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The ubiquitous noise in quantum system hinders the advancement of quantum information processing and has driven the emergence of different hardware-efficient quantum error correction protocols. Among them, qubits with structured noise, especially with biased noise, are one of the most promising platform to achieve fault-tolerance due to the high error thresholds of quantum error correction codes tailored for them. Nevertheless, their quantum operations are challenging and the demonstration of their performance beyond the fault-tolerant threshold remain incomplete. Here, we leverage Schr\"odinger cat states in a scalable planar superconducting nonlinear oscillator to thoroughly characterize the high-fidelity single-qubit quantum operations with systematic quantum tomography and benchmarking tools, demonstrating the state-of-the-art performance of operations crossing the fault-tolerant threshold of the XZZX surface code. These results thus embody a transformative milestone in the exploration of quantum systems with structured error channels. Notably, our framework is extensible to other types of structured-noise systems, paving the way for systematic characterization and validation of novel quantum platforms with structured noise., Comment: 19 pages, 12 figures

Dissipative tunneling remains a cornerstone effect in quantum mechanics. In chemistry, it plays a crucial role in governing the rates of chemical reactions, often modeled as the motion along the reaction coordinate from one potential well to another. The relative positions of energy levels in these wells strongly influence the reaction dynamics. Chemical research will benefit from a fully adjustable, asymmetric double-well equipped with precise measurement capabilities of the tunneling rates. In this paper, we show a quantum simulator system that consists of a continuously driven Kerr parametric oscillator with a third order non-linearity that can be operated in the quantum regime to create a fully tunable asymmetric double-well. Our experiment leverages a low-noise, all-microwave control system with a high-efficiency readout, based on a tunnel Josephson junction circuit, of the which-well information. We explore the reaction rates across the landscape of tunneling resonances in parameter space. We uncover two new and counter-intuitive effects: (i) a weak asymmetry can significantly decrease the activation rates, even though the well in which the system is initialized is made shallower, and (ii) the width of the tunneling resonances alternates between narrow and broad lines as a function of the well depth and asymmetry. We predict by numerical simulations that both effects will also manifest themselves in ordinary chemical double-well systems in the quantum regime. Our work is a first step for the development of analog molecule simulators of proton transfer reactions based on quantum superconducting circuits., Comment: Edited some of the text and figures for clarity and corrected typos

Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes, particularly grid state encodings, offer a pathway to scalable fault-tolerant quantum computing in superconducting circuits. By leveraging the large Hilbert space of bosonic modes, quantum error correction can operate at the single physical unit level, therefore reducing drastically the hardware requirements to bring fault-tolerant quantum computing to scale. Going beyond the well-known Gottesman-Kitaev-Preskill (GKP) code, we discuss how using multiple bosonic modes to encode a single qubit offers increased protection against control errors and enhances its overall error-correcting capabilities. Given recent successful demonstrations of critical components of this architecture, we argue that it offers the shortest path to achieving fault tolerance in gate-based quantum computing processors with a MHz logical clock rate., Comment: This is a perspective paper presenting Nord Quantique's vision towards hardware-efficient FTQC

Bosonic codes offer a hardware-efficient strategy for quantum error correction by redundantly encoding quantum information in the large Hilbert space of a harmonic oscillator. However, experimental realizations of these codes are often limited by ancilla errors propagating to the encoded logical qubit during syndrome measurements. The Kerr-cat qubit has been proposed as an ancilla for these codes due to its theoretically-exponential noise bias, which would enable fault-tolerant error syndrome measurements, but the coupling required to perform these syndrome measurements has not yet been demonstrated. In this work, we experimentally realize driven parametric coupling of a Kerr-cat qubit to a high-quality-factor microwave cavity and demonstrate a gate set enabling universal quantum control of the cavity. We measure the decoherence of the cavity in the presence of the Kerr-cat and discover excess dephasing due to heating of the Kerr-cat to excited states. By engineering frequency-selective dissipation to counteract this heating, we are able to eliminate this dephasing, thereby demonstrating a high on-off ratio of control. Our results pave the way toward using the Kerr-cat to fault-tolerantly measure error syndromes of bosonic codes.

The Kerr-cat qubit is a bosonic qubit in which multi-photon Schrodinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on-chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum non-demolition readout fidelity of 99.6% for a cat with 8 photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X(90) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to 10 photons in the oscillator achieving a bit-flip time higher than 1 ms and only a linear decrease in the phase-flip time, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint.

