Operating the autoparametric cat qubit at the sweet spot in flux of the memory frequency

Cat codes promise hardware-efficient quantum error correction, where the logical |0⟩ and |1⟩ are the coherent states |±α⟩ of a harmonic mode called the memory. The bit-flip time increases exponentially with the photon number |α|² while the phase-flip rate only increases linearly. Cat qubits can been stabilized using either Hamiltonian or dissipative engineering, in which case the memory mode exchanges photons with its environment by pairs. In 2023, we introduced a design in which the memory mode is coupled to a lossy buffer mode at twice the memory resonance frequency. This autoparametric circuit does not require any pumping, and allowed us to reach the strongest two-photon dissipation to date with a rate of photon pair loss κ₂/2π ≈ 2 MHz leading to a 0.3 s bit-flip time.

This circuit presents first order insensitivity to flux noise at a sweet spot of the flux threading its loop. However, in its previous design, the flux is already constrained to ensure the autoparametric frequency matching condition. We propose and experimentally demonstrate a new design where an additional SQUID tunes the buffer frequency independently. With this device, it becomes possible to reach a much lower memory dephasing rate than before. This work paves the way to stabilizing four-component cat qubits with an autoparametric design, for which low memory dephasing and self-Kerr rates are instrumental.