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 growing understanding of the physics of superconductor-semiconductor nanostruc- tures is a key driver for the development of emerging quantum technologies. The elemen- tary excitations of these hybrid nanostructures are Andreev bound states. To further our knowledge about their intricate physics, new tools must be used to study them. This thesis describes the use of magnetic-field compatible superconducting circuits to study and ma- nipulate Andreev bound states and their spin in hybrid superconducting-semiconducting nanowire Josephson junctions. First, we provide an introduction to the physical models describing Andreev bound states in superconducting circuits and the general methodology used for the circuit design, device fabrication and experimental setups in the experiments of this work. We then move on to an initial set of two experiments in Chapters 4 and 5, where we inductively shunt a superconducting resonator with a nanowire-based radio-frequency su- perconducting quantum interference device (rf-SQUID). This allows us to study Andreev bound states in InAs/Al nanowire Josephson junctions using circuit quantum electrody- namics techniques under various external conditions. In Chapter 4 we use pulsed detection of Andreev bound state parity to demonstrate par- ity selective spectroscopy. The main result of this Chapter was the discovery of microwave- induced parity polarization, that allows one to set the bound state parity in-situ using microwave pulses. We then study the evolution of the microwave spectrum of Andreev bound states in a magnetic field in Chapter 5. Here we find a multitude of phenomena that arise because of the rich interplay between spin-orbit coupling, the Zeeman effect, super- conductivity, and electron-electron interactions. We observe evidence of spin-polarizing microwave transitions, the anomalous Josephson effect, and transitions involving triplet Andreev spins. In Chapter 6 we explore an alternative material and junction fabrication method in combination with the same circuitry. Specifically, we excite Andreev bound states in InS- b/Al Josephson junctions defined by shadow-wall lithography. We observe low density, high-transparency Andreev bound states in a range of devices and reproduce the directly spin-polarizing microwave transition observed in Chapter 5. The results of this Chap- ter demonstrate the viability of combining hybrid circuit quantum electrodynamics with advanced material combinations and fabrication geometries. In the final experiment, Chapter 7, we move back to InAs/Al based junctions. This Chapter uses previous results from Chapter 5 and works demonstrating the use of a single superconducting spin as a quantum bit, as a stepping stone. Here, we embed two super- conducting spin qubits in a single SQUID and demonstrate strong longitudinal coupling between them over a distance much larger than their wavelengths. The results and methods developed in this dissertation pave the way for continued ex- ploration of the intricating physics of superconducting spins and demonstrate early steps towards their use as a new platform for quantum computing.@en

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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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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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

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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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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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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