Stabilization of a four-component Schrödinger cat state by reservoir engineering in a high-impedance circuit

In recent years, Schrödinger cat states stabilized by engineered dissipation have developed into serious candidates for error-protected qubits. In particular, robust suppression of the bit flips of a logical qubit encoded in a two-component cat state has been demonstrated. However, this qubit remains subject to phase flips. In contrast, a logical qubit encoded in a four-component cat state could be protected against both bit flips and phase flips. In this talk I will report on progress towards the stabilization of a four-legged cat state by engineered dissipation. Our engineering method relies on a driven Josephson ring embedded in a high-impedance circuit to activate a 5-photon joint transition of a target oscillator and a dissipative ancillary mode.