Superconducting & hybrid quantum hardware

Substrate surface preparation is a key step in the fabrication of electronic devices. In III--V semiconductor platforms, e.g. used in HEMTs and lasers, removal of the native substrate oxide is extremely important, where improper removal will negatively affect end-of-line device performance. However, the impact of substrate preparation in hybrid superconductor--semiconductor (S--Sm) systems relevant to quantum information applications remains poorly understood. This study compares three surface preparations for the deposition of sputtered Nb films on InP: (i) no intentional oxide removal (control), (ii) \textit{in-situ} Ar⁺ milling, and (iii) S-passivation. \textit{In-situ} Ar⁺ milling reduces the O concentration at the metal--substrate (MS) interface, but also roughens the InP surface, increasing the effective thickness of the Nb--InP interface and promoting O incorporation through extended defects in the Nb film. S-passivation suppresses interfacial O more effectively while preserving a sharper and smoother buried interface. It also yields Nb films with higher superconducting transition temperatures and less structural damage than the Ar⁺-milled samples. Despite these materials improvements, the microwave response is comparable across the three preparations. At single photon powers, the highest internal quality factors, Qi, are approximately 1.30×10⁵ (130k) for the control resonators, 9.7×10⁴ (97k) for the S-passivated resonators, and 8.4×10⁴ (84k) for the Ar⁺-milled resonators. These results suggest that the present devices are not primarily limited by dielectric loss at the buried Nb--InP interface.

Native oxide formation (NbOx) at the niobium (Nb) metal–air interface is a source of microwave loss and performance variability in superconducting resonators. We introduce vapor-phase hexamethyldisilazane (HMDS) as a dry surface passivation treatment compatible with standard nanofabrication workflows. In five independent fabrication runs, HMDS-passivated resonators consistently demonstrate improved internal quality factor (Qi) and narrower performance distribution relative to paired unpassivated controls. The Qi improvement occurs across the full microwave power range, suggesting NbOx suppression as a contributing mechanism. Statistical depth profile analysis of Nb oxidation state by electron energy loss spectroscopy corroborates this mechanism, revealing smaller chemical shifts and shallower oxidation depth in passivated specimens relative to the control. Furthermore, re-measurement after 60 days of ambient storage shows that HMDS-passivated resonators retain their Qi, indicating their ambient stability. These results establish vapor-phase HMDS as a surface passivation strategy with strong potential for superconducting quantum devices.

The unitary synthesis problem (Aaronson-Kuperberg, CCC 2007) asks whether every $n$-qubit unitary $U$ is computable by efficient quantum circuits relative to some classical oracle f = fU depending on $U$. Recently, Lombardi-Ma-Wright (STOC 2024) proved that Haar-random unitaries cannot be efficiently synthesized by algorithms that make 1 query (or poly$(n)$ parallel queries) to an arbitrary classical oracle. In this work, we prove several results about the hardness (and easiness!) of variants of unitary synthesis. Our results include: (1) 1-query vs. 2-query unitary synthesis: we prove 1-query lower bounds for synthesizing random permutation unitaries P x⟩ = π(x)⟩, as well as random alternating-basis phase unitaries F2 · H n · F1. This gives 1-query lower bounds for "explicit" families of unitaries that have efficient (even 2-query) synthesis algorithms. (2) Upper bound for complex phase unitaries: we also consider complex phase unitaries x⟩ αx x⟩, which have a clean 2-query synthesis algorithm with no obvious 1-query algorithm. In this case, we prove an upper bound: there are 1-query algorithms (relative to binary phase oracles) that constant-approximate these unitaries in diamond distance. In order to prove our lower bounds, we introduce and analyze two new cryptographic games: the oracle state search game and the oracle Choi state game. Compared to prior work, our framework is mathematically simple, more flexible in what it can prove, and more accurately captures the hardness of synthesizing unitaries that are not "fully random". Finally, we also use the search game to prove a new hardness-of-approximation result for quantum programs (synthesizing unitaries relative to quantum advice) for phase unitaries, giving a sharper separation between 1-query unitary synthesis and quantum programs.

Abstract Van der Waals (vdW) superconductors remain superconducting down to the monolayer limit, enabling the exploration of emergent physical phenomena and functionality driven by reduced dimensionality. Here, we report the characterization of the kinetic inductance of atomically thin NbSe 2, a two-dimensional van der Waals superconductor, using superconducting coplanar waveguides and microwave measurement techniques familiar to circuit quantum electrodynamics (cQED). The kinetic inductance scales inversely with the number of NbSe 2 layers, reaching 1.2 nH/ □ in the monolayer limit. Furthermore, the measured kinetic inductance exhibits a thickness-dependent crossover from clean- to dirty-limit behavior, with enhanced dirty-limit contributions emerging in the ultra-thin regime. These effects are likely driven by increased surface scattering, multi-band superconductivity, and geometric confinement. Additionally, the self-Kerr nonlinearity of the NbSe 2 films ranges from K/2π = −0.006 to −14.7 Hz/photon, indicating its strong potential in applications requiring compact, nearly linear, high-inductance superconducting quantum devices and detectors. The fabrication and characterization techniques demonstrated here are extensible to the investigation of other two-dimensional superconductors.

The superconducting diode effect is an asymmetry in the critical current with respect to the supercurrent polarity. One impetus driving recent interest in the effect is its dependence on intrinsic or microscopic symmetry breaking mechanisms. Here, we study the superconducting diode effect in gated planar Josephson junctions fabricated on a superconductor--semiconductor heterostructure under an in-plane magnetic field. We observe two gate-driven inversions of the diode polarity in the vicinity of zero field, as well as a third-harmonic component in the dependence of the diode efficiency on the in-plane field angle. We analyze the Lifshitz invariant for an arbitrary spin--orbit coupling and show that multiple polarity inversions are possible in the presence of both linear and cubic Dresselhaus terms, where the Rashba parameter varies monotonically with gate voltage. Numerical calculations of the diode efficiency further reveal the presence of higher harmonics in its field-angle dependence in the presence of spin--orbit coupling.

Non-Hermitian systems exhibit phenomena absent from Hermitian systems, including exceptional points (EPs), at which two or more eigenvectors coalesce. Conventional implementations rely on gain and loss, which strongly limit quantum coherence. Here, following a proposal by Wang and Clerk (PRA 2019), we realize a closed four-mode quantum system that emulates the dynamics of a PT dimer - two coupled resonators with balanced gain and loss - without engineered dissipation. The four modes are implemented as harmonics of a superconducting coplanar-waveguide resonator, with parametric couplings engineered using a current-pumped SNAIL. We use this device as a sensor for small variations in the PT dimer coupling strength. From signal-to-noise-ratio measurements, we observe enhanced sensitivity near the EP in a non-quantum-limited regime.

Quantum interconnects distribute entanglement via controlled light-matter interactions for quantum computing and sensing applications. Many entanglement generation schemes use coherent, reversible interactions that require precisely calibrated pulses to execute. In contrast, driven-dissipative protocols use a continuous-wave drive in the presence of correlated dissipation to stabilize entanglement in protected (dark) states. However, the same dissipation that generates the entanglement also limits its utility once the stabilization protocol ends. Here, we engineer a superconducting system of two giant artificial atoms coupled sequentially to a waveguide, with tunable individual and correlated dissipation enabled by interference between coupling points. Continuously driving the atoms through the waveguide exploits correlated dissipation to generate remote entanglement. We then tune the qubit frequencies in situ to suppress individual dissipation and thereby preserve the entanglement, achieving a Bell-state fidelity F = 0.89 +/- 0.02. This demonstration indicates that the driven dissipation of giant atoms is a viable approach for distributing entanglement across quantum networks.

