Abstract We have designed a tunable nonlinear resonator terminated by a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement). Such a device possesses a Kerr-free point in which the external magnetic flux allows to suppress the Kerr interaction. We have excited photons near this Kerr-free point and characterized the device using a transmon qubit. The excitation spectrum of the qubit allows to observe photon-number-dependent frequency shifts about nine times larger than the qubit linewidth. Our study demonstrates a compact integrated platform for continuous-variable quantum processing that combines large couplings, considerable relaxation times and excellent control over the photon mode structure in the microwave domain.
Abstract We have designed a tunable nonlinear resonator terminated by a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement). Such a device possesses a Kerr-free point in which the external magnetic flux allows to suppress the Kerr interaction. We have excited photons near this Kerr-free point and characterized the device using a transmon qubit. The excitation spectrum of the qubit allows to observe photon-number-dependent frequency shifts about nine times larger than the qubit linewidth. Our study demonstrates a compact integrated platform for continuous-variable quantum processing that combines large couplings, considerable relaxation times and excellent control over the photon mode structure in the microwave domain.
Three-wave mixing is a key process in superconducting quantum information processing, being involved in quantum-limited amplification and parametric coupling between superconducting cavities. These operations can be implemented by superconducting nonlinear asymmetric inductive element (SNAIL)-based devices that present a Kerr-free flux-bias point where unwanted parasitic effects, such as Stark shift, are suppressed. However, with a single flux-bias parameter, these circuits can only host one Kerr-free point, limiting the range of their applications. In this Letter, we demonstrate how to overcome this constraint by introducing the gradiometric SNAIL, a doubly flux biased superconducting circuit in which both effective inductance and Kerr coefficient can be independently tuned. Experimental data show the capability of the gradiometric SNAIL to suppress the Kerr effect in a three-wave mixing parametric amplifier over a continuum of flux bias points corresponding to a 1.7 GHz range of operating frequencies.
Scalable, high-fidelity quantum-state readout remains a central challenge in the development of large-scale superconducting quantum processors. Conventional dispersive readout architectures depend on bulky isolators and external amplifiers, introducing significant hardware overhead and limiting opportunities for on-chip information processing. In this work, we propose a novel approach that embeds a nonlinear Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) into the readout chain, enabling coherent and directional processing of readout signals directly on-chip. This embedded SNAIL platform allows frequency-multiplexed resonators to interact through engineered couplings, forming a tunable readout-amplifier-output architecture that can manipulate quantum readout data \textit{in situ}. Through theoretical modeling and numerical optimization, we show that this platform enhances fidelity, suppresses measurement-induced decoherence, and simplifies hardware complexity. These results establish the hybridized SNAIL as a promising building block for scalable and coherent quantum-state readout in next-generation processors.
Bosonic codes encoded in superconducting cavities offer a hardware-efficient path to fault tolerance by exploiting the infinite dimensionality of a single harmonic oscillator. However, the non-linear mixing elements required for autonomous stabilization introduce parasitic self-Kerr interactions that induce deterministic dephasing and limit coherence times. We introduce a control framework based on resonant Kerr-cancellation dynamics using a Superconducting Nonlinear Asymmetric Inductive Element (SNAIL). By tuning the external magnetic flux to a symmetry-protected sweet spot, we eliminate the fourth-order non-linearity while maintaining the third-order mixing required for confinement. We derive an analytical stability threshold χaa<0.1κconf necessary to restore the exponential suppression of bit-flip errors. Analysis of spectroscopic data confirms that operating below this threshold eliminates the phase-space shearing observed in previous experiments. This protocol establishes the physical conditions required to surpass the break-even point in continuous variable quantum information.
