Superconducting parametric amplifiers play a crucial role in the preparation and readout of quantum states at microwave frequencies, enabling high-fidelity measurements of superconducting qubits. Most existing implementations of these amplifiers rely on the nonlinearity from Josephson junctions, superconducting quantum interference devices, or disordered superconductors. Additionally, frequency tunability arises typically from either flux or current biasing. In contrast, semiconductor-based parametric amplifiers are tunable by local electric fields, which impose a smaller thermal load on the cryogenic setup than current and flux biasing and lead to vanishing crosstalk to other on-chip quantum systems. In this work, we present a gate-tunable parametric amplifier that operates without Josephson junctions, using a proximitized semiconducting nanowire. This design achieves near-quantum-limited performance, featuring more than 20-dB gain and a 30-MHz gain-bandwidth product. The absence of Josephson junctions results in advantages, including substantial saturation powers of -120 dBm, magnetic field compatibility up to 500mT, and frequency tunability over a range of 15 MHz. Our realization of a parametric amplifier supplements efforts towards gate-controlled superconducting electronics, further advancing the abilities for high-performing quantum measurements of semiconductor-based and superconducting quantum devices.

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Andreev bound states are fermionic states localized in weak links between superconductors which can be occupied with spinful quasiparticles. Microwave experiments using superconducting circuits with InAs/Al nanowire Josephson junctions have recently enabled probing and coherent manipulation of Andreev states but have remained limited to zero or small magnetic fields. Here, we use a flux-tunable superconducting circuit compatible in magnetic fields up to 1T to perform spectroscopy of spin-polarized Andreev states up to ∼250mT, beyond which the spectrum becomes gapless. We identify singlet and triplet states of two quasiparticles occupying different Andreev states through their dispersion in magnetic field. These states are split by exchange interaction and couple via spin-orbit coupling, analogously to two-electron states in quantum dots. We also show that the magnetic field allows to drive a direct spin-flip transition of a single quasiparticle trapped in the junction. Finally, we measure a gate- and field-dependent anomalous phase shift of the Andreev spectrum, of magnitude up to ∼0.7π. Our observations demonstrate alternative ways to manipulate Andreev states in a magnetic field and reveal spin-polarized triplet states that carry supercurrent.

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Fluxons in a superconducting loop can be coherently coupled by quantum phase slips occurring at a weak link such as a Josephson junction. If Cooper pair tunneling at the junction occurs through a resonant level, then 2π quantum phase slips are suppressed, and fluxons are predominantly coupled by 4π quantum phase slips. We analyze this scenario by computing the coupling between fluxons as the level is brought into resonance with the superconducting condensate. The results indicate that the 4π-dominated regime can be observed directly in the transition spectrum for circuit parameters typical of a fluxonium qubit. We also show that if the inductive energy of the loop is much smaller than the plasma frequency of the junction, then the low-energy Hamiltonian of the circuit is dual to that of a topological superconducting island. These findings can inform experiments on bifluxon qubits as well as the design of novel types of protected qubits.

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Andreev spin qubits have recently emerged as an alternative qubit platform with realizations in semiconductor–superconductor hybrid nanowires. In these qubits, the spin degree of freedom of a quasiparticle trapped in a Josephson junction is intrinsically spin–orbit coupled to the supercurrent across the junction. This interaction has previously been used to perform spin readout, but it has also been predicted to facilitate inductive multi-qubit coupling. Here we demonstrate a strong supercurrent-mediated longitudinal coupling between two distant Andreev spin qubits. We show that it is both gate- and flux-tunable into the strong coupling regime and, furthermore, that magnetic flux can be used to switch off the coupling in situ. Our results demonstrate that integrating microscopic spin states into a superconducting qubit architecture can combine the advantages of both semiconductors and superconducting circuits and pave the way to fast two-qubit gates between distant spins.

