Superconducting gatemon qubit based on a proximitized two-dimensional electron gas

Coherent Control of a Few-Channel Hole Type Gatemon Qubit

Gatemon qubits are the electrically tunable cousins of superconducting transmon qubits. In this work, we demonstrate the full coherent control of a gatemon qubit based on hole carriers in a Ge/Si core/shell nanowire, with the longest coherence times in group IV material gatemons to date. The key to these results is a high-quality Josephson junction obtained using a straightforward and reproducible annealing technique. We demonstrate that the transport through the narrow junction is dominated by only two quantum channels, with transparencies up to unity. This novel qubit platform holds great promise for quantum information applications, not only because it incorporates technologically relevant materials, but also because it provides new opportunities, like an ultrastrong spin-orbit coupling in the few-channel regime of Josephson junctions.

Surface Bio-engineered Polymeric Nanoparticles

Surface bio-engineering of polymeric nanoparticles (PNPs) has emerged as a cornerstone in contemporary biomedical research, presenting a transformative avenue that can revolutionize diagnostics, therapies, and drug delivery systems. The approach involves integrating bioactive elements on the surfaces of PNPs, aiming to provide them with functionalities to enable precise, targeted, and favorable interactions with biological components within cellular environments. However, the full potential of surface bio-engineered PNPs in biomedicine is hampered by obstacles, including precise control over surface modifications, stability in biological environments, and lasting targeted interactions with cells or tissues. Concerns like scalability, reproducibility, and long-term safety also impede translation to clinical practice. In this review, these challenges in the context of recent breakthroughs in developing surface-biofunctionalized PNPs for various applications, from biosensing and bioimaging to targeted delivery of therapeutics are discussed. Particular attention is given to bonding mechanisms that underlie the attachment of bioactive moieties to PNP surfaces. The stability and efficacy of surface-bioengineered PNPs are critically reviewed in disease detection, diagnostics, and treatment, both in vitro and in vivo settings. Insights into existing challenges and limitations impeding progress are provided, and a forward-looking discussion on the field's future is presented. The paper concludes with recommendations to accelerate the clinical translation of surface bio-engineered PNPs.

Supercurrent in the Presence of Direct Transmission and a Resonant Localized State

We study the current-phase relation (CPR) of an InSb-Al nanowire Josephson junction in parallel magnetic fields up to 700 mT. At high magnetic fields and in narrow voltage intervals of a gate under the junction, the CPR exhibits π shifts. The supercurrent declines within these gate intervals and shows asymmetric gate voltage dependence above and below them. We detect these features sometimes also at zero magnetic field. The observed CPR properties are reproduced by a theoretical model of supercurrent transport via interference between direct transmission and a resonant localized state.

Utilizing Gate-Controlled Supercurrent for All-Metallic Tunable Superconducting Microwave Resonators

Hybridizing a microwave mode with a quantum state requires precise frequency matching of a superconducting microwave resonator and the corresponding quantum object. However, fabrication always brings imperfections in geometry and material properties, causing deviations from the desired operating frequencies. An effective and universal strategy for their resonant coupling is to tune the frequency of a resonator, as quantum states like phonons are hardly tunable. Here, we demonstrate gate-tunable, titanium-nitride (TiN)-based superconducting resonators by implementing a nanowire inductor whose kinetic inductance is tuned via the gate-controlled supercurrent (GCS) effect. We investigate their responses for different gate biases and observe 4% (∼150 MHz) frequency tuning with decreasing internal quality factors. We also perform temperature-controlled experiments to support phonon-related mechanisms in the GCS effect and the resonance tuning. The GCS effect-based method proposed in this study provides an effective route for locally tunable resonators that can be employed in various hybrid quantum devices.

Parity-conserving Cooper-pair transport and ideal superconducting diode in planar germanium

Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a [Formula: see text] CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with ≈ 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on  the same silicon technology compatible platform.

Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet-Andreev states

Light-matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting-semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current-phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current-phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet-Andreev states, our study rules out this scenario. The distortion of the current-phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light-matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet-Andreev states in mesoscopic devices.

Zeeman- and Orbital-Driven Phase Shifts in Planar Josephson Junctions

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to φ0 = 0.5π, which are consistent with a Zeeman field coupling to highly transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit, and orbital effects in InAs/Al JJs, giving improved understanding of phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics.

Dynamical Polarization of the Fermion Parity in a Nanowire Josephson Junction

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.