The dielectric loss of silicon nitride (Si$_3$N$_4$) limits the performance of microwave-frequency devices that rely on this material for sensing, signal processing, and quantum communication. Using superconducting resonant circuits, we measure the cryogenic loss tangent of either as-deposited or high-temperature annealed stoichiometric Si$_3$N$_4$ as a function of drive strength and temperature. The internal loss behavior of the electrical resonators is largely consistent with the standard tunneling model of two-level systems (TLS), including damping caused by resonant energy exchange with TLS and by the relaxation of non-resonant TLS. We further supplement the TLS model with a self-heating effect to explain an increase in the loss observed in as-deposited films at large drive powers. Critically, we demonstrate that annealing remedies this anomalous power-induced loss, reduces the relaxation-type damping by more than two orders of magnitude, and reduces the resonant-type damping by a factor of three. Employing infrared absorption spectroscopy, we find that annealing reduces the concentration of hydrogen in the Si$_3$N$_4$, suggesting that hydrogen impurities cause substantial dissipation., Comment: 11 pages, 7 figures

The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a bosonic system with resilience against single-photon loss, the predominant error in most bosonic systems. Here we present experimental results demonstrating quantum error correction of GKP states based on reservoir engineering of a superconducting device. Error correction is made autonomous through an unconditional reset of an auxiliary transmon qubit. The lifetime of the logical qubit is shown to be increased from quantum error correction, therefore reaching the point at which more errors are corrected than generated., Comment: 6 pages, 3 figures + 26 pages, 12 figures

We present a way to achieve fully directional, quantum-limited phase-preserving amplification in a four-port, four-mode superconducting Josephson circuit by utilizing interference between six parametric processes that couple all four modes. Full directionality, defined as the reverse isolation surpassing forward gain between the matched input and output ports of the amplifier, ensures its robustness against impedance mismatch that might be present at its output port during applications. Unlike existing directional phase-preserving amplifiers, both the minimal back-action and the quantum-limited added noise of this amplifier remains unaffected by noise incident on its output port. In addition, the matched input and output ports allow direct on-chip integration of these amplifiers with other circuit QED components, facilitating scaling up of superconducting quantum processors.

Quantum fluctuations constitute the primary noise barrier limiting cavity-based axion dark matter searches. In an experiment designed to mimic a real axion search, we employ a quantum-enhanced sensing technique to detect a synthetic axion-like microwave tone at an unknown frequency weakly coupled to a resonator, demonstrating a factor of 5.6 acceleration relative to a quantum-limited search for the same tone. The acceleration comes from increases to both the visibility bandwidth and the peak visibility of a detector. This speedup is achieved by dynamically coupling the resonator mode to a second (readout) mode with balanced swapping and two-mode squeezing interactions. A small fractional imbalance between the two interaction rates yields further scan rate enhancement and we demonstrate that an 8-fold acceleration can be achieved., Comment: 9 pages, 5 figures

We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing, in combination with the Kerr interaction creates an effective static two-well potential in the frame rotating at half the frequency of the sinusoidal driving force. Remarkably, these degeneracies can be turned on-and-off on demand, and their number is tunable. We find that when the detuning $\Delta$ between the frequency of the oscillator and characteristic frequency of the drive equals an even multiple of the Kerr coefficient $K$, $\Delta/K = 2m$, the oscillator displays $m + 1$ exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. The degeneracies stem from the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime creating a super-protected cat qubit in the ground state manifold of our oscillator. {Our results demonstrate the relationship between degeneracies and noise protection in quantum systems.

By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schr\"odinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.

In chemical reactions, the interplay between coherent evolution and dissipation is central to determining key properties such as the rate and yield. Of particular interest are cases where two potential energy surfaces cross at features known as conical intersections (CIs), resulting in nonadiabatic dynamics that may promote ultrafast and highly efficient reactions when rovibrational damping is present. A prominent chemical reaction that involves a CI is the cis-trans isomerization reaction in rhodopsin, which is crucial to vision. CIs in real molecular systems are typically investigated via optical pump-probe spectroscopy, which has demanding spectral bandwidth and temporal resolution requirements, and where precise control of the environment is challenging. A complementary approach for understanding chemical reactions is to use quantum simulators that can provide access to a wider range of observables, though thus far combining strongly interacting linear (rovibrational) and nonlinear (electronic) degrees of freedom with engineered dissipation has yet to be demonstrated. Here, we create a tunable CI in a hybrid qubit-oscillator circuit QED processor and simultaneously track both a reactive wave-packet and electronic qubit in the time-domain. We identify dephasing of the electronic qubit as the mechanism that drives wave-packet branching along the reactive coordinate in our model. Furthermore, we directly observe enhanced branching when the wave-packet passes through the CI. Thus, the forces that influence a chemical reaction can be viewed as an effective measurement induced dephasing rate that depends on the position of the wave-packet relative to the CI. Our results set the groundwork for more complex simulations of chemical dynamics, offering deeper insight into the role of dissipation in determining macroscopic quantities of interest such as the quantum yield of a chemical reaction.

Quantum superpositions of macroscopically distinct classical states, so-called Schr\"{o}dinger cat states, are a resource for quantum metrology, quantum communication, and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors. However, several challenges have to be overcome in order for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here, we experimentally demonstrate a novel method for the generation and stabilization of Schr\"{o}dinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing in a superconducting microwave resonator. We show an increase in transverse relaxation time of the stabilized, error-protected qubit over the single-photon Fock-state encoding by more than one order of magnitude. We perform all single-qubit gate operations on time-scales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control with the robustness against errors intrinsic to stabilized macroscopic states and open up the possibility of using these states as resources in quantum information processing., Comment: Corrected typos. See journal reference for accepted version