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The Josephson effect is a quintessential topic of condensed matter physics. It has stimulated decades of fundamental research, leading to a plethora of applications from metrology to outer space. In addition, it is set to play a crucial role in the development of quantum computers, forming the dissipationless non-linear inductance that lies at the core of superconducting qubits. While they are traditionally realized using oxide based tunnel barriers, in this thesis we construct Josephson junctions from non-insulating materials such as semiconducting nanowires and quantum dots. We investigate how their highly nontrivial interplay with superconductivity can lead to new effects, both of fundamental interest and of relevance for quantum applications. To study these effects we make use the exhaustive toolbox available for superconducting circuits, allowing us to probe the junction behavior to beyond what is possible with conventional transport techniques. The first experimental chapter of this thesis examines the behaviour of a transmon that hosts a highly transparent semiconducting weak-link as the Josephson junction. In this system we find spectroscopic evidence for the predicted vanishing of Coulomb effects in open superconducting islands, in accordance with theoretical predictions from 1999. In the second experiment we deterministically place a quantum dot inside the junction of a transmon circuit. We then demonstrate that by using microwave spectroscopy we are able to accurately probe the energy-phase relationship of the Josephson junction over a vast regime of parameter space. This reveals the remnants of a quantum phase transition, and allows us to probe the time dynamics of the junction parity. We subsequently use the same type of device to reveal the predicted spin-splitting of the Andreev bound states in a quantum dot with superconducting leads, as brought about by the spin-orbit interaction. When combined with a magnetic field, this is shown to result in the anomalous Josephson effect. Furthermore, we demonstrate that transitions between the spin-split quantum dot states can be directly driven with microwaves. This motivated the investigation of a novel superconducting spin qubit, performed in the fourth experiment. Here we demonstrate rapid, all-electric qubit manipulation in addition to detailed coherence characterization. We ultimately show signatures of strong coherent coupling between the superconducting spin qubit and the transmon into which it is embedded, setting the stage for future research of this nascent qubit platform. In the fifth and final experiment, we utilize a different approach compared to the preceding chapters. While we once-more construct transmons based on semiconducting weak-links, we now do so to leverage the intrinsic magnetic field resilience of semiconducting nanowires. This allows us to use a single device to study the mitigation of phonon-induced quasiparticle losses by trapping the phonons using both super and normal-state conductors. This thesis concludes by discussing several ideas and proposals that aim to leverage the alternative Josephson junctions studied in this thesis. Combined with the results of the preceding chapters, this shows that hybrid superconducting circuits can be used to obtain deep insights into the fundamental physics governing their constituent junctions, and opens avenues towards building better qubits.@en

Spectroscopy of a Josephson junction device with an embedded quantum dot reveals the presence of a contribution to level splitting in external magnetic field that is proportional to cosϕ, where ϕ is the gauge-invariant phase difference across the junction. To elucidate the origin of this unanticipated effect, we systematically study the Zeeman splitting of spinful subgap states in the superconducting Anderson impurity model. The magnitude of the splitting is renormalized by the exchange interaction between the local moment and the continuum of Bogoliubov quasiparticles in a variant of the Knight shift phenomenon. The leading term in the shift is linear in the hybridisation strength Γ (quadratic in electron hopping), while the subleading term is quadratic in Γ (quartic in electron hopping) and depends on ϕ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the ϕ-dependent part is largest for experimentally relevant parameters beyond the perturbative regime where it is investigated using numerical renormalization group calculations. Such magnetic-field-tunable coupling between the quantum dot spin and the Josephson current could find wide use in superconducting spintronics.@en

Quantum error correction will be an essential ingredient in realizing fault-tolerant quantum computing. However, most correction schemes rely on the assumption that errors are sufficiently uncorrelated in space and time. In superconducting qubits, this assumption is drastically violated in the presence of ionizing radiation, which creates bursts of high-energy phonons in the substrate. These phonons can break Cooper pairs in the superconductor and, thus, create quasiparticles over large areas, consequently reducing qubit coherence across the quantum device in a correlated fashion. A potential mitigation technique is to place large volumes of normal or superconducting metal on the device, capable of reducing the phonon energy to below the superconducting gap of the qubits. To investigate the effectiveness of this method, we fabricate a quantum device with four nominally identical nanowire-based transmon qubits. On the device, half of the niobium-titanium-nitride ground plane is replaced with aluminum (Al), which has a significantly lower superconducting gap. We deterministically inject high-energy phonons into the substrate by voltage biasing a galvanically isolated Josephson junction. In the presence of the small-gap material, we find a factor of 2–5 less degradation in the injection-dependent qubit lifetimes and observe that the undesired excited qubit state population is mitigated by a similar factor. We furthermore turn the Al normal with a magnetic field, finding no change in the phonon protection. This suggests that the efficacy of the protection in our device is not limited by the size of the superconducting gap in the Al ground plane. Our results provide a promising foundation for protecting superconducting-qubit processors against correlated errors from ionizing radiation.@en

Josephson junctions in InAs nanowires proximitized with an Al shell can host gate-tunable Andreev bound states. Depending on the bound state occupation, the fermion parity of the junction can be even or odd. Coherent control of Andreev bound states has recently been achieved within each parity sector, but it is impeded by incoherent parity switches due to excess quasiparticles in the superconducting environment. Here, we show that we can polarize the fermion parity dynamically using microwave pulses by embedding the junction in a superconducting LC resonator. We demonstrate polarization up to 94%±1% (89%±1%) for the even (odd) parity as verified by single shot parity readout. Finally, we apply this scheme to probe the flux-dependent transition spectrum of the even or odd parity sector selectively, without any postprocessing or heralding.

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Spin qubits in semiconductors are a promising platform for producing highly scalable quantum computing devices. However, it is difficult to realize multiqubit interactions over extended distances. Superconducting spin qubits provide an alternative by encoding a qubit in the spin degree of freedom of an Andreev level. These Andreev spin qubits have an intrinsic spin–supercurrent coupling that enables the use of recent advances in circuit quantum electrodynamics. The first realization of an Andreev spin qubit encoded the qubit in the excited states of a semiconducting weak link, leading to frequent decay out of the computational subspace. Additionally, rapid qubit manipulation was hindered by the need for indirect Raman transitions. Here we use an electrostatically defined quantum dot Josephson junction with large charging energy, which leads to a spin-split doublet ground state. We tune the qubit frequency over a frequency range of 10 GHz using a magnetic field, which also enables us to investigate the qubit performance using direct spin manipulation. An all-electric microwave drive produces Rabi frequencies exceeding 200 MHz. We embed the Andreev spin qubit in a superconducting transmon qubit, demonstrating strong coherent qubit–qubit coupling. These results are a crucial step towards a hybrid architecture that combines the beneficial aspects of both superconducting and semiconductor qubits.

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We use a hybrid superconductor-semiconductor transmon device to perform spectroscopy of a quantum dot Josephson junction tuned to be in a spin-1/2 ground state with an unpaired quasiparticle. Because of spin-orbit coupling, we resolve two flux-sensitive branches in the transmon spectrum, depending on the spin of the quasiparticle. A finite magnetic field shifts the two branches in energy, favoring one spin state and resulting in the anomalous Josephson effect. We demonstrate the excitation of the direct spin-flip transition using all-electrical control. Manipulation and control of the spin-flip transition enable the future implementation of charging energy protected Andreev spin qubits.

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We report the detection of a gate-tunable kinetic inductance in a hybrid InAs/Al nanowire. For this purpose, we embed the nanowire into a quarter-wave coplanar waveguide resonator and measure the resonance frequency of the circuit. We find that the resonance frequency can be changed via the gate voltage that controls the electron density of the proximitized semiconductor and thus the nanowire inductance. Applying Mattis-Bardeen theory, we extract the gate dependence of the normal-state conductivity of the nanowire, as well as its superconducting gap. Our measurements complement existing characterization methods for hybrid nanowires and provide a useful tool for gate-controlled superconducting electronics.

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We realize a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by a gate-defined quantum dot in an InAs-Al nanowire. Microwave spectroscopy of the transition spectrum of the transmon allows us to probe the ground-state parity of the quantum dot as a function of the gate voltages, the external magnetic flux, and the magnetic field applied parallel to the nanowire. The measured parity phase diagram is in agreement with that predicted by a single-impurity Anderson model with superconducting leads. Through continuous-time monitoring of the circuit, we furthermore resolve the quasiparticle dynamics of the quantum dot Josephson junction across the phase boundaries. Our results can facilitate the realization of semiconductor-based 0-π qubits and Andreev qubits.

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Hybrid superconducting circuits, which integrate nonsuperconducting elements into a circuit quantum electrodynamics (cQED) architecture, expand the possible applications of cQED. Building hybrid circuits that work in large magnetic fields presents even further possibilities, such as the probing of spin-polarized Andreev bound states and the investigation of topological superconductivity. Here we present a magnetic-field compatible hybrid fluxonium with an electrostatically tuned semiconducting nanowire as its nonlinear element. We operate the fluxonium in magnetic fields up to 1 T and use it to observe the f0-Josephson effect. This combination of gate tunability and field compatibility opens avenues for the control of spin-polarized phenomena using superconducting circuits and enables the use of the fluxonium as a readout device for topological qubits.

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Isolation from the environment determines the extent to which charge is confined on an island, which manifests as Coulomb oscillations, such as charge dispersion. We investigate the charge dispersion of a nanowire transmon hosting a quantum dot in the junction. We observe rapid suppression of the charge dispersion with increasing junction transparency, consistent with the predicted scaling law, which incorporates two branches of the Josephson potential. We find improved qubit coherence times at the point of highest suppression, suggesting novel approaches for building charge-insensitive qubits.

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We study the effect of gate-induced electric fields on the properties of semiconductor-superconductor hybrid nanowires which represent a promising platform for realizing topological superconductivity and Majorana zero modes. Using a self-consistent Schrödinger-Poisson approach that describes the semiconductor and the superconductor on equal footing, we are able to access the strong tunneling regime and identify the impact of an applied gate voltage on the coupling between semiconductor and superconductor. We discuss how physical parameters such as the induced superconducting gap and Landé g factor in the semiconductor are modified by redistributing the density of states across the interface upon application of an external gate voltage. Finally, we map out the topological phase diagram as a function of magnetic field and gate voltage for InAs/Al nanowires.

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We study the effect of external electric fields on superconductor-semiconductor coupling by measuring the electron transport in InSb semiconductor nanowires coupled to an epitaxially grown Al superconductor. We find that the gate voltage induced electric fields can greatly modify the coupling strength, which has consequences for the proximity induced superconducting gap, effective g-factor, and spin-orbit coupling, which all play a key role in understanding Majorana physics. We further show that level repulsion due to spin-orbit coupling in a finite size system can lead to seemingly stable zero bias conductance peaks, which mimic the behavior of Majorana zero modes. Our results improve the understanding of realistic Majorana nanowire systems.

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