Arrays of Josephson junctions can be tuned through anomalous metallic, quantum-critical, and insulating regimes. We introduce an alternative experimental probe, capturing microwave radiation across all three regimes, using a two-dimensional array of superconductor-semiconductor hybrid Josephson junctions as a model system. Our approach allows calibration of the sample’s circuit parameters and provides isolation from measurement back-action effects. We measure the radiation temperature of the anomalous metal and find that it is hotter than both the quantum-critical and insulating regimes. We further show that the anomalous metallic regime is more susceptible to additional heating than other regimes, explaining its emergence in otherwise thermalized systems. Turning to the quantum-critical regime, we discover nonlinear scaling of radiative noise with applied bias, consistent with theoretical predictions of universal nonequilibrium behavior at quantum-critical points.

Andreev bound states are coherent electron-hole superpositions that form in a normal metal through repeated Andreev reflection at a superconducting interface. When the length of a superconducting segment is comparable to the coherence length, the bound states on opposite sides of the segment hybridize through quasiparticle tunneling. In a periodic array, these hybridized Andreev bound states form energy bands below the superconducting gap. We develop a theoretical framework for transport in such Andreev crystals. We demonstrate that, at high interface transparency, a constant phase bias between neighboring superconductors renders the bands: one band contains only right-moving and the other only left-moving electronic states. This property leads to a directional conductance that enables the device to operate as a flux- and bias-voltage-tunable filter that allows signal transmission in only one direction.

Non-Hermitian Hamiltonians with complex eigenenergies are useful tools for describing the dynamics of open quantum systems. In particular, parity and time (PT) symmetric Hamiltonians have generated interest due to the emergence of exceptional-point degeneracies, where both eigenenergies and eigenvectors coalesce as the energy spectrum transitions from real to complex valued. Because of the abrupt spectral response near exceptional points, such systems have been proposed as candidates for precision quantum sensing. In this Letter, we emulate a passive PT dimer using a two-mode, non-Hermitian system of superconducting qubits comprising one high-coherence qubit coupled to an intentionally lossy qubit via a tunable coupler. The loss is introduced by strongly coupling the qubit to a continuum of photonic modes in an open waveguide environment. Using both pulsed and continuous-wave measurements, we characterize the system dynamics near the exceptional point. We observe a behavior broadly consistent with an ideal passive PT dimer with some corrections due to the tunable coupler element. We extract the complex eigenenergies associated with the two modes and calculate the sensitivity as a function of the coupling strength. Confirming theoretical predictions, we observe no sensitivity enhancement near the quantum exceptional point. This Letter elucidates the limitations of exceptional-point systems as candidates for quantum-enhanced sensing. We establish waveguide quantum electrodynamics as a versatile platform for exploring non-Hermitian quantum dynamics in superconducting circuits.

The gatemon qubits, made of transparent superconducting-semiconducting Josephson junctions, typically have even weaker anharmonicity than the opaque AlOx-junction transmons. However, flux-frustrated gatemons can acquire a much stronger anharmonicity, originating from the interference of the higher-order harmonics of the supercurrent. Here we investigate this effect of enhanced anharmonicity in split-junction gatemon devices based on InAs-Al 2D heterostructure. We find that anharmonicity in excess of 100% can be routinely achieved at the half-integer flux sweet-spot without any need for electrical gating or excessive sensitivity to the offset charge noise. We verified that such intrinsically large anharmonicity enables our devices to be driven coherently with raw Rabi frequencies exceeding 100 MHz, without any pulse shaping, simplifying implementation and control compared to traditional gatemons and transmons. Furthermore, by analyzing a relatively high-resolution spectroscopy of the device transitions as a function of flux, we were able to extract fine details of the current-phase relation, to which transport measurements would hardly be sensitive. The strong anharmonicity of our anharmonic tunable transmons, along with their bare-bones design, can prove to be a precious resource that transparent superconducting-semiconducting junctions bring to quantum information processing.

Developing a dark matter detector with wide mass tunability is an immensely desirable property, yet, it is challenging due to maintaining strong sensitivity. Resonant cavities for dark matter detection have traditionally employed mechanical tuning, moving parts around to change electromagnetic boundary conditions. However, these cavities have proven challenging to operate in sub-Kelvin cryogenic environments due to differential thermal contraction, low heat capacities, and low thermal conductivities. Instead, we develop an electronically tunable cavity architecture by coupling a superconducting 3D microwave cavity with a dc flux tunable superconducting quantum interference device. With a flux delivery system engineered to maintain high coherence in the cavity, we perform a hidden-photon dark matter search below the quantum-limited threshold. A microwave photon counting technique is employed through repeated quantum nondemolition measurements using a transmon qubit. With this device, we perform a hidden-photon search and constrain the kinetic mixing angle to ϵ<8.2×10^{-15} in a tunable band from 5.672 to 5.694 GHz. By coupling multimode tunable cavities to the transmon, wider hidden-photon searching ranges are possible.

The promise of tantalum for realizing superconducting quantum devices has generated interest in its compound films, particularly nitrides. Among these, cubic-phase tantalum carbonitride (TaCxN1−x) offers reduced susceptibility to oxidation and a high critical temperature, yet its microwave properties remain largely unexplored. Here, we investigate plasma-enhanced atomic layer deposition of cubic-phase TaCxN1−x thin films for superconducting microwave circuits. Structural and transport measurements reveal nanocrystalline morphology with sub-10 nm grains and superconductivity in the dirty limit. Coplanar waveguide resonators exhibit moderately high kinetic inductance (16.8 pH/sq for 30 nm films) with potential for enhancement through dimensional scaling. The films also support high internal quality factors exceeding 105 at 50 mK in the single-photon regime, comparable to granular aluminum. Loss analysis identifies the two-level systems as the dominant limiting mechanism, with potential for further reduction through interface engineering. These results establish atomic layer deposited TaCxN1−x as a promising material for scalable, low-loss, high-inductance superconducting circuits.

Doping-induced superconductivity in group-IV elements may enable quantum functionalities in material systems accessible with well-established semiconductor technologies. Non-equilibrium hyperdoping of group-III atoms into C, Si or Ge can yield superconductivity; however, its origin is obscured by structural disorder and dopant clustering. Here we report the epitaxial growth of hyperdoped Ga:Ge films and trilayer heterostructures by molecular-beam epitaxy with extreme hole concentrations (nh = 4.15 × 1021 cm−3, 17.9% Ga substitution) that yield superconductivity with a critical temperature of Tc = 3.5 K. Synchrotron-based X-ray absorption and scattering methods reveal that Ga dopants are substitutionally incorporated within the Ge lattice, introducing a tetragonal distortion to the crystal unit cell. Our findings, corroborated by first-principles calculations, suggest that the structural order of Ga dopants creates a narrow band for the emergence of superconductivity in Ge, establishing hyperdoped Ga:Ge as a low-disorder, epitaxial superconductor–semiconductor platform. The epitaxial growth of hyperdoped Ga:Ge films and trilayer heterostructures by molecular-beam epitaxy yield superconductivity with a critical temperature of 3.5 K and may enable quantum functionalities in this material system, which is accessible with well-established semiconductor technologies.

We study the low-energy physics of planar Josephson junction structures realized in a quasi-two-dimensional semiconductor system proximity coupled to narrow superconducting films. Using both a recursive Green's function approach and an effective Hamiltonian approximation, we investigate the topological superconducting phase predicted to emerge in this type of system. We first characterize the effects associated with varying the electrostatic potentials applied within the unproximitized semiconductor regions. We then address the problem of optimizing the width of the superconductor films and identifying the optimal regimes characterized by large topological gap values. We find that structures with narrow superconducting films of widths ranging between about 100 and 2004pt0exnm can support topological superconducting phases with gaps up to $40%$ of the parent superconducting gap, significantly larger than those characterizing the corresponding wide-superconductor structures. This work represents the first component of a proposed comprehensive strategy to address this optimization problem in planar Josephson junction structures and realize robust topological devices.