Gate-Tunable Critical Current of the Three-Dimensional Niobium Nanobridge Josephson Junction

Recent studies have shown that the critical currents of several metallic superconducting nanowires and Dayem bridges can be locally tuned by using a gate voltage (Vg). Here, we report a gate-tunable Josephson junction structure constructed from a three-dimensional (3D) niobium nanobridge junction (NBJ) with a voltage gate on top. Measurements up to 6 K showed that the critical current of this structure can be tuned to zero by increasing Vg. The critical gate voltage was reduced to 16 V and may possibly be reduced further by reducing the thickness of the insulation layer between the gate and the NBJ. Furthermore, the flux modulation generated by Josephson interference of two parallel 3D NBJs can also be tuned by using Vg in a similar manner. Therefore, we believe that this gate-tunable Josephson junction structure is promising for superconducting circuit fabrication at high integration levels.

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

The Schottky barrier transistor in emerging electronic devices

This paper explores how the Schottky barrier (SB) transistor is used in a variety of applications and material systems. A discussion of SB formation, current transport processes, and an overview of modeling are first considered. Three discussions follow, which detail the role of SB transistors in high performance, ubiquitous and cryogenic electronics. For high performance computing, the SB typically needs to be minimized to achieve optimal performance and we explore the methods adopted in carbon nanotube technology and two-dimensional electronics. On the contrary for ubiquitous electronics, the SB can be used advantageously in source-gated transistors and reconfigurable field-effect transistors (FETs) for sensors, neuromorphic hardware and security applications. Similarly, judicious use of an SB can be an asset for applications involving Josephson junction FETs.

Evolution of 4π-Periodic Supercurrent in the Presence of an In-Plane Magnetic Field

In the presence of a 4π-periodic contribution to the current phase relation, for example in topological Josephson junctions, odd Shapiro steps are expected to be missing. While missing odd Shapiro steps have been observed in several material systems and interpreted in the context of topological superconductivity, they have also been observed in topologically trivial junctions. Here, we study the evolution of such trivial missing odd Shapiro steps in Al-InAs junctions in the presence of an in-plane magnetic field B^θ. We find that the odd steps reappear at a crossover B^θ value, exhibiting an in-plane field angle anisotropy that depends on spin-orbit coupling effects. We interpret this behavior by theoretically analyzing the Andreev bound state spectrum and the transitions induced by the nonadiabatic dynamics of the junction and attribute the observed anisotropy to mode-to-mode coupling. Our results highlight the complex phenomenology of missing Shapiro steps and the underlying current phase relations in planar Josephson junctions designed to realize Majorana states.

Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.

A gate-tunable graphene Josephson parametric amplifier

With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to advances in microwave quantum optics¹. Of these elements, quantum-limited parametric amplifiers^2-4 are essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of μeV)^5,6. They are also used to generate non-classical states of light that can be a resource for quantum enhanced detection⁷. Superconducting parametric amplifiers, such as quantum bits, typically use a Josephson junction as a source of magnetically tunable and dissipation-free non-linearity. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable non-linear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires^8,9, a two-dimensional electron gas¹⁰, carbon nanotubes¹¹ and graphene^12,13. However, given the challenge of balancing non-linearity, dissipation, participation and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. Here, we demonstrate a parametric amplifier leveraging a graphene Josephson junction and show that its working frequency is widely tunable with a gate voltage. We report gain exceeding 20 dB and noise performance close to the standard quantum limit. Our results expand the toolset for electrically tunable superconducting quantum circuits. They also offer opportunities for the development of quantum technologies such as quantum computing, quantum sensing and for fundamental science¹⁴.

Experimentally revealing anomalously large dipoles in the dielectric of a quantum circuit

Quantum two-level systems (TLSs) intrinsic to glasses induce decoherence in many modern quantum devices, such as superconducting qubits. Although the low-temperature physics of these TLSs is usually well-explained by a phenomenological standard tunneling model of independent TLSs, the nature of these TLSs, as well as their behavior out of equilibrium and at high energies above 1 K, remain inconclusive. Here we measure the non-equilibrium dielectric loss of TLSs in amorphous silicon using a superconducting resonator, where energies of TLSs are varied in time using a swept electric field. Our results show the existence of two distinct ensembles of TLSs, interacting weakly and strongly with phonons, where the latter also possesses anomalously large electric dipole moment. These results may shed new light on the low temperature characteristics of amorphous solids, and hold implications to experiments and applications in quantum devices using time-varying electric fields.

