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Resonant Kerr-Cancellation Dynamics in Dissipative Bosonic Stabilization

QNFO

Published Dec 1, 2025• 0 citations
Publisher

Abstract

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 $\chi_{aa} < 0.1 \kappa_{conf}$ 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.

DOI
10.5281/zenodo.17782621

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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\chi_{aa} < 0.1 \kappa_{conf}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.
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.
Over the past decade, autonomous stabilization of bosonic qubits has emerged as a promising approach for hardware-efficient protection of quantum information. However, applying these techniques to more complex encodings than the Schrödinger cat code requires exquisite control of high-order wave mixing processes. The challenge is to enable specific multiphotonic dissipation channels while avoiding unintended nonlinear interactions. In this work, we leverage a genuine six-wave mixing process enabled by a near Kerr-free Josephson element to enforce dissipation of quartets of excitations in a high-impedance superconducting resonator. Owing to residual nonlinearities stemming from stray inductances in our circuit, this dissipation channel is only effective when the resonator holds a specific number of photons. Applying it to the fourth excited state of the resonator, we show an order-of-magnitude enhancement of the state decay rate while only marginally impacting the relaxation and coherence of lower-energy states. Given that stray inductances could be strongly reduced through simple modifications in circuit design and that our methods can be adapted to activate even higher-order dissipation channels, these results pave the way toward the dynamical stabilization of four-component Schrödinger cat qubits and even more complex bosonic qubits.
Quantum computing crucially relies on maintaining quantum coherence for the duration of a calculation. Bosonic quantum error correction protects this coherence by encoding qubits into superpositions of noise-resilient oscillator states. In the case of the Kerr-cat qubit (KCQ), these states derive their stability from being the quasi-degenerate ground states of an engineered Hamiltonian in a driven nonlinear oscillator. KCQs are experimentally compatible with on-chip architectures and high-fidelity operations, making them promising candidates for a scalable bosonic quantum processor. However, their bit-flip time must increase further to fully leverage these advantages. Here, we present direct evidence that the bit-flip time in a KCQ is limited by leakage out of the qubit manifold and experimentally mitigate this process. We coherently control the leakage population and measure it to be > 9%, twelve times higher than in the undriven system. We then cool this population back into the KCQ manifold with engineered dissipation, identify conditions under which this suppresses bit-flips, and demonstrate increased bit-flip times up to 3.6 milliseconds. By employing both Hamiltonian confinement and engineered dissipation, our experiment combines two paradigms for Schrödinger-cat qubit stabilization. Our results elucidate the interplay between these stabilization processes and indicate a path towards fully realizing the potential of these qubits for quantum error correction.
Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.
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.
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.