Thin films of vanadium silicide (V-silicide) in the A15 cubic phase (V3Si) are promising for superconducting quantum devices due to their high transition temperature and potential compatibility with scalable semiconductor fabrication. However, solid-phase synthesis often yields secondary silicide phases that degrade performance. Here, we investigate the influence of substrate properties using two silicon-on-insulator architectures: one with a polycrystalline HfO2 buried layer (group A) and the other with amorphous SiO2 (group B). Both systems exhibit superconductivity consistent with V3Si formation, yet structural analysis reveals mixed-phase films in both cases. Crucially, only group A maintains an atomically sharp and chemically stable interface, a prerequisite for phase purity. Prolonged annealing in group A reduces the unwanted V5Si3 phase but also leads to the emergence of Si-rich VSi2, likely due to localized substrate degradation. Preliminary atomic-resolution imaging suggests that HfO2 crystallinity may promote local phase-selective nucleation. These findings highlight the importance of substrate design in promoting phase control and maintaining interfacial integrity in superconducting silicides.

The development of superconducting quantum circuits increasingly involves the exploration of chemically distinct materials and complex multilayered structures. Accelerating this trend may benefit from low-damage, materials-agnostic patterning techniques that are compatible with a broad range of materials. Here, we investigate the utility of low-energy ion beam etching (IBE), a physical patterning technique, as an alternative to reactive ion etching for fabricating low-loss superconducting resonators. We use niobium (Nb) resonators as a test platform, leveraging their well-characterized performance metrics for benchmarking. To address IBE-induced surface redeposition, we introduce an in situ aluminum capping layer combined with targeted post-fabrication chemical treatment. This strategy yields resonators with internal quality factors as high as 6 × 105 in the single-photon regime at 50 mK. These results establish low-energy IBE as a promising patterning technique for superconducting devices, with the potential to accelerate development across chemically diverse and multilayered material platforms.

Planar Josephson junctions (JJs) have emerged as a promising platform for the realization of topological superconductivity and Majorana zero modes. To obtain robust quasi one-dimensional (1D) topological superconducting states using planar JJs, limiting the number of 1D Andreev bound states'subbands that can be present, and increasing the size of the topological superconducting gap, are two fundamental challenges. It has been suggested that both problems can be addressed by properly designing the interfaces between the JJ's normal region and the superconducting leads. We fabricated Josephson junctions with periodic hole structures on the superconducting contact leads on InAs heterostructures with epitaxial superconducting Al. By depleting the chemical potential inside the hole region with a top gate, we observed an enhancement of the supercurrent across the junction. Such an enhancement is reproduced in theoretical simulations. The theoretical analysis shows that the enhancement of the JJ's critical current is achieved when the hole depletion is such to optimize the matching of quasiparticles'wave-function at the normal/superconductor interface. These results show how the combination of carefully designed patterns for the Al coverage, and external gates, can be successfully used to tune the density and wave functions'profiles in the normal region of the JJ, and therefore open a new avenue to tune some of the critical properties, such as number of subbands and size of the topological gap, that must be optimized to obtain robust quasi 1D superconducting states supporting Majorana bound states.

A numerical workflow for the manuscript "Higher-level heating and the identifiability of loss-parameter exponents in low-frequency superconducting qubits".

By coupling a semiconductor-based planar Josephson junction to a superconducting microwave resonator, we investigate the Andreev bound states in the junction using dispersive readout techniques. Using electrostatic gating to create a narrow constriction in the junction, our measurements unveil a strong coupling interaction between the resonator and the Andreev bound states. This enables the mapping of isolated tunable Andreev bound states that can reach near-unity transparency along with an average induced superconducting gap of ∼ 150 µ eV. Exploring the gate parameter space further elucidates a nonmonotonic evolution of multiple Andreev bound states with varying gate voltage. Complementary tight-binding calculations of an Al-InAs planar Josephson junction with strong Rashba spin-orbit coupling provide insight into possible mechanisms responsible for such behavior. Our findings highlight the subtleties of the Andreev spectrum of Josephson junctions fabricated on superconductor-semiconductor heterostructures, offering potential applications in probing topological states in these hybrid platforms.

We present a new style of fluxonium qubit, gatemonium, based on an all-superconductor-semiconductor hybrid platform. The linear inductance is achieved using 600 planar Al - In As Josephson junctions (JJs) in series. By tuning the single junction with a gate voltage, we demonstrate electrostatic control of the effective Josephson energy, tuning the weight of the fictitious phase particle. One- and two-tone spectroscopy of the gatemonium transitions further reveal details of the hybrid plasmon-fluxon spectrum. Accounting for the nonsinusoidal current-phase relation of the single junction, we fit the measured spectra to extract charging and inductive energies. We conduct time-domain characterization of the plasmon modes and find that energy-relaxation times are limited by inductive loss, possibly in the thin aluminum film. We discuss future directions for this platform in gate-voltage-tunable high-plasma-frequency enhanced-impedance junction arrays, and enhanced coherence times for voltage-tunable architectures.

Can superconductivity arise from strong repulsive interactions between electrons in a lattice model with topological bands? Here, the authors answer this question in the affirmative via DMRG numerical simulations of an interacting spinful bilayer Hofstadter model featuring low-lying bands of opposite Chern number. Furthermore, by developing a new technique to probe the pairing symmetry in number-conserving DMRG, the authors demonstrate that superconductivity is $p$-wave, tantalizingly reminiscent of nodal pairing recently observed in twisted bilayer graphene, which shares many structural similarities with their model. This work thus showcases the possibility of an all-electronic pairing mechanism in the strong coupling limit in two dimensions, which can be tested directly with cold fermions in an optical lattice.

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a semiconductor-superconductor two-dimensional Josephson junction array. Tuned by an electrostatic top gate, the system exhibits separate superconducting (S), anomalous metal (M*), and insulating (I) phases, bordered by separatrices of the temperature-dependent sheet resistance Rs. We find that the gate-dependent BKT transition temperature falls to zero at the S-M* boundary, suggesting incomplete vortex-antivortex pairing in the M* phase. In the S phase, Rs is roughly proportional to the perpendicular magnetic field at the BKT transition, as expected, while in the M* phase, Rs deviates from its zero-field value as a power law in the field with exponent close to 1/2 at low temperature. An in-plane magnetic field eliminates the M* phase, leaving a small scaling exponent at the S-I boundary, which we interpret as a remnant of the incipient M* phase.

Majorana bound states (MBSs) are quasiparticles that are their own antiparticles. They are predicted to emerge as zero-energy modes localized at the boundary of a topological superconductor. No intrinsic topological superconductor is known to date. However, by interfacing conventional superconductors and semiconductors with strong spin-orbit coupling, it is possible to create a system hosting topological states. Hence, epitaxial superconductors and semiconductors have emerged as an attractive material system with atomically sharp interfaces and broad flexibility in device fabrications incorporating Josephson junctions. We discuss the basics of topological superconductivity and provide insight into how to go beyond current state-of-the-art experiments. We argue that the ultimate success in realizing MBS physics requires the observation of non-Abelian braiding and fusion experiments. Published by the American Physical Society 2024

The integration of niobium (Nb) into emerging superconducting circuits can enhance their performance and function. However, growth of high purity Nb can be challenging due to its high reactivity with oxygen. Here, we examine the role of residual oxygen inside the growth chamber in transforming the structural, chemical, and superconducting properties of Nb films. We demonstrate that an increase in unintentional oxygen impurities lowers the superconducting critical temperature of Nb. This evolution coincides with the reduction of Nb crystal domains, which are separated by highly disordered oxygen-rich regions. Moreover, chemical analysis reveals the formation of niobium monoxide within the film during growth. These findings provide a comprehensive picture of how residual oxygen in the growth chamber can affect the properties of the Nb films. This study contributes to the materials science and engineering knowledge of superconducting Nb growth.