Selective control of conductance modes in multi-terminal Josephson junctions

The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of a multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work, we employ a quantum point contact geometry in three-terminal Josephson devices to demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presence of superconducting coupling. These results establish a full platform on which to realize tunable Andreev bound state spectra in multi-terminal Josephson junctions.

Multiterminal Josephson junctions may provide a novel way to realize topologically non-trivial band structures in an n-dimensional phase space. Here, the authors experimentally demonstrate the proposed necessary conditions to measure these states.

Low-Temperature Characteristics of Nanowire Network Demultiplexer for Qubit Biasing

In current quantum computers, most qubit control electronics are connected to the qubit chip inside the cryostat by cables at room temperature. This poses a challenge when scaling the quantum chip to an increasing number of qubits. We present a lateral nanowire network 1-to-4 demultiplexer design fabricated by selective area grown InGaAs on InP, suitable for on chip routing of DC current for qubit biasing. We have characterized the device at cryogenic temperatures, and at 40 mK the device exhibits a minimum inverse subthreshold slope of 2 mV/dec, which is encouraging for low power operation. At low drain bias, the transmission breaks up into several resonance peaks due to a rough conduction band edge; this is qualitatively explained by a simple model based on a 1D real space tight-binding nonequilibrium Green's functions model.

Microwave response of a metallic superconductor subject to a high-voltage gate electrode

Processes that lead to the critical-current suppression and change of impedance of a superconductor under the application of an external voltage is an active area of research, especially due to various possible technological applications. In particular, field-effect transistors and radiation detectors have been developed in the recent years, showing the potential for precision and sensitivity exceeding their normal-metal counterparts. In order to describe the phenomenon that leads to the critical-current suppression in metallic superconducting structures, a field-effect hypothesis has been formulated, stating that an electric field can penetrate the metallic superconductor and affect its characteristics. The existence of such an effect would imply the incompleteness of the underlying theory, and hence indicate an important gap in the general comprehension of superconductors. In addition to its theoretical value, a complete understanding of the phenomenon underneath the electric-field response of the superconductor is important in the light of the related technological applications. In this paper, we study the change of the characteristics of a superconductor implementing a coplanar-waveguide resonator as a tank circuit, by relating our measurements to the reactance and resistance of the material. Namely, we track the state of the superconductor at different voltages and resulting leakage currents of a nearby gate electrode which is not galvanically connected to the resonator. By comparing the effects of the leakage current and of a change in the temperature of the system, we conclude that the observed behaviour in the superconductor is mainly caused by the heat that is deposited by the leakage current, and bearing the experimental uncertainties, we are not able to observe the effect of the applied electric field in our sample. In addition, we present a relatively good quantitative agreement between the Mattis–Bardeen theory of a heated superconductor and the experimental observations. Importantly, we do not claim this work to nullify the results of previous works, but rather to provide inspiration for future more thorough experiments and analysis using the methods presented here.

Integration of Topological Insulator Josephson Junctions in Superconducting Qubit Circuits

The integration of semiconductor Josephson junctions (JJs) in superconducting quantum circuits provides a versatile platform for hybrid qubits and offers a powerful way to probe exotic quasiparticle excitations. Recent proposals for using circuit quantum electrodynamics (cQED) to detect topological superconductivity motivate the integration of novel topological materials in such circuits. Here, we report on the realization of superconducting transmon qubits implemented with (Bi_0.06Sb_0.94)₂Te₃ topological insulator (TI) JJs using ultrahigh vacuum fabrication techniques. Microwave losses on our substrates, which host monolithically integrated hardmasks used for the selective area growth of TI nanostructures, imply microsecond limits to relaxation times and, thus, their compatibility with strong-coupling cQED. We use the cavity-qubit interaction to show that the Josephson energy of TI-based transmons scales with their JJ dimensions and demonstrate qubit control as well as temporal quantum coherence. Our results pave the way for advanced investigations of topological materials in both novel Josephson and topological qubits.

