Symmetrically Threaded SQUIDs As Next Generation Kerr-cat Qubits

Kerr-cat qubits are bosonic qubits with autonomous protection against bit-flips. They have been studied widely using driven Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) oscillators. We theoretically investigate an alternate circuit for the Kerr-cat qubit, namely Symmetrically Threaded SQUIDs (STS). We perform the circuit analysis and derive the Gorini-Kossakowski-Sudarshan-Lindblad (GKLS) master equation for the Kerr-cat qubit attached to a thermal environment. We find that the lifetime time of the coherent states ($T_\alpha$) of the Kerr-cat qubit is the same in both the STS and SNAIL circuits for weak Kerr nonlinearity. However, the STS Kerr-cat qubits have the additional benefit of being resistant against higher order photon dissipation effects, resulting in significantly longer $T_\alpha$ even with stronger Kerr nonlinearity on the order of $10{~\rm MHz}$. We also examine the effects of strong flux driving and asymmetric Josephson junctions on $T_\alpha$. Unlike the SNAIL design, we find a dip in $T_\alpha$ of the STS Kerr-cat qubit for weak two-photon drive. However, we show that the dip can be mitigated by applying a suitable drive-dependent detuning. 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. The robustness of the STS Kerr-cat qubit makes it a promising component for fault-tolerant quantum processors.