Planar Josephson junctions provide a platform to host topological superconductivity, which, through manipulating Majorana bound states (MBS), could enable fault-tolerant quantum computing. However, what constitutes experimental signatures of topological superconductivity and how MBS can be detected remains strongly debated. In addition to spurious effects that mimic MBS, there is a challenge to discern the inherent topological signals in realistic systems with many topologically trivial Andreev bound states, determining the transport properties of Josephson junctions. Guided by the advances in microwave spectroscopy, we theoretically study Al/InAs-based planar Josephson junction embedded into a radio-frequency superconducting quantum interference device to identify microwave signatures of topological superconductivity. Remarkably, by exploring the closing and reopening of a topological gap, we show that even in a wide planar Josephson junction with many Andreev bound states, such a topological signature is distinguishable in the resonance frequency shift of a microwave drive and the half-slope feature of the microwave absorption spectrum. Our findings provide an important step towards experimental detection of non-Abelian statistics and implementing scalable topological quantum computing.

The physics of superconductivity in magic-angle twisted bilayer graphene (MATBG) is a topic of keen interest in moiré systems research, and it may provide insight into the pairing mechanism of other strongly correlated materials such as high-Tc superconductors. Here, we use DC-transport and microwave circuit quantum electrodynamics (cQED) to measure directly the superfluid stiffness of superconducting MATBG via its kinetic inductance. We find the superfluid stiffness to be much larger than expected from conventional Fermi liquid theory; rather, it is comparable to theoretical predictions involving quantum geometric effects that are dominant at the magic angle. The temperature dependence of the superfluid stiffness follows a power-law, which contraindicates an isotropic BCS model; instead, the extracted power-law exponents indicate an anisotropic superconducting gap, whether interpreted within the Fermi liquid framework or by considering quantum geometry of flat-band superconductivity. Moreover, a quadratic dependence of the superfluid stiffness on both DC and microwave current is observed, which is consistent with Ginzburg-Landau theory. Taken together, our findings indicate that MATBG is an unconventional superconductor with an anisotropic gap and strongly suggest a connection between quantum geometry, superfluid stiffness, and unconventional superconductivity in MATBG. The combined DC-microwave measurement platform used here is applicable to the investigation of other atomically thin superconductors.

We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply e-i Ht for an unknown local Hamiltonian H = ∑a = 1m λa Ea on $n$ qubits, the goal is to recover $H$. This problem is already well-understood under the assumption that the interaction terms, Ea, are given, and only the interaction strengths, λa, are unknown. But how efficiently can we learn a local Hamiltonian without prior knowledge of its interaction structure? We present a new, general approach to Hamiltonian learning that not only solves the challenging structure learning variant, but also resolves other open questions in the area, all while achieving the gold standard of Heisenberg-limited scaling. In particular, our algorithm recovers the Hamiltonian to ε error with total evolution time O((n)/ε), and has the following appealing properties: (1) it does not need to know the Hamiltonian terms; (2) it works beyond the short-range setting, extending to any Hamiltonian $H$ where the sum of terms interacting with a qubit has bounded norm; (3) it evolves according to $H$ in constant time $t$ increments, thus achieving constant time resolution. As an application, we can also learn Hamiltonians exhibiting power-law decay up to accuracy ε with total evolution time beating the standard limit of 1/ε².

The tunneling of Cooper pairs across a Josephson junction (JJ) allows for the nonlinear inductance necessary to construct superconducting qubits, amplifiers, and various other quantum circuits. An alternative approach using hybrid superconductor-semiconductor JJs can enable superconducting qubit architectures with all electric control. Here we present continuous-wave and time-domain characterization of gatemon qubits and coplanar waveguide resonators based on an InAs two-dimensional electron gas. We show that the qubit undergoes a vacuum Rabi splitting with a readout cavity, and we drive coherent Rabi oscillations between the qubit ground and first excited states. We measure qubit relaxation times to be T 1 = 100 ns over a 1.5 GHz tunable band. We detail the loss mechanisms present in these materials through a systematic study of the quality factors of coplanar waveguide resonators. While various loss mechanisms are present in III-V gatemon circuits, we detail future directions in enhancing the relaxation times of qubit devices on this platform. Published by the American Physical Society 2024

Uniformly random unitaries, i.e. unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that "look" sufficiently Haar random while also being efficient to implement. Two different notions of derandomisation have emerged: $t$-designs are random unitaries that information-theoretically reproduce the first $t$ moments of the Haar measure, and pseudorandom unitaries (PRUs) are random unitaries that are computationally indistinguishable from Haar random. In this work, we take a unified approach to constructing $t$-designs and PRUs. For this, we introduce and analyse the "$PFC$ ensemble", the product of a random computational basis permutation $P$, a random binary phase operator $F$, and a random Clifford unitary $C$. We show that this ensemble reproduces exponentially high moments of the Haar measure. We can then derandomise the $PFC$ ensemble to show the following: (1) Linear-depth $t$-designs. We give the first construction of a (diamond-error) approximate $t$-design with circuit depth linear in $t$. This follows from the $PFC$ ensemble by replacing the random phase and permutation operators with their $2t$-wise independent counterparts. (2) Non-adaptive PRUs. We give the first construction of PRUs with non-adaptive security, i.e. we construct unitaries that are indistinguishable from Haar random to polynomial-time distinguishers that query the unitary in parallel on an arbitary state. This follows from the $PFC$ ensemble by replacing the random phase and permutation operators with their pseudorandom counterparts. (3) Adaptive pseudorandom isometries. We show that if one considers isometries (rather than unitaries) from $n$ to n + ω(n) qubits, a small modification of our PRU construction achieves general adaptive security.

Abstract There has recently been a surge of interest in studying the superconducting diode effect (SDE) partly due to the possibility of uncovering the intrinsic properties of a material system. A change of sign of the SDE at finite magnetic field has previously been attributed to different mechanisms. Here, we observe the SDE in epitaxial Al-InAs Josephson junctions with strong Rashba spin-orbit coupling (SOC). We show that this effect strongly depends on the orientation of the in-plane magnetic field. In the presence of a strong magnetic field, we observe a change of sign in the SDE. Simulation and measurement of supercurrent suggest that depending on the superconducting widths, WS, this sign change may not necessarily be related to 0–π or topological transitions. We find that the strongest sign change in junctions with narrow WS is consistent with SOC-induced asymmetry of the critical current under magnetic-field inversion, while in wider WS, the sign reversal could be related to 0–π transitions and topological superconductivity.

In superconducting systems in which inversion and time-reversal symmetry are simultaneously broken the critical current for positive and negative current bias can be different. For superconducting systems formed by Josephson junctions (JJs) this effect is termed Josephson diode effect. In this paper, we study the Josephson diode effect for a superconducting quantum interference device (SQUID) formed by a topological JJ with a 4π-periodic current-phase relationship and a topologically trivial JJ. We show how the fractional Josephson effect manifests in the Josephson diode effect with the application of a magnetic field and how tuning properties of the trivial SQUID arm can lead to diode polarity switching. We then investigate the ac response and show that the polarity of the diode effect can be tuned by varying the ac power and discuss differences between the ac diode effect of asymmetric SQUIDs with no topological JJ and SQUIDs in which one JJ is topological.

Pseudorandom unitaries (PRUs) are ensembles of efficiently implementable unitary operators that cannot be distinguished from Haar random unitaries by any quantum polynomial-time algorithm with query access to the unitary. We present a simple PRU construction that is a concatenation of a random Clifford unitary, a pseudorandom binary phase operator, and a pseudorandom permutation operator. We prove that this PRU construction is secure against non-adaptive distinguishers assuming the existence of quantum-secure one-way functions. This means that no efficient quantum query algorithm that is allowed a single application of U poly(n) can distinguish whether an $n$-qubit unitary $U$ was drawn from the Haar measure or our PRU ensemble. We conjecture that our PRU construction remains secure against adaptive distinguishers, i.e. secure against distinguishers that can query the unitary polynomially many times in sequence, not just in parallel.

We investigate the interplay between the quantum Hall (QH) effect and superconductivity in InAs surface quantum well (SQW)/NbTiN heterostructures using a quantum point contact (QPC). We use QPC to control the proximity of the edge states to the superconductor. By measuring the upstream and downstream resistances of the device, we investigate the efficiency of Andreev conversion at the InAs/NbTiN interface. Our experimental data is analyzed using the Landauer-B\"uttiker formalism, generalized to allow for Andreev reflection processes. We show that by varying the voltage of the QPC, VQPC, the average Andreev reflection, $A$, at the QH-SC interface can be tuned from 50% to ∼10%. The evolution of $A$ with VQPC extracted from the measurements exhibits plateaus separated by regions for which $A$ varies continuously with VQPC. The presence of plateaus suggests that for some ranges of VQPC the QPC might be pinching off almost completely from the QH-SC interface some of the edge modes. Our work shows an experimental setup to control and advance the understanding of the complex interplay between superconductivity and QH effect in two-dimensional gas systems.

Quenched disorder slows down the scrambling of quantum information. Using a bottom-up approach, we formulate a kinetic theory of scrambling in a correlated metal near a superconducting transition, following the scrambling dynamics as the impurity scattering rate is increased. Within this framework, we rigorously show that the butterfly velocity $v$ is bounded by the light-cone velocity vlc set by the Fermi velocity. We analytically identify a disorder-driven dynamical transition occurring at small but finite disorder strength between a spreading of information characterized at late times by a discontinuous shock wave propagating at the maximum velocity vlc, and a smooth traveling wave belonging to the Fisher or Kolmogorov-Petrovsky-Piskunov (FKPP) class and propagating at a slower, if not considerably slower, velocity $v$. In the diffusive regime, we establish the relation v²/λFKPP∼Del, where λFKPP is the Lyapunov exponent set by the inelastic scattering rate and Del is the elastic diffusion constant.

The sudden depinning of vortices with increasing current through a super-semihybrid Josephson junction array results in a burst of differential resistance at integer and half-integer peaks of critical current. A striking feature is the split feature at $f=0$, indicating the absence of vortices at precisely zero field. The flat-topped portion at $f=1/2$ and the slanted top part at $f=1$ also reveal features of how the dynamical transition occurs.

We describe the generation of entangling gates on superconductor-semiconductor hybrid qubits by ac voltage modulation of the Josephson energy. Our numerical simulations demonstrate that the unitary error can be below 10⁻⁵ in a variety of 75-ns-long two-qubit gates (CZ, iSWAP, and iSWAP) implemented using parametric resonance. We analyze the conditional $ZZ$ phase and demonstrate that the CZ gate needs no further phase-correction steps, while the $ZZ$ phase error in swap-type gates can be compensated by choosing pulse parameters. With decoherence considered, we estimate that qubit relaxation time needs to exceed 700.2em0ex to achieve the 99.9% fidelity threshold.

We study the problem of learning a local quantum Hamiltonian $H$ given copies of its Gibbs state ρ= e-βH/tr(e-βH) at a known inverse temperature $β>0$. Anshu, Arunachalam, Kuwahara, and Soleimanifar (arXiv:2004.07266) gave an algorithm to learn a Hamiltonian on $n$ qubits to precision $ε$ with only polynomially many copies of the Gibbs state, but which takes exponential time. Obtaining a computationally efficient algorithm has been a major open problem [Alhambra'22 (arXiv:2204.08349)], [Anshu, Arunachalam'22 (arXiv:2204.08349)], with prior work only resolving this in the limited cases of high temperature [Haah, Kothari, Tang'21 (arXiv:2108.04842)] or commuting terms [Anshu, Arunachalam, Kuwahara, Soleimanifar'21]. We fully resolve this problem, giving a polynomial time algorithm for learning $H$ to precision $ε$ from polynomially many copies of the Gibbs state at any constant $β> 0$. Our main technical contribution is a new flat polynomial approximation to the exponential function, and a translation between multi-variate scalar polynomials and nested commutators. This enables us to formulate Hamiltonian learning as a polynomial system. We then show that solving a low-degree sum-of-squares relaxation of this polynomial system suffices to accurately learn the Hamiltonian.

Quasiparticle (QP) effects play a significant role in the coherence and fidelity of superconducting quantum circuits.The Andreev bound states of high-transparency Josephson junctions can act as low-energy traps for QPs, providing a mechanism for studying the dynamics and properties of both the QPs and the junction.Using locally injected and thermal QPs, we study QP loss and QP poisoning in epitaxial Al-InAs Josephson junctions incorporated in a superconducting quantum interference device (SQUID) galvanically shorting a superconducting resonator to ground.We observe changes in the resonance line shape and frequency shifts consistent with QP trapping into and clearing out of the ABSs of the junctions when the junctions are phase biased.By monitoring the QP trapping and clearing mechanisms in time, we find a time scale of O(1 µs) for these QP dynamics, consistent with the presence of phonon-mediated QP-QP interactions.Our measurements suggest that electron-phonon interactions play a significant role in the relaxation mechanisms of our system, while electron-photon interactions and electron-phonon interactions govern the clearing mechanisms.Our results highlight the QP-induced dissipation and complex QP dynamics in superconducting quantum circuits fabricated on superconductor-semiconductor heterostructures.

The use of electric fields to modify chemical reactions is a promising, emerging technique in catalysis. However, there exist few guiding principles, and rational design requires assumptions about the transition state or explicit atomistic calculations. Here, we present a linear free energy relationship, familiar in other areas of physical organic chemistry and catalysis, that microscopically relates field-induced changes in the activation energy to those in the reaction energy, connecting kinetic and thermodynamic behaviors. We verify our theory using first-principles electronic structure calculations of a symmetric SN2 reaction and the dehalogenation of an aryl halide on gold surfaces and observe hallmarks of linear free energy relationships, such as the shifting to early and late transition states. We also report and explain a counterintuitive case, where the constant of proportionality relating the activation and reaction energies is negative.

We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.

Superconducting germanium films are an intriguing material for possible applications in fields such as cryogenic electronics and quantum bits. Recently, there has been a great deal of progress in hyperdoping of Ga doped Ge using ion implantation. Thin film growth of such a material would be advantageous, allowing homoepitaxy of doped and undoped Ge films and opening possibilities for vertical Josephson junctions. Here, we present our studies on the growth of one layer of hyperdoped superconducting germanium thin film via molecular beam epitaxy. We observe a fragile superconducting phase, which is extremely sensitive to processing conditions and can easily phase-segregate, forming a percolated network of pure gallium metal. By suppressing phase segregation through temperature control, we find a superconducting phase that is unique and appears coherent to the underlying Ge substrate.

Abstract Adoption of fast, parametric coupling elements has improved the performance of superconducting qubits, enabling recent demonstrations of quantum advantage in randomized sampling problems. The development of low loss, high contrast couplers is critical for scaling up these systems. We present a blueprint for a gate-tunable coupler realized with a two-dimensional electron gas in an InAs/InGaAs heterostructure. Rigorous numerical simulations of the semiconductor and high frequency electromagnetic behavior of the coupler and microwave circuitry yield an on/off ratio of more than one order of magnitude. We give an estimate of the dielectric-limited loss from the inclusion of the coupler in a two qubit system, with coupler coherences ranging from a few to tens of microseconds.

We study quantum transport and AC Josephson effect of hexagonal boron nitride encapsulated graphene (BGB) Josephson junctions (JJs). Our experiments reveal the emergence of the half-integer Shapiro steps in the n-type regime with high electron carrier densities. We attribute this observation to the gate-tunable transmission probability of the graphene junction. Our numerical simulations are consistent with the appearance of half-integer Shapiro steps at high transparency, which suggests a skewed current phase relationship in the graphene JJ.

We build a parametric amplifier with a Josephson field-effect transistor (JoFET) as the active element. The resonant frequency of the device is field-effect tunable over a range of 20.2em0exGHz. The JoFET amplifier has 200.2em0exdB of gain, 40.2em0exMHz of instantaneous bandwidth, and a 1-dB compression point of-125.50.2em0exdBm when operated at a fixed resonance frequency.

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100 G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Quenched disorder slows down the scrambling of quantum information. Using a bottom-up approach, we formulate a kinetic theory of scrambling in a correlated metal near a superconducting transition, following the scrambling dynamics as the impurity scattering rate is increased. Within this framework, we rigorously show that the butterfly velocity $v$ is bounded by the light cone velocity v lc set by the Fermi velocity. We analytically identify a disorder-driven dynamical transition occurring at small but finite disorder strength between a spreading of information characterized at late times by a discontinuous shock wave propagating at the maximum velocity v lc, and a smooth traveling wave belonging to the Fisher or Kolmogorov-Petrovsky-Piskunov (FKPP) class and propagating at a slower, if not considerably slower, velocity $v$. In the diffusive regime, we establish the relation v²/λ FKPP ∼ D el where λ FKPP is the Lyapunov exponent set by the inelastic scattering rate and D el is the elastic diffusion constant.

We describe the generation of entangling gates on superconductor-semiconductor hybrid qubits by ac voltage modulation of the Josephson energy. Our numerical simulations demonstrate that the unitary error can be below 10⁻⁵ in a variety of 75-ns-long two-qubit gates (CZ, $i$SWAP, and iSWAP) implemented using parametric resonance. We analyze the conditional ZZ phase and demonstrate that the CZ gate needs no further phase correction steps, while the ZZ phase error in SWAP-type gates can be compensated by choosing pulse parameters. With decoherence considered, we estimate that qubit relaxation time needs to exceed 70μs to achieve the 99.9% fidelity threshold.

Voltage-tunable superconductor-semiconductor devices offer a unique platform to realize dynamic tunability in superconducting quantum circuits. By galvanically connecting a gated InAs-Al Josephson junction to a coplanar waveguide resonator, we demonstrate the use of a superconducting element with wideband gate tunability. We show that the resonant frequency is controlled via a gate-tunable Josephson inductance and that the nonlinearity of the InAs-Al junction is nondissipative as is the case with conventional AlOx-Al junctions. As the gate voltage is decreased, the inductive participation of the junction increases up to 44%, resulting in the resonant frequency being tuned by over 20.2em0exGHz. Utilizing the wide tunability of the device, we demonstrate that two resonant modes can be adjusted such that they strongly hybridize, exhibiting an avoided-level crossing with a coupling strength of 510.2em0exMHz. Implementing such voltage-tunable resonators is the first step toward realizing wafer-scale continuous voltage control in superconducting circuits for qubit-qubit coupling, quantum limited amplifiers, and quantum memory platforms.

There has recently been a surge of interest in studying the superconducting diode effect (SDE) partly due to the possibility of uncovering the intrinsic properties of a material system. A change of sign of the SDE at finite magnetic field has previously been attributed to different mechanisms. Here, we observe the SDE in epitaxial Al-InAs Josephson junctions with strong Rashba spin-orbit coupling (SOC). We show that this effect strongly depends on the orientation of the in-plane magnetic field. In the presence of a strong magnetic field, we observe a change of sign in the SDE. Simulation and measurement of supercurrent suggest that depending on the superconducting widths, WS, this sign change may not necessarily be related to 0--$π$ or topological transitions. We find that the strongest sign change in junctions with narrow WS is consistent with SOC-induced asymmetry of the critical current under magnetic-field inversion, while in wider WS, the sign reversal could be related to 0--$π$ transitions and topological superconductivity.

High Resolution Image Download MS PowerPoint Slide 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.

The microscopic origin of $1/f$ magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here we apply weak in-plane magnetic fields to a capacitively-shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent $1/f$ noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure dephasing time in fields up to B=100~G. With direct noise spectroscopy, we further observe a transition from a $1/f$ to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of $1/f$ flux noise in superconducting circuits.

Routing quantum information between non-local computational nodes is a foundation for extensible networks of quantum processors. Quantum information transfer between arbitrary nodes is generally mediated either by photons that propagate between them or by resonantly coupling nearby nodes. The utility is determined by the type of emitter, propagation channel and receiver. Conventional approaches involving propagating microwave photons have limited fidelity due to photon loss and are often unidirectional, whereas architectures that use direct resonant coupling are bidirectional in principle but can generally accommodate only a few local nodes. Here we demonstrate high-fidelity, on-demand, directional, microwave photon emission. We do this using an artificial molecule comprising two superconducting qubits strongly coupled to a bidirectional waveguide, effectively creating a chiral microwave waveguide. Quantum interference between the photon emission pathways from the molecule generates single photons that selectively propagate in a chosen direction. This circuit will also be capable of photon absorption, making it suitable for building interconnects within extensible quantum networks. Light could be used to carry quantum information in networks, but this requires methods to prepare and control individual photons. A superconducting circuit can controllably emit photons in either direction along a microwave waveguide.

As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multiqubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique naturally builds on standard process tomography and T1/T2 measurement protocols, characterizes and accounts for state-preparation and measurement errors, and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.

Transparent contact interfaces in superconductor–graphene hybrid systems are critical for realizing superconducting quantum applications. Here, we examine the effect of the edge contact fabrication process on the transparency of the superconducting aluminum–graphene junction. We show significant improvement in the transparency of our superconductor–graphene junctions by promoting the chemical component of the edge contact etch process. Our results compare favorably with state-of-the-art graphene Josephson junctions. The findings of our study contribute to advancing the fabrication knowledge of edge-contacted superconductor–graphene junctions.

Abstract To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. Such representations ignore redundant features and treat parameters such as velocity and position separately because they can be useful for making statements about different experimental settings. Here, we capture this notion by formally defining the concept of operationally meaningful representations. We present an autoencoder architecture with attention mechanism that can generate such representations and demonstrate it on examples involving both classical and quantum physics. For instance, our architecture finds a compact representation of an arbitrary two-qubit system that separates local parameters from parameters describing quantum correlations.

In the presence of a 4$π$-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 Bθ. We find that the odd steps reappear at a crossover Bθ 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 non-adiabatic dynamics of the junction. 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.

The anomalous Hall effect, a hallmark of broken time-reversal symmetry and spin–orbit coupling, is frequently observed in magnetically polarized systems. However, its realization in nominally non-magnetic systems remains elusive. Here, we report on the observation of the anomalous Hall effect in nominally non-magnetic KTaO3. Anomalous Hall effect emerges in reduced KTaO3 and shows an extrinsic to intrinsic crossover. A paramagnetic behavior is observed in reduced samples and confirmed using first principles calculations. The observed anomalous Hall effect follows the oxygen vacancy-induced magnetization response, suggesting that the localized magnetic moments of the oxygen vacancies scatter conduction electrons asymmetrically and give rise to the anomalous Hall effect. The anomalous Hall conductivity is found to be insensitive to the scattering rate in the low temperature limit (T < 5 K), implying that the Berry curvature of the electrons on the Fermi surface controls the anomalous Hall effect. Our observations provide a detailed picture of many-body interactions, which trigger the anomalous Hall effect in a non-magnetic system.

The intersection of two-dimensional superconductivity and topologically nontrivial states hosts a wide range of quantum phenomena, including Majorana fermions. We report on the observation of two-dimensional superconductivity and weak anti-localization at the TiOx/KTaO3 (111) interfaces. A remnant, saturating resistance persists below the transition temperature as superconducting puddles fail to reach phase coherence. Signatures of weak anti-localization are observed near the superconducting transition, suggesting the coexistence of superconducting fluctuations and quantum coherent quasiparticle effects. The superconducting interfaces show roughly one order of magnitude larger weak anti-localization correction, compared to non-superconducting interfaces, alluding to a relatively large coherence length in these interfaces.