Detecting Induced p±ip Pairing at the Al-InAs Interface with a Quantum Microwave Circuit

Superconductor-semiconductor hybrid devices are at the heart of several proposed approaches to quantum information processing, but their basic properties remain to be understood. We embed a two-dimensional Al-InAs hybrid system in a resonant microwave circuit, probing the breakdown of superconductivity due to an applied magnetic field. We find a fingerprint from the two-component nature of the hybrid system, and quantitatively compare with a theory that includes the contribution of intraband p±ip pairing in the InAs, as well as the emergence of Bogoliubov-Fermi surfaces due to magnetic field. Separately resolving the Al and InAs contributions allows us to determine the carrier density and mobility in the InAs.

Miniaturizing Transmon Qubits Using van der Waals Materials

Quantum computers can potentially achieve an exponential speedup versus classical computers on certain computational tasks, recently demonstrated in superconducting qubit processors. However, the capacitor electrodes that comprise these qubits must be large in order to avoid lossy dielectrics. This tactic hinders scaling by increasing parasitic coupling among circuit components, degrading individual qubit addressability, and limiting the spatial density of qubits. Here, we take advantage of the unique properties of van der Waals (vdW) materials to reduce the qubit area by >1000 times while preserving the capacitance while maintaining quantum coherence. Our qubits combine conventional aluminum-based Josephson junctions with parallel-plate capacitors composed of crystalline layers of superconducting niobium diselenide and insulating hexagonal boron nitride. We measure a vdW transmon T₁ relaxation time of 1.06 μs, demonstrating a path to achieve high-qubit-density quantum processors with long coherence times, and the broad utility of layered heterostructures in low-loss, high-coherence quantum devices.

Superconducting Contacts to a Monolayer Semiconductor

We demonstrate superconducting vertical interconnect access (VIA) contacts to a monolayer of molybdenum disulfide (MoS2), a layered semiconductor with highly relevant electronic and optical properties. As a contact material we use MoRe, a superconductor with a high critical magnetic field and high critical temperature. The electron transport is mostly dominated by a single superconductor/normal conductor junction with a clear superconductor gap. In addition, we find MoS2 regions that are strongly coupled to the superconductor, resulting in resonant Andreev tunneling and junction-dependent gap characteristics, suggesting a superconducting proximity effect. Magnetoresistance measurements show that the bandstructure and the high intrinsic carrier mobility remain intact in the bulk of the MoS2. This type of VIA contact is applicable to a large variety of layered materials and superconducting contacts, opening up a path to monolayer semiconductors as a platform for superconducting hybrid devices.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

High-energy quasiparticle injection into mesoscopic superconductors

At non-zero temperatures, superconductors contain excitations known as Bogoliubov quasiparticles (QPs). The mesoscopic dynamics of QPs inform the design of quantum information processors, among other devices. Knowledge of these dynamics stems from experiments in which QPs are injected in a controlled fashion, typically at energies comparable to the pairing energy^1-5. Here we perform tunnel spectroscopy of a mesoscopic superconductor under high electric fields. We observe QP injection due to field-emitted electrons with 10⁶ times the pairing energy, an unexplored regime of QP dynamics. Upon application of a gate voltage, the QP injection decreases the critical current and, at sufficiently high electric field, a field-emission current (<0.1 nA in our device) switches the mesoscopic superconductor into the normal state, consistent with earlier observations⁶. We expect that high-energy injection will be useful for developing QP-tolerant quantum information processors, will allow rapid control of resonator quality factors and will enable the design of electric-field-controlled superconducting devices with new functionality.

Tuning Supercurrent in Josephson Field-Effect Transistors Using h-BN Dielectric

Epitaxial Al-InAs heterostructures appear as a promising materials platform for exploring mesoscopic and topological superconductivity. A unique property of Josephson junction field effect transistors (JJ-FETs) fabricated on these heterostructures is the ability to tune the supercurrent using a metallic gate. Here, we report the fabrication and measurement of gate-tunable Al-InAs JJ-FETs in which the gate dielectric in contact with the InAs is produced by mechanically exfoliated hexagonal boron nitride (h-BN) followed by dry transfer. We discuss a versatile fabrication process that enables compatibility between layered material transfer and Al-InAs heterostructures that allows us to achieve full gate-tunability of supercurrent by using only 5 nm thick h-BN flakes. Our study shows that pristine properties of epitaxial Josephson junctions, such as product of normal resistance and critical current, I_cR_n, are preserved. Furthermore, complementary measurements confirm that using h-BN dielectric changes the channel density less when compared to atomic layer deposition of Al₂O₃.

