Superconducting high-kinetic inductance materials like granular aluminum (grAl) are a versatile part of the circuit quantum electrodynamics (cQED) toolbox, provided their losses at microwave frequencies are low enough. To further advance the use of grAl in quantum devices, it is indispensable to identify the dominant loss mechanisms. The standard approach pairs electromagnetic simulations of resonator geometry with measured temperature and power dependence of resonance frequency and loss rate. Most materials follow the phenomenological theory of two-level systems (TLSs) at low temperatures, resulting in an initial decrease of the resonance frequency with increasing temperature. In our work, we observe an opposite behavior at the lowest temperatures: The resonance frequency initially increases with both temperature and readout power, contradicting the standard TLS model predictions. We are able to explain a part of the data by an alternative mechanism associated with the effect of superconducting quasiparticles in a granular system with spatially-nonuniform gap. Yet, the observed change in the resonance frequency with temperature is not matched by a proportional change in the loss rate. We also observe anomalous positive frequency responses following high-energy events, characterized by several time scales. While anomalous behavior has been reported previously in grAl, the disagreement with standard models is particularly visible in our devices thanks to their exceptionally low loss rates.

We present a flip-chip architecture for an array of coupled superconducting qubits, in which circuit components reside inside individual microwave enclosures. In contrast to other flip-chip approaches, the qubit chips in our architecture are electrically floating, which guarantees a simple, fully modular assembly of capacitively coupled circuit components, such as qubit, control, and coupling structures as well as reduced crosstalk between the components. We validate the concept with a chain of three nearest neighbor coupled generalized flux qubits in which the center qubit acts as a frequency-tunable coupler. Using this coupler, we demonstrate a transverse coupling on/off ratio≈50, zz−crosstalk ≈0.7 kHz between resonant qubits and isolation between the qubit enclosures>60 dB.

Entanglement generation lies at the heart of many quantum networking protocols as it enables distributed and modular quantum computing. For superconducting qubits, entanglement fidelity is typically limited by photon loss in the links that connect these qubits together. We propose and realize a new scheme for heralded entanglement generation that almost entirely circumvents this limit. We produce Bell states with 92±1% state fidelity, including state preparation and measurement (SPAM) errors, between separated superconducting bosonic qubits in a high-loss regime where direct deterministic state transfer fails. Our scheme exploits simple but fundamental physics found in microwave links, specifically the ability to treat our communication channel as a single standing wave mode. Combining this with local measurements on bosonically encoded qubits allows us to herald entanglement with success probabilities approaching the scheme's upper limit of 50

Lumped-element inductors are an integral component in the circuit QED toolbox. However, it is challenging to build inductors that are simultaneously compact, linear and low-loss with standard approaches that either rely on the geometric inductance of superconducting thin films or on the kinetic inductance of Josephson junctions arrays. In this work, we overcome this challenge by utilizing the high kinetic inductance offered by superconducting granular aluminum (grAl). We demonstrate lumped-element inductors with a few nH of inductance that are up to $100$ times more compact than inductors built from pure aluminum (Al). To characterize the properties of these linear inductors, we first report on the performance of lumped-element resonators built entirely out of grAl with sheet inductances varying from $30-320\,$pH/sq and self-Kerr non-linearities of $0.2-20\,\mathrm{Hz/photon}$. Further, we demonstrate ex-situ integration of these grAl inductors into hybrid resonators with Al or tantalum (Ta) capacitor electrodes without increasing total internal losses. Interestingly, the measured internal quality factors systematically decrease with increasing room-temperature resistivity of the grAl film for all devices, indicating a trade-off between compactness and internal loss. For our lowest resistivity grAl films, we measure quality factors reaching $3.5 \times 10^6$ for the all-grAl devices and $4.5 \times 10^6$ for the hybrid grAl/Ta devices, similar to state-of-the-art quantum circuits. Our loss analysis suggests that the surface loss factor of grAl is similar to that of pure Al for our lowest resistivity films, while the increasing losses with resistivity could be explained by increasing conductor loss in the grAl film.