Kerr-cat qubits are bosonic qubits offering autonomous bit-flip protection, traditionally studied using driven superconducting nonlinear asymmetric inductive element (SNAIL) oscillators. Here, we theoretically explore an alternative circuit for Kerr-cat qubits based on symmetrically threaded superconducting quantum interference devices (SQUIDs). The symmetrically threaded SQUID (STS) architecture employs a simplified flux-pumped design that suppresses two-photon dissipation, a dominant loss mechanism in high-Kerr regimes, by engineering the drive Hamiltonian’s flux operator to generate only even-order harmonics. By fulfilling two critical criteria for practical Kerr-cat qubit operation, the STS emerges as an ideal platform: (1) a static Hamiltonian with diluted Kerr nonlinearity (achieved via the STS’s middle branch) and (2) a drive Hamiltonian restricted to even harmonics, which ensures robust two-photon driving with reduced dissipation. For weak Kerr nonlinearity, we find that the coherent state lifetime ( T α ) is similar between STS and SNAIL circuits. However, STS Kerr-cat qubits exhibit enhanced resistance to higher-order photon dissipation, enabling significantly extended T α even with stronger Kerr nonlinearities (approximately 10 MHz). In contrast to SNAIL, STS Kerr-cat qubits display a T α dip under weak two-photon driving for a high Kerr coefficient. We demonstrate that this dip can be suppressed by applying drive-dependent detuning, enabling Kerr-cat qubit operation with only eight Josephson junctions (of energies 80 GHz); fewer junctions suffice for higher junction energies. We further validate the robustness of the STS design by studying the impact of strong flux driving and asymmetric Josephson junctions on T α . With the proposed design and considering a cat size of ten photons, we predict T α of the order of tens of milliseconds, even in the presence of multiphoton heating and dephasing effects. The robustness of the STS Kerr-cat qubit makes it a promising component for fault-tolerant quantum processors.
We measure photon occupancy in a thin-film superconducting lumped element resonator coupled to a transmon qubit at 20mK and find a nonlinear dependence on the applied microwave power. The transmon-resonator system was operated in the strong dispersive regime, where the ac Stark shift $(2\ensuremath{\chi})$ due to a single microwave photon present in the resonator was larger than the linewidth $(\mathrm{\ensuremath{\Gamma}})$ of the qubit transition. When the resonator was coherently driven at 5.474 325 GHz, the transition spectrum of the transmon at 4.982 GHz revealed well-resolved peaks, each corresponding to an individual photon number-state of the resonator. From the relative peak heights we obtain the occupancy of the photon states and the average photon occupancy n of the resonator. We observe a nonlinear variation of n with the applied drive power Prf for n<5 and compare our results to numerical simulations of the system-bath master equation in the steady state, as well as to a semiclassical model for the resonator that includes the Jaynes-Cummings interaction between the transmon and the resonator. We find good quantitative agreement using both models and analysis reveals that the nonlinear behavior is principally due to shifts in the resonant frequency caused by a qubit-induced Jaynes-Cummings nonlinearity.
Nonlinear microwave resonators are a versatile tool in quantum information processing, enabling parametric amplification, continuous variable quantum computing, and engineered mode interactions. Many of these applications especially benefit from cubic nonlinearities enabling three-wave mixing; at the same time, they are limited by quartic nonlinearities giving rise to undesired Kerr effects. A recurrent challenge is therefore to engineer resonators with a finite cubic nonlinearity while suppressing quartic terms. Here, we investigate a superconducting resonator hosting two weak links fabricated from an aluminum-capped indium arsenide nanowire. We characterize the Kerr nonlinearity as a function of magnetic flux and gate bias, showing that it can be tuned to zero with either control parameter. Furthermore, we experimentally demonstrate three-wave mixing in a semiconductor-superconductor hybrid device, establishing nonzero cubic nonlinearity. An effective model based on Andreev bound states qualitatively captures the observed trends. Our results validate semiconductor-superconductor hybrid devices as a promising platform for tunable nonlinear superconducting circuits, with applications in parametric amplification, quantum control of bosonic modes, and engineering interactions between microwave modes.