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 withstandard 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 30−320pH/sq and self-Kerr non-linearities of 0.2−20Hz/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 3.5×106 for the all-grAl devices and 4.5×106 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.
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 readoutresonator 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.
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 morethan 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. By leveraging the beamsplitter coupling already required for single-qubit gates, this scheme permits minimal connectivity 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.
A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is todesign a system where errors can be detected and converted into erasures. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. In this work, we implement such a dual-rail cavity qubit and use it to demonstrate a projective logical measurement with erasure detection. 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 ∼0.2% per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 170 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.
An accurate understanding of the Josephson effect is the keystone of quantum information processing with superconducting hardware. Here we show that the celebrated sinφ current-phaserelation (CφR) of Josephson junctions (JJs) fails to fully describe the energy spectra of transmon artificial atoms across various samples and laboratories. While the microscopic theory of JJs contains higher harmonics in the CφR, these have generally been assumed to give insignificant corrections for tunnel JJs, due to the low transparency of the conduction channels. However, this assumption might not be justified given the disordered nature of the commonly used AlOx tunnel barriers. Indeed, a mesoscopic model of tunneling through an inhomogeneous AlOx barrier predicts contributions from higher Josephson harmonics of several %. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The measurement of Josephson harmonics in the CφR of standard tunnel junctions prompts a reevaluation of current models for superconducting hardware and it offers a highly sensitive probe towards optimizing tunnel barrier uniformity.
The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computations. To this end, we introducethe circuit-QED dual-rail qubit in which our physical qubit is encoded in the single-photon subspace of two superconducting cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers completely new capabilities. Using a single transmon ancilla, we describe a universal gate set that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors due to the cavity and transmon in all of these operations can be detected and converted to erasure errors, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit delivers an optimal hierarchy of errors and rates, and is expected to be well below the relevant QEC thresholds with today’s devices.
The innate complexity of solid state physics exposes superconducting quantum circuits to interactions with uncontrolled degrees of freedom degrading their coherence. By using a simplestabilization sequence we show that a superconducting fluxonium qubit is coupled to a two-level system (TLS) environment of unknown origin, with a relatively long energy relaxation time exceeding 50ms. Implementing a quantum Szilard engine with an active feedback control loop allows us to decide whether the qubit heats or cools its TLS environment. 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 the qubit are each other’s dominant loss mechanism and that the qubit relaxation is independent of the TLS populations. Understanding and mitigating TLS environments is therefore not only crucial to improve qubit lifetimes but also to avoid non-Markovian qubit dynamics.
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 gradiometricfluxonium 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 Φ0/2 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 100Φ0. However, even for states biased in the vicinity of 1Φ0, 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.
Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulatingphoton number n¯ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing n¯ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a function of n¯, up to n¯≈200. Despite the fact that we observe the expected decrease of the dispersive shift with increasing readout power, the signal-to-noise ratio continuously improves with increasing n¯. Even without the use of a parametric amplifier, at n¯=74, we measure fidelities of 99% and 93% for feedback-assisted ground and excited state preparation, respectively.
We developed a versatile integrated control and readout instrument for experiments with superconducting quantum bits (qubits), based on a field-programmable gate array (FPGA) platform.Using this platform, we perform measurement-based, closed-loop feedback operations with 428ns platform latency. The feedback capability is instrumental in realizing active reset initialization of the qubit into the ground state in a time much shorter than its energy relaxation time T1. We show experimental results demonstrating reset of a fluxonium qubit with 99.4% fidelity, using a readout-and-drive pulse sequence approximately 1.5μs long. Compared to passive ground state initialization through thermalization, with the time constant given by T1= 80μs, the use of the FPGA-based platform allows us to improve both the fidelity and the time of the qubit initialization by an order of magnitude.