Cavity quantum electrodynamics, which explores the granularity of light by coupling a resonator to a nonlinear emitter1, has played a foundational role in the development of modern quantum information science and technology. In parallel, the field of condensed matter physics has been revolutionized by the discovery of underlying topological2–4, often arising from the breaking of time-reversal symmetry, as in the case of the quantum Hall effect. In this work, we explore the cavity quantum electrodynamics of a transmon qubit in a topologically nontrivial Harper–Hofstadter lattice5. We assemble the lattice of niobium superconducting resonators6 and break time-reversal symmetry by introducing ferrimagnets7 before coupling the system to a transmon qubit. We spectroscopically resolve the individual bulk and edge modes of the lattice, detect Rabi oscillations between the excited transmon and each mode and measure the synthetic-vacuum-induced Lamb shift of the transmon. Finally, we demonstrate the ability to employ the transmon to count individual photons8 within each mode of the topological band structure. This work opens the field of experimental chiral quantum optics9, enabling topological many-body physics with microwave photons 10,11 and providing a route to backscatter-resilient quantum communication. Edge modes in chiral topological systems can carry quantum information without backscattering. A topological lattice of superconducting resonators has been coupled to a qubit, providing a platform for chiral quantum electrodynamics and communication.

Indium arsenide (InAs) near surface quantum wells (QWs) are promising for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work, we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance, consistent with a very high Andreev conversion. We analyze the experimental data using the Landauer-Büttiker formalism, generalized to allow for Andreev reflection processes. We attribute the high efficiency of Andreev conversion in our devices to the large transparency of the InAs/NbTiN interface and the consequent strong hybridization of the QH edge modes with the states in the superconductor.

A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems.

Dielectrics with low loss at microwave frequencies are imperative for high-coherence solid-state quantum computing platforms. Here we study the dielectric loss of hexagonal boron nitride (hBN) thin films in the microwave regime by measuring the quality factor of parallel-plate capacitors (PPCs) made of NbSe2–hBN–NbSe2 heterostructures integrated into superconducting circuits. The extracted microwave loss tangent of hBN is bounded to be at most in the mid-10−6 range in the low-temperature, single-photon regime. We integrate hBN PPCs with aluminium Josephson junctions to realize transmon qubits with coherence times reaching 25 μs, consistent with the hBN loss tangent inferred from resonator measurements. The hBN PPC reduces the qubit feature size by approximately two orders of magnitude compared with conventional all-aluminium coplanar transmons. Our results establish hBN as a promising dielectric for building high-coherence quantum circuits with substantially reduced footprint and with a high energy participation that helps to reduce unwanted qubit cross-talk. Parallel-plate capacitors of the two-dimensional materials hBN and NbSe2 are integrated with aluminium Josephson junctions to realize transmon qubits with coherence times reaching 25 μs.

The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.

The intersection of two-dimensional superconductivity and topologically nontrivial states hosts a wide range of quantum phenomena, including Majorana fermions. Coexistence of topologically nontrivial states and superconductivity in a single material, however, remains elusive. Here, we report on the observation of two-dimensional superconductivity and weak anti-localization at the TiOx/KTaO3(111) interfaces. A remnant, saturating resistance persists below the transition temperature as superconducting puddles fail to reach phase coherence. Signatures of weak anti-localization are observed below the superconducting transition, suggesting the coexistence of superconductivity and weak anti-localization. The superconducting interfaces show roughly one order of magnitude larger weak anti-localization correction, compared to non-superconducting interfaces, alluding to a relatively large coherence length in these interfaces.

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 strong fingerprint from the two-component nature of the hybrid system, and quantitatively compare with a theory that includes the contribution of intraband p ± i p 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.

Superconductor-semiconductor hybrids are platforms for realizing effective $p$-wave superconductivity. Spin-orbit coupling, combined with the proximity effect, causes the two-dimensional semiconductor to inherit p ± i p intraband pairing, and application of magnetic field can then result in transitions to the normal state, partial Bogoliubov Fermi surfaces, or topological phases with Majorana modes. Experimentally probing the hybrid superconductor-semiconductor interface is challenging due to the shunting effect of the conventional superconductor. Consequently, the nature of induced pairing remains an open question. Here, we use the circuit quantum electrodynamics architecture to probe induced superconductivity in a two dimensional Al-InAs hybrid system. We observe a strong suppression of superfluid density and enhanced dissipation driven by magnetic field, which cannot be accounted for by the depairing theory of an $s$-wave superconductor. These observations are explained by a picture of independent intraband p ± i p superconductors giving way to partial Bogoliubov Fermi surfaces, and allow for the first characterization of key properties of the hybrid superconducting system.

The critical properties characterizing the formation of the Floquet time crystal in the prethermal phase are investigated analytically in the periodically driven $O(N)$ model. In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and the absence of long-range spatial order from the nontrivial phase where long-range spatial order is accompanied by period-doubling dynamics. In the vicinity of the critical line, with a combination of dimensional expansion and exact solution for N→∞, we determine the exponent ν that characterizes the divergence of the spatial correlation length of the equal-time correlation functions, the exponent β characterizing the growth of the amplitude of the order parameter, as well as the initial-slip exponent θ of the aging dynamics when a quench is performed from deep in the trivial phase to the critical line. The exponents ν,β,θ are found to be identical to those in the absence of the drive. In addition, the functional form of the aging is found to depend on whether the system is probed at times that are small or large compared to the drive period. The spatial structure of the two-point correlation functions, obtained as a linear response to a perturbing potential in the vicinity of the critical line, is found to show algebraic decays that are longer ranged than in the absence of a drive, and besides being period doubled are also found to oscillate in space at the wave vector ω/(2v), v being the velocity of the quasiparticles, and ω being the drive frequency.

High-fluence gallium (Ga⁺) implantation at medium energies is proven to be an effective tool in forming superconducting (SC) thin films in germanium (Ge). By changing the post-implantation annealing conditions nanocrystalline to single-crystalline Ge matrices have been produced. Irrespective of crystallinity, such processes have mostly led to supersaturated Ge:Ga films where superconductivity is controlled by the extent of coherent coupling between Ga precipitates. Here we use Ga⁺ implantation energy as a means to tailor the spatial distribution and the coupling energy of the Ga precipitates. By systematic structural and magneto-transport studies, we unravel the complex connection between the internal structure of Ge:Ga films and their global SC parameters. At the shallowest implantation depth, we observe the strongest coupling leading to a robust superconductivity that sustains parallel magnetic fields as high as 9.95 T, above the conventional Pauli paramagnetic limit and consistent with a quasi-2D geometry. Further measurements at mK temperatures revealed an anomalous upturn in perpendicular critical field B⊥ vs temperature whose curvature and thus origin may be tuned between weakly coupled SC arrays and vortex glass states with quenched disorder. This warrants future investigations into Ge:Ga films for applications where tunable disorder is favorable, including test-beds for quantum phase transitions and superinductors in quantum circuits.

We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZMs) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in a 1DTS is to use T junctions, which allows one to maneuver MZMs in such a manner as to achieve braiding. In this paper, we propose a scheme for implementing quantum logical gates in a purely one-dimensional geometry without T junctions, instead replacing it with an auxiliary qubit. This has the additional benefit of introducing a non-Clifford gate, corresponding to one- and two-logical-qubit $Z$ rotations. We first design a topologically protected logical $Z$ gate based entirely on local interactions within the 1DTS. Using an auxiliary qubit coupled to the topological superconductors, we extend the $Z$ gate to non-Clifford single- and multiqubit arbitrary rotations with partial topological protection. Finally, to perform universal quantum computing, we introduce a scheme for performing arbitrary unitary rotations, albeit without topological protection. We develop a formalism based on unitary braids which creates transitions between different topological phases of the 1DTS system. The unitary formalism can be simply converted to an equivalent adiabatic scheme, which we numerically simulate, and we show that high-fidelity operations should be possible with reasonable parameters.

Qubits on solid state devices could potentially provide the rapid control necessary for developing scalable quantum information processors. Materials innovation and design breakthroughs have increased functionality and coherence of qubits substantially over the past two decades. Here, we show by improving interface between InAs as a semiconductor and Al as a superconductor, one can reliably fabricate voltage-controlled Josephson junction field effect transistor (JJ-FET) that can be used as tunable qubits, resonators, and coupler switches. We find that bandgap engineering is crucial in realizing a two-dimensional electron gas near the surface. In addition, we show how the coupling between the semiconductor layer and the superconducting contacts can affect qubit properties. We present the anharmonicity and coupling strengths from one and two-photon absorption in a quantum two level system fabricated with a JJ-FET.

The critical properties characterizing the formation of the Floquet time crystal are investigated analytically in the periodically driven $O(N)$ model. In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and absence of long-range spatial order from the non-trivial phase where long-range spatial order is accompanied by period-doubling dynamics. In the vicinity of the critical line, with a combination of dimensional expansion and exact solution for N→∞, we determine the exponent ν that characterizes the divergence of the spatial correlation length of the equal-time correlation functions, the exponent β characterizing the growth of the amplitude of the order-parameter, as well as the initial-slip exponent θ of the aging dynamics when a quench is performed from deep in the trivial phase to the critical line. The exponents ν, β, θ are found to be identical to those in the absence of a drive. In addition, the functional form of the aging is found to depend on whether the system is probed at times that are small or large compared to the drive period. The spatial structure of the two-point correlation functions, obtained as a linear response to a perturbing potential in the vicinity of the critical line, is found to show algebraic decays that are longer ranged than in the absence of a drive, and besides being period-doubled, are also found to oscillate in space at the wave-vector ω/(2 v), $v$ being the velocity of the quasiparticles, and ω being the drive frequency.

We fabricate Josephson junction field-effect transistors (JJ-FETs) using InAs quantum well heterostructure as the channel, epitaxial Al as superconducting electrodes, and scaled-down Al2O3gate dielectrics. A systematic investigation of the gate voltage (VG) dependence of the critical current, normal state conductance, and characteristic voltage of the JJ-FETs coupled with capacitance measurements reveals different VGregimes in the proximity effect characterization of JJ-FETs. Self-consistent Poisson-Schrödinger simulations allow us to associate these VGregimes with the carriers populating one or more subbands at different vertical locations in the heterostructure. We also discuss the importance of oxide/channel interface quality and its impact on the practical implementation of JJ-FET Boolean logic gates with signal restoration.

High Resolution Image Download MS PowerPoint Slide 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 c R n, are preserved. Furthermore, complementary measurements confirm that using h-BN dielectric changes the channel density less when compared to atomic layer deposition of Al 2 O 3.

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a π jump in the junction phase with an increasing in-plane magnetic field B_{∥}. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in B_{∥}. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.

Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.

Experiments realize a multiterminal Josephson junction, in which superconducting phase-coherence builds up between multiple supercurrents, providing a tool for exploring novel superconductivity and fault-tolerant quantum computing.

Realization of superconductivity in Group IV semiconductors could have a\nstrong impact in the direction quantum technologies will take in the future.\nTherefore, it is imperative to understand the nature of the superconducting\nphases in materials such as Silicon and Germanium. Here, we report systematic\nsynthesis and characterization of superconducting phases in hyperdoped\nGermanium prepared by Gallium ion implantation beyond its solubility limits.\nThe resulting structural and physical characteristics have been tailored by\nchanging the implantation energy and activation annealing temperature.\nSurprisingly, in addition to the poly-crystalline phase with weakly-coupled\nsuperconducting Ga clusters we find a nano-crystalline phase with quasi-2D\ncharacteristics consisting of a thin Ga film constrained near top surfaces. The\nnew phase shows signatures of strong disorder such as anomalous B\ c\ntemperature dependence and crossings in magentoresistance isotherms. Apart from\nusing hyperdoped Ge as a potential test-bed for studying signatures of quantum\nphase transitions (e.g. quantum Griffith singularity), our results suggest the\npossibility of integration of hyperdoped Ge nano-crystalline phase into\nsuperconducting circuits due to its 2D nature.\n

Realization of superconductivity in Group IV semiconductors could have a strong impact in the direction quantum technologies will take in the future. Therefore, it is imperative to understand the nature of the superconducting phases in materials such as Silicon and Germanium. Here, we report systematic synthesis and characterization of superconducting phases in hyperdoped Germanium prepared by Gallium ion implantation beyond its solubility limits. The resulting structural and physical characteristics have been tailored by changing the implantation energy and activation annealing temperature. Surprisingly, in addition to the poly-crystalline phase with weakly-coupled superconducting Ga clusters we find a nano-crystalline phase with quasi-2D characteristics consisting of a thin Ga film constrained near top surfaces. The new phase shows signatures of strong disorder such as anomalous Bc temperature dependence and crossings in magentoresistance isotherms. Apart from using hyperdoped Ge as a potential test-bed for studying signatures of quantum phase transitions (e.g. quantum Griffith singularity), our results suggest the possibility of integration of hyperdoped Ge nano-crystalline phase into superconducting circuits due to its 2D nature.

Abstract We demonstrate a robust superconducting proximity effect in InAs0.5Sb0.5 quantum wells grown with epitaxial Al contacts, which has important implications for mesoscopic and topological superconductivity. Unlike more commonly studied InAs and InSb semiconductors, bulk InAs0.5Sb0.5 supports stronger spin–orbit coupling and a larger g-factor. However, these potentially desirable properties have not been previously measured in epitaxial heterostructures with superconductors, which could serve as a platform for fault-tolerant topological quantum computing. Through structural and transport characterization, we observe high-quality interfaces and a strong spin–orbit coupling. We fabricate Josephson junctions based on InAs0.5Sb0.5 quantum wells and observe a strong proximity effect. With a contact separation of 500 nm, these junctions exhibit products IcRN = 270 μV and IexRN = 230 μV of normal resistance RN, critical current Ic, and excess current Iex. Both of these quantities demonstrate a robust and long-range proximity effect with highly transparent contacts.

Quantum computing, sensing, and communications are emerging technologies that may circumvent known limitations of their existing traditional counterparts. While the promises of these technologies are currently narrow in scope, it is possible that they will broadly impact our lives by revolutionizing the capabilities of data centers and medical diagnostics, for example. At the heart of these technologies is the use of a quantum object to contain information, called a quantum bit or qubit. Current realizations of qubits exist in a broad variety of material systems, including individual spins in semiconductors or insulators, superconducting circuits, and trapped ions. Further advancement of qubits requires significant contributions from materials science in areas of materials selection, synthesis, fabrication, simulation and characterization. Here, we discuss some of the needs and opportunities for contributions to advance the fundamental understanding of materials used in quantum information applications.

Managing the interaction of materials with insertion layers and nonconventional molecular beam epitaxy growth conditions allows for interfaces that are more precise but requires judicious examination of the multiple possible design variables. Here, we show a comparison between As- and Sb-containing insertion layers between Al and two binaries with different group V elements and demonstrate that antimonide layers greatly improve the interface. In addition to depositing Al at extremely slow growth rates onto cold (below 0 °C) substrates, the reactivity is particularly minimized with AlSb insertion layers, which improves interface abruptness, preserves the underlying semiconductor layer’s crystalline properties, and produces flatter superconductor surfaces.

Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4$π$ periodic current phase relation. The experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. Here, we report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is found to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4$π$ periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4$π$ Josephson junctions in relationship to topological superconductivity.

Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While realizing MBS has focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experiments in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing.