charge tunneling in the device with a signal-to-noise ratio of up to 15 in 1μs. Our measurements show that gigahertz-frequency resonators may serve as a universal tool for fast tuneup and high-fidelity readout of semiconductor qubits.@en

We report direct detection of charge tunneling between a quantum dot and a superconducting island through radio-frequency gate sensing. We are able to resolve spin-dependent quasiparticle tunneling as well as two-particle tunneling involving Cooper pairs. The quantum dot can act as an RF-only sensor to characterize the superconductor addition spectrum, enabling us to access subgap states without transport. Our results provide guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the parity-dependent tunneling between dots and islands.

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