In this Letter the following original sentence has been amended for clarity: “As the Kramers theorem does not hold in the presence of a non-zero weak-link phase bias φ, the splitting of the spin states requires an additional ingredient.”; it has been changed to: “Although the presence of a non-zero weak-link phase bias φ breaks time-reversal symmetry so that the Kramers theorem does not hold, this alone is insufficient to lift the spin degeneracy—an additional effect is required.” The online versions of the Letter have been amended.

Little–Parks oscillations of a hollow superconducting cylinder are of interest for flux-driven topological superconductivity in single Rashba nanowires. The oscillations are typically symmetric in the orientation of the applied magnetic flux. Using double InAs nanowires coated by an epitaxial superconducting Al shell which, despite the non-centro-symmetric geometry, behaves effectively as one hollow cylinder, we demonstrate that a small misalignment of the applied parallel field with respect to the axis of the nanowires can produce field-asymmetric Little–Parks oscillations. These are revealed by the simultaneous application of a magnetic field perpendicular to the misaligned parallel field direction. The asymmetry occurs in both the destructive regime, in which superconductivity is destroyed for half-integer quanta of flux through the shell, and in the non-destructive regime, where superconductivity is depressed but not fully destroyed at these flux values.

Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this Rapid Communication, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demonstrate a direct spin to supercurrent conversion, the superconducting equivalent of the Pauli spin blockade. This effect can be exploited in hybrid quantum architectures coupling the quantum states of spin systems and superconducting circuits.

Inhomogeneous superconductors can host electronic excitations, known as Andreev bound states (ABSs), below the superconducting energy gap. With the advent of topological superconductivity, a new kind of zero-energy ABS with exotic qualities, known as a Majorana bound state (MBS), has been discovered. A special property of MBS wavefunctions is their non-locality, which, together with non-Abelian braiding, is the key to their promise in topological quantum computation. We focus on hybrid superconductor–semiconductor nanowires as a flexible and promising experimental platform to realize one-dimensional topological superconductivity and MBSs. We review the main properties of ABSs and MBSs, state-of-the-art techniques for their detection and theoretical progress beyond minimal models, including different types of robust zero modes that may emerge without a band-topological transition.

Readout and control of electrostatically confined electrons in semiconductors are key primitives of quantum information processing with solid-state spin qubits^1,2. In superconductor–semiconductor heterostructures, localized electronic modes known as Andreev levels result from confinement that is provided by the pair potential^3,4. Unlike electronic modes confined exclusively via electrostatic effects, Andreev levels carry supercurrent. Therefore, they naturally integrate with the techniques of circuit quantum electrodynamics (cQED) that have been developed in the field of superconducting qubits and used to detect pairs of quasiparticles that are trapped in Andreev levels^5–8. Here, we demonstrate single-shot cQED readout of the spin of an individual quasiparticle trapped in the Andreev levels of a semiconductor nanowire Josephson element. Owing to a spin-orbit interaction in the nanowire, this ‘superconducting spin’ directly determines the flow of supercurrent through the element. We harnessed this spin-dependent supercurrent to achieve both a zero-field spin splitting and a long-range interaction between the quasiparticle and a superconducting microwave resonator^9–13. Measurement of the resultant spin-dependent resonator frequency yielded quantum non-demolition spin readout with 92% fidelity in 1.9 μs, which enabled us to monitor the quasiparticle spin in real time. These results pave the way for superconducting spin qubits that operate at zero magnetic field and for time-domain measurements of Majorana zero modes^{9,10,12,14,15}.

The Cooper-pair transistor (CPT), a small superconducting island enclosed between two Josephson weak links, is the atomic building block of various superconducting quantum circuits. Utilizing gate-tunable semiconductor channels as weak links, the energy scale associated with the Josephson tunneling can be changed with respect to the charging energy of the island, tuning the extent of its charge fluctuations. Here, we directly demonstrate this control by mapping the energy level structure of a CPT made of an indium arsenide nanowire with a superconducting aluminum shell. We extract the device parameters based on the exhaustive modeling of the quantum dynamics of the phase-biased nanowire CPT and directly measure the even-odd parity occupation ratio as a function of the device temperature, relevant for superconducting and prospective topological qubits.

We present an experimental study of flux- and gate-tunable nanowire transmons with state-of-the-art relaxation time allowing quantitative extraction of flux and charge noise coupling to the Josephson energy. We evidence coherence sweet spots for charge, tuned by voltage on a proximal side gate, where first order sensitivity to switching two-level systems and background 1/f noise is minimized. Next, we investigate the evolution of a nanowire transmon in a parallel magnetic field up to 70 mT, the upper bound set by the closing of the induced gap. Several features observed in the field dependence of qubit energy relaxation and dephasing times are not fully understood. Using nanowires with a thinner, partially covering Al shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation and other applications.

The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gate-tunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gate-tunable junction based on an aluminum-proximitized indium arsenide nanowire. We demonstrate coherent manipulation of these bound states, and track the bound-state fermion parity in real time. Individual parity-switching events due to nonequilibrium quasiparticles are observed with a characteristic timescale Tparity=160±10 μs. The Tparity of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.

Parity control of superconducting islands hosting Majorana zero modes (MZMs) is required to operate topological qubits made from proximitized semiconductor nanowires. We test this control by studying parity effects in hybrid InAs-Al single-Cooper-pair transistors (SCPTs) to evaluate the feasibility of this material system. In particular, we investigate the gate-charge modulation of the supercurrent and observe a consistent 2e-periodic pattern indicating a general lack of low-energy subgap states in these nanowires at zero magnetic field. In a parallel magnetic field, an even-odd pattern develops with a gate-charge spacing that oscillates as a function of field demonstrating that the modulation pattern is sensitive to the presence of a single bound state. In addition, we find that the parity lifetime of the SCPT decreases exponentially with magnetic field as the bound state approaches zero energy. Our work shows that aluminum is the preferred superconductor for future topological qubit experiments and highlights the important role that quasiparticle traps and superconducting gap engineering would play in these qubits. Moreover, we demonstrate a means by which bound states can be detected in devices with superconducting leads.

Difficulties in obtaining high-performance p-type transistors and gate insulator charge-trapping effects present two major challenges for III-V complementary metal-oxide semiconductor (CMOS) electronics. We report a p-GaAs nanowire metal-semiconductor field-effect transistor (MESFET) that eliminates the need for a gate insulator by exploiting the Schottky barrier at the metal-GaAs interface. Our device beats the best-performing p-GaSb nanowire metal-oxide-semiconductor field effect transistor (MOSFET), giving a typical subthreshold swing of 62 mV/dec, within 4% of the thermal limit, on-off ratio ∼10⁵, on-resistance ∼700 kω, contact resistance ∼30 kω, peak transconductance 1.2 μS/μm, and high-fidelity ac operation at frequencies up to 10 kHz. The device consists of a GaAs nanowire with an undoped core and heavily Be-doped shell. We carefully etch back the nanowire at the gate locations to obtain Schottky-barrier insulated gates while leaving the doped shell intact at the contacts to obtain low contact resistance. Our device opens a path to all-GaAs nanowire MESFET complementary circuits with simplified fabrication and improved performance.

The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates, providing a highly scalable and in situ variation of the device properties. In addition, semiconductors with large g-factor and spin-orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as † 0 Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gate-tunable, high transmission probabilities up to 0.9, which is required for gate-tunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spin-split pair of ABS and observe symmetry-broken ABS, a direct consequence of the spin-orbit coupling in the semiconductor.