Four-photon dissipative phase-space stabilization of binomial code

The logical qubits encoded in rotation symmetric bosonic codes such as mod-4 cat, binomial or pair-cat codes, require stabilization mechanisms in both modulo photon numbers and modulo oscillator phases in order to preserve the logical information. There are experiments showing parity corrections for these codes that realize stabilization with respect to the modulo photon number. However, no experiment has yet demonstrated a sufficiently effective mechanism for stabilizing the conjugate modulo phase, which requires at least a four-photon stabilization process. In this talk, we report experimental progress in realizing a four-photon driven-dissipative process that stabilizes a binomial code in a superconducting microwave cavity. The process operates alongside our previously implemented autonomous parity-selective photon-addition scheme for correction of single-photon loss. This together achieves a complete first-order protection of a logical qubit using fully passive, continuous quantum error correction.