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arXiv:2405.11375 · PRX Quantum

Symmetrically Threaded Superconducting Quantum Interference Devices as Next-Generation Kerr-Cat Qubits

Bibek Bhandari, Irwin Huang, Ahmed Hajr, Kagan Yanik, Bingcheng Qing, Ke Wang, David Santiago, Justin Dressel, Irfan A. Siddiqi, Andrew N. Jordan

Published Jul 28, 2025• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/c661-yr2z

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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 propose a flux-pumped superconducting parametric amplifier based on symmetrically threaded superconducting quantum interference devices (SQUIDs) that achieves a Kerr-free operating point under suitable drive conditions. Eliminating the Kerr nonlinearity is advantageous for quantum-limited amplification, as it mitigates unwanted distortions in squeezing and prevents degradation of both gain and quantum efficiency in the high-gain strong drive regime. By replacing the central junction in the symmetrically threaded SQUIDs (STS) configuration with a linear inductor, we find that the Kerr-nonlinearity can be eliminated and the effective Hamiltonian reduces to that of a degenerate parametric amplifier (DPA), up to higher-order corrections in the zero-point fluctuations of the superconducting phase operator. We show that the deviations from ideal DPA behavior introduced by these higher-order terms are significantly weaker than those associated with a Kerr nonlinearity. Consequently, the STS design can be driven strongly while maintaining near-quantum-limited performance at the Kerr-free point. Our analysis predicts phase-preserving gain and efficiency approaching the quantum limit, with robust operation demonstrated up to 25 dB of gain.
The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger 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 nondemolition readout fidelity of 99.6% for a cat with eight photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X ( π / 2 ) 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 ten photons in the oscillator, achieving a bit-flip time higher than 1 ms and only a linear increase in the phase-flip rate, 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. Published by the American Physical Society 2024
Quantum computing promises exponential advantages for simulating quantum systems and solving certain computational problems beyond the reach of classical computers, but the fragility of qubits and the resulting errors present a major challenge for scalable implementations. One promising approach is to engineer qubits whose physical noise processes are intrinsically biased, enabling more efficient quantum error correction. This dissertation investigates quantum computing with superconducting Kerr-cat qubits, a bosonic qubit architecture in which qubit states are encoded in coherent states of a nonlinear oscillator stabilized by a two-photon drive. This stabilization creates an effective double-well pseudo-potential that strongly suppresses bit-flip errors while enabling universal quantum control, leading to a noise-biased qubit. A superconducting device architecture based on SNAIL nonlinear oscillators is developed to realize Kerr-cat qubits with tunable parameters and high coherence, integrating readout resonators, dedicated filters, and microwave control lines for measurement and manipulation. Universal single-qubit gates are implemented using engineered single-photon and two-photon drives to deform the pseudo-potential, and a cat-quadrature readout method is employed to achieve high-fidelity quantum nondemolition measurement. The performance of the qubits is systematically characterized through lifetime measurements and benchmarking protocols, including quantum process tomography, gate set tomography, and dihedral randomized benchmarking, revealing a strongly biased noise structure with high performance. These results establish an experimental framework for the design, control, and characterization of Kerr-cat qubits and demonstrate their potential as hardware-efficient building blocks for scalable fault-tolerant quantum computing.
Kerr-cat qubits offer a hardware-efficient route to fault-tolerant quantum computing by suppressing bit-flip errors exponentially, while phase-flip errors increase only linearly with the mean photon number. To maintain this protection, entangling operations must be bias-preserving, ensuring that phase-flip errors occurring during the gate do not propagate into bit-flip errors. In this paper, we propose an asymmetrically threaded SQUID (ATS) parametric coupler to implement high-fidelity, bias-preserving entangling gates between Kerr-cat qubits. By engineering a photon-number asymmetry between the control and target modes, we enable fast gate operations that suppress non-adiabatic leakage without complex pulse shaping. Through numerical simulations of the full circuit Hamiltonian, we demonstrate a bias-preserving CX gate achieving 99.69% fidelity in the absence of photon loss for a gate duration of 50 ns. Under a single-photon loss rate of 100 kHz, our protocol yields a noise bias of 9922, exceeding the noise bias of a naive non-bias-preserving CX implementation by approximately a factor of 570. These results support the ATS coupler as a valuable building block for concatenated cat-qubit architectures.
Cat qubits exhibit a strong noise bias, meaning that errors are predominantly confined to a single error channel, which can be corrected using a simple one-dimensional error correction code. As a result, cat qubits quadratically reduce the number of physical qubits required to realise a fully protected logical qubit compared with conventional surface codes. Recently a Kerr cat qubit was for the first time controlled with four-wave mixing in a SNAIL device. In this project we propose a circuit architecture adapted for four-wave mixing in the form of a capacitively shunted Josephson junction array which we call Kerr Josephson junction array oscillator (KJJA-oscillator). The device is fixed in frequency and not flux tunable, making it resilient to flux noise. Moreover the device strongly suppresses high order non-linearities, and therefore offers low intrinsic dephasing. The mathematical description of the KJJA-oscillator is developed, from which two KJJA-oscillators is designed. With four wave mixing the squeezing term of the Kerr Hamiltonian is realised with two separate drives slightly detuned from the cavity. This makes it possible to place cavities in the full frequency range of the signal generator. The Kerr is chosen as a neutral value in the trade-off between fast operations and long coherence times, based of previous results in the literature. The fabricated chip is characterised and found to exhibit low coherence times, most likely due to low fabrication quality. There is no known direct readout mechanism for four-wave mixing known to the author, instead an ancillary transmon was used to perform parity measurements. To showcase the readout mechanism Wigner-tomography of the vacuum state was measured. Due to the time constraints of the thesis there was not time to stabilise cats and show noise biasing properties. The chip will in the future be used to show how noise biasing scales with increasing cat state size and for demonstration of a universal single gate set.
Flux-pump induced degradation of T1T_1T1​ for dissipative cat qubits
Dissipative stabilization of cat qubits autonomously corrects for bit flip errors by ensuring that reservoir-engineered two-photon losses dominate over other mechanisms inducing phase flip errors. To describe the latter, we derive an effective master equation for an asymmetrically threaded SQUID based superconducting circuit used to stabilize a dissipative cat qubit. We analyze the dressing of relaxation processes under drives in time-dependent Schrieffer-Wolff perturbation theory for weakly anharmonic bosonic degrees of freedom, and in numerically exact Floquet theory. We find that spurious single-photon decay rates can increase under the action of the parametric pump that generates the required interactions for cat-qubit stabilization. Our analysis feeds into mitigation strategies that can inform current experiments, and the methods presented here can be extended to other circuit implementations.