Flux Tunable Superconducting Quantum Circuit Based on Weyl Semimetal MoTe2

Weyl semimetals have drawn considerable attention for their exotic topological properties in many research fields. When in combination with s-wave superconductors, the supercurrent can be carried by their topological surface channels, forming junctions mimicking the behavior of Majorana bound states. Here, we present a transmon-like superconducting quantum intereference device (SQUID) consisting of lateral junctions made of Weyl semimetal Td-MoTe₂ and superconducting leads of niobium nitride (NbN). The SQUID is coupled to a readout cavity made of molybdenum rhenium (MoRe), whose response at high power reveals the existence of the constituting Josephson junctions (JJs). The loop geometry of the circuit allows the resonant frequency of the readout cavity to be tuned by the magnetic flux. We demonstrate a JJ made of MoTe₂ and a flux-tunable transmon-like circuit based on Weyl semimetals. Our study provides a platform to utilize topological materials in SQUID-based quantum circuits for potential applications in quantum information processing.

Highly Transparent Gatable Superconducting Shadow Junctions

Gate-tunable junctions are key elements in quantum devices based on hybrid semiconductor-superconductor materials. They serve multiple purposes ranging from tunnel spectroscopy probes to voltage-controlled qubit operations in gatemon and topological qubits. Common to all is that junction transparency plays a critical role. In this study, we grow single-crystalline InAs, InSb, and InAs_1-xSb_x semiconductor nanowires with epitaxial Al, Sn, and Pb superconductors and in situ shadowed junctions in a single-step molecular beam epitaxy process. We investigate correlations between fabrication parameters, junction morphologies, and electronic transport properties of the junctions and show that the examined in situ shadowed junctions are of significantly higher quality than the etched junctions. By varying the edge sharpness of the shadow junctions, we show that the sharpest edges yield the highest junction transparency for all three examined semiconductors. Further, critical supercurrent measurements reveal an extraordinarily high I_CR_N, close to the KO-2 limit. This study demonstrates a promising engineering path toward reliable gate-tunable superconducting qubits.

Parity-Protected Superconductor-Semiconductor Qubit

Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.

Suppressed Charge Dispersion via Resonant Tunneling in a Single-Channel Transmon

We demonstrate strong suppression of charge dispersion in a semiconductor-based transmon qubit across Josephson resonances associated with a quantum dot in the junction. On resonance, dispersion is drastically reduced compared to conventional transmons with corresponding Josephson and charging energies. We develop a model of qubit dispersion for a single-channel resonance, which is in quantitative agreement with experimental data.

Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions

We demonstrate concomitant measurement of phase-dependent critical current and Andreev bound state spectrum in a highly transmissive InAs Josephson junction embedded in a dc superconducting quantum interference device (SQUID). Tunneling spectroscopy reveals Andreev bound states with near unity transmission probability. A nonsinusoidal current-phase relation is derived from the Andreev spectrum, showing excellent agreement with the one extracted from the SQUID critical current. Both measurements are reconciled within a short junction model where multiple Andreev bound states, with various transmission probabilities, contribute to the entire supercurrent flowing in the junction.

Controlled dc Monitoring of a Superconducting Qubit

Creating a transmon qubit using semiconductor-superconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a field-effect transistor. Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normal-state resistance. Gradually opening the field-effect transistor to the monitoring circuit allows the influence of weak-to-strong dc monitoring of a "live" qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gate-controlled environmental coupling.

Universal Tool for Single-Photon Circuits: Quantum Router Design

We demonstrate that the non-Hermitian Hamiltonian approach can be used as a universal tool to design and describe a performance of single photon quantum electrodynamical circuits (cQED). As an example of the validity of this method, we calculate a novel six port quantum router, constructed from four qubits and three open waveguides. We have obtained analytical expressions, which describe the transmission and reflection coefficients of a single photon in general form taking into account the spread qubit’s parameters. We show that, due to naturally derived interferences, in situ tuning the probability of photon detection in desired ports.

Two-Dimensional Material Tunnel Barrier for Josephson Junctions and Superconducting Qubits

Quantum computing based on superconducting qubits requires the understanding and control of the materials, device architecture, and operation. However, the materials for the central circuit element, the Josephson junction, have mostly been focused on using the AlO_x tunnel barrier. Here, we demonstrate Josephson junctions and superconducting qubits employing two-dimensional materials as the tunnel barrier. We batch-fabricate and design the critical Josephson current of these devices via layer-by-layer stacking N layers of MoS₂ on the large scale. Based on such junctions, MoS₂ transmon qubits are engineered and characterized in a bulk superconducting microwave resonator for the first time. Our work allows Josephson junctions to access the diverse material properties of two-dimensional materials that include a wide range of electrical and magnetic properties, which can be used to study the effects of different material properties in superconducting qubits and to engineer novel quantum circuit elements in the future.

Ballistic superconductivity and tunable π-junctions in InSb quantum wells

Planar Josephson junctions (JJs) made in semiconductor quantum wells with large spin-orbit coupling are capable of hosting topological superconductivity. Indium antimonide (InSb) two-dimensional electron gases (2DEGs) are particularly suited for this due to their large Landé g-factor and high carrier mobility, however superconducting hybrids in these 2DEGs remain unexplored. Here we create JJs in high quality InSb 2DEGs and provide evidence of ballistic superconductivity over micron-scale lengths. A Zeeman field produces distinct revivals of the supercurrent in the junction, associated with a 0-π transition. We show that these transitions can be controlled by device design, and tuned in-situ using gates. A comparison between experiments and the theory of ballistic π-Josephson junctions gives excellent quantitative agreement. Our results therefore establish InSb quantum wells as a promising new material platform to study the interplay between superconductivity, spin-orbit interaction and magnetism.

Evidence of topological superconductivity in planar Josephson junctions

Majorana zero modes-quasiparticle states localized at the boundaries of topological superconductors-are expected to be ideal building blocks for fault-tolerant quantum computing^1,2. Several observations of zero-bias conductance peaks measured by tunnelling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor-semiconductor nanowires^3-8. On the other hand, two-dimensional systems offer the alternative approach of confining Majorana channels within planar Josephson junctions, in which the phase difference φ between the superconducting leads represents an additional tuning knob that is predicted to drive the system into the topological phase at lower magnetic fields than for a system without phase bias^9,10. Here we report the observation of phase-dependent zero-bias conductance peaks measured by tunnelling spectroscopy at the end of Josephson junctions realized on a heterostructure consisting of aluminium on indium arsenide. Biasing the junction to φ ≈ π reduces the critical field at which the zero-bias peak appears, with respect to φ = 0. The phase and magnetic-field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. As well as providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures¹¹ and are scalable to the complex geometries needed for topological quantum computing^9,12,13.

Germanium Quantum-Well Josephson Field-Effect Transistors and Interferometers

Hybrid superconductor-semiconductor structures attract increasing attention owing to a variety of potential applications in quantum computing devices. They can serve the realization of topological superconducting systems as well as gate-tunable superconducting quantum bits. Here, we combine a SiGe/Ge/SiGe quantum-well heterostructure hosting high-mobility two-dimensional holes and aluminum superconducting leads to realize prototypical hybrid devices, such as Josephson field-effect transistors (JoFETs) and superconducting quantum interference devices (SQUIDs). We observe gate-controlled supercurrent transport with Ge channels as long as one micrometer and estimate the induced superconducting gap from tunnel spectroscopy measurements. Transmission electron microscopy reveals the diffusion of Ge into the Al contacts, whereas no Al is detected in the Ge channel.

Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures

Quantum coherence and control is foundational to the science and engineering of quantum systems^1,2. In van der Waals materials, the collective coherent behaviour of carriers has been probed successfully by transport measurements^3-6. However, temporal coherence and control, as exemplified by manipulating a single quantum degree of freedom, remains to be verified. Here we demonstrate such coherence and control of a superconducting circuit incorporating graphene-based Josephson junctions. Furthermore, we show that this device can be operated as a voltage-tunable transmon qubit^7-9, whose spectrum reflects the electronic properties of massless Dirac fermions travelling ballistically^4,5. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying van der Waals materials using microwave photons in coherent quantum circuits.

Majorana Superconducting Qubit

We propose a platform for universal quantum computation that uses conventional s-wave superconducting leads to address a topological qubit stored in spatially separated Majorana bound states in a multiterminal topological superconductor island. Both the manipulation and readout of this "Majorana superconducting qubit" are realized by tunnel couplings between Majorana bound states and the superconducting leads. The ability of turning on and off tunnel couplings on demand by local gates enables individual qubit addressability while avoiding cross-talk errors. By combining the scalability of superconducting qubit and the robustness of topological qubits, the Majorana superconducting qubit may provide a promising and realistic route towards quantum computation.