Superconducting standing-wave parametric amplifiers are crucial for the readout of microwave quantum devices. Despite significant improvements in recent years, the need to operate near an instability point imposes a fundamental constraint: the instantaneous bandwidth decreases with increasing amplifier gain. Here we show that it is possible to obtain parametric amplification without instability by using two simultaneous drives that activate phase-preserving gain and frequency conversion. Realized in a granular aluminum dimer with Kerr nonlinearity, our method demonstrates a sixfold bandwidth increase at 20 dB gain, surpasses the conventional gain-bandwidth scaling up to 25 dB, and remains near the quantum limit.

Quantum control of a linear oscillator using a static dispersive coupling to a nonlinear ancilla underpins a wide variety of experiments in circuit QED. Extending this control to more than one oscillator while minimizing the required connectivity to the ancilla would enable hardware-efficient multi-mode entanglement and measurements. We show that the spectrum of an ancilla statically coupled to a single mode can be made to depend on the joint photon number in two modes by applying a strong parametric beamsplitter coupling between them. This ‘joint-photon number-splitting’ regime extends single-oscillator techniques to two-oscillator control, which we use to realize a hardware-efficient erasure check for a dual-rail qubit encoded in two superconducting cavities. This scheme leverages the high-fidelity beamsplitter coupling already required for single- and two-qubit gates while permitting minimal crosstalk between circuit elements. Furthermore, the flexibility to choose the pulse shape allows us to limit the susceptibility to different error channels. We use this scheme to detect leakage errors with a missed erasure fraction of (9.0 ± 0.5) × 10−4 while incurring an erasure rate of 2.92 ± 0.01% and a Pauli error rate of 0.31 ± 0.01%, both of which are dominated by cavity errors.

We demonstrate a qubit-readout architecture where the dispersive coupling is entirely mediated by a kinetic inductance. This allows us to engineer the dispersive shift of the readout resonator independent of the qubit and resonator capacitances. We validate the pure kinetic coupling concept and demonstrate various generalized flux qubit regimes from plasmon to fluxon, with dispersive shifts ranging from 60 kHz to 2 MHz at the half-flux quantum sweet spot. We achieve readout performances comparable to conventional architectures with quantum state preparation fidelities of 99.7% and 92.7% for the ground and excited states, respectively, and below 0.1% leakage to non-computational states.

In a superconducting weak link, the supercurrent is carried by Andreev bound states (ABSs) formed by the phase-coherent reflection of electrons and their time-reversed partners. A single, highly transmissive ABS can serve as an ideal, compact two-level system, due to a potentially large energy difference to the next ABS. While the coherent manipulation of such Andreev levels qubits (ALQs) has been demonstrated, a long-range coupling between two ALQs, necessary for advanced qubit architectures, has not been achieved, yet. Here, we demonstrate a coherent remote coupling between two ALQs, mediated by a microwave photon in a novel superconducting microwave cavity coupler. The latter hosts two modes with different coupling rates to an external port. This allows us to perform fast readout of each qubit using the strongly coupled mode, while the weakly coupled mode is utilized to mediate the coupling between the qubits. When both qubits are tuned into resonance with the latter mode, we find excitation spectra with avoided-crossings, in very good agreement with the Tavis-Cummings model. Based on this model, we identify highly entangled two-qubit states for which the entanglement is mediated over a distance of six millimeters. This work establishes ALQs as compact and scalable solid-state qubits.

Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlOx) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current-phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlOx barrier. Here we show that the standard current-phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlOx barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlOx-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.

A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to design a system where errors can be detected and converted into erasures. Such a system utilizing erasure qubits are known to have relaxed requirements for quantum error correction. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. However, experimental characterization and demonstration of a dual-rail cavity qubit has not yet been realized. In this work, we implement such a dual-rail cavity qubit; we demonstrate a projective logical measurement with integrated erasure detection and use it to measure dual-rail qubit idling errors. We measure logical state preparation and measurement errors at the $0.01\%$-level and detect over $99\%$ of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability $\sim 0.2\%$ per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 140 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

The innate complexity of solid-state physics exposes superconducting quantum circuits to interactions with uncontrolled degrees of freedom degrading their coherence. By implementing a quantum Szilard engine with an active feedback control loop, we show that a superconducting fluxonium qubit is coupled to a two-level system (TLS) environment of unknown origin, with a relatively long intrinsic energy relaxation time exceeding 50 ms. The TLSs can be cooled down, resulting in a four times lower qubit population, or they can be heated to manifest themselves as a negative-temperature environment corresponding to a qubit population of ~80%. We show that the TLSs and qubit are the dominant loss mechanism for each other and that qubit relaxation is independent of the TLS populations. Understanding and mitigating TLS environments is, therefore, not only crucial to improve the qubit lifetimes but also to avoid non-Markovian qubit dynamics. The performance of superconducting qubits is often limited by spurious two-level systems. Now, a qubit operating as a heat engine manipulates its bath of nearby two-level systems, providing insights into their dynamics and interactions.

We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at 0 or Φ_0/2 effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding 100 Φ_0. However, even for states biased in the vicinity of 1 Φ_0, we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor.

Mesoscopic Josephson junctions, consisting of overlapping superconducting electrodes separated by a nanometre-thin oxide layer, provide a precious source of nonlinearity for superconducting quantum circuits. Here we show that in a fluxonium qubit, the role of the Josephson junction can also be played by a lithographically defined, self-structured granular aluminium nanojunction: a superconductor-insulator-superconductor Josephson junction obtained in a single-layer, zero-angle evaporation. The measured spectrum of the resulting qubit, which we nickname gralmonium, is indistinguishable from that of a standard fluxonium. Remarkably, the lack of a mesoscopic parallel plate capacitor gives rise to an intrinsically large granular aluminium nanojunction charging energy in the range of tens of gigahertz, comparable to its Josephson energy. We measure coherence times in the microsecond range and we observe spontaneous jumps of the value of the Josephson energy on timescales from milliseconds to days, which offers a powerful diagnostics tool for microscopic defects in superconducting materials.

Simon Günzler, ∗ Patrick Winkel, ∗ Dennis Rieger, Kiril Borisov, Martin Spiecker, Alexey V. Ustinov, 2, 4 Ioan M. Pop, 2, 3 and Wolfgang Wernsdorfer 2, 3, 5, † Institute for Quantum Materials and Technology, Karlsruher Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany Russian Quantum Center, National University of Science and Technology MISIS, 119049 Moscow, Russia Institut Néel, CNRS and Université Joseph Fourier, Grenoble, France (Dated: July 14, 2021)

Superconducting quantum interference devices (SQUIDs) are among the most sensitive detectors for out-of-plane magnetic field components. However, due to their periodic response with short modulation period M = 1 Φ_0, determined by the magnetic flux quantum Φ_0 ≈ 2.068× 10^-15 Wb, it is difficult to infer the value of the magnetic flux unambiguously, especially in case the magnetic flux enclosed in the SQUID loop changes by many flux quanta. Here, we demonstrate that by introducing a second degree of freedom in the form of a second SQUID, we substantially enhance the modulation period M of our device without sacrificing sensitivity. As a proof of concept, we implement our idea by embedding two asymmetric direct current SQUIDs into a common tank circuit. By measuring the reflection coefficient of the device, we extract the two lowest energy eigenfrequencies as a function of the external magnetic flux created by a superconducting field coil, from which we experimentally deduce a modulation period M ≥ 15 Φ_0, as well as the magnetic offset-field B_0 = 22 nT present in our experiment.

Fast discrimination between quantum states of superconducting artificial atoms is an important ingredient for quantum information processing. In circuit quantum electrodynamics, increasing the signal-field amplitude in the readout resonator, dispersively coupled to the artificial atom, improves the signal-to-noise ratio and increases the measurement strength. Here, we employ this effect over 2 orders of magnitude in readout power, made possible by the unique combination of a dimer-Josephson-junction-array amplifier with a large dynamic range and the fact that the readout of our granular aluminum fluxonium artificial atom remains quantum nondemolition (QND) at relatively large photon numbers in the readout resonator, up to n = 110. Using Bayesian inference, this allows us to detect quantum jumps faster than the readout-resonator response time 2/kappa, where kappa is the bandwidth of the readout resonator.