Symmetrically Threaded Superconducting Quantum Interference Devices As Next Generation Kerr-cat Qubits

We theoretically explore an alternative circuit for Kerr-cat qubits based on symmetrically threaded Superconducting Quantum Interference Devices (SQUID). The Symmetrically Threaded SQUIDs (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 ($T_\alpha$) is similar between STS and SNAIL circuits. However, STS Kerr-cat qubits exhibit enhanced resistance to higher-order photon dissipation, enabling significantly extended $T_\alpha$ even with stronger Kerr nonlinearities ($\sim$10 MHz). In contrast to SNAIL, STS Kerr-cat qubits display a $T_\alpha$ dip under weak two-photon driving for 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 $T_\alpha$. With the proposed design and considering a cat size of 10 photons, we predict $T_\alpha$ of the order of tens of milliseconds, even in the presence of multi-photon heating and dephasing effects.