Exponentially robust control of bosonic modes using dissipative cat qubits

In circuit quantum electrodynamics, control of linear bosonic modes is enabled by coupling to a nonlinear ancