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

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 (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mi>α</a:mi></a:msub></a:math>) is similar between STS and SNAIL circuits. However, STS Kerr-cat qubits exhibit enhanced resistance to higher-order photon dissipation, enabling significantly extended <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mi>α</c:mi></c:msub></c:math> even with stronger Kerr nonlinearities (approximately <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>10</e:mn></e:math> MHz). In contrast to SNAIL, STS Kerr-cat qubits display a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>T</g:mi><g:mi>α</g:mi></g:msub></g:math> 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>T</i:mi><i:mi>α</i:mi></i:msub></i:math>. With the proposed design and considering a cat size of ten photons, we predict <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>T</k:mi><k:mi>α</k:mi></k:msub></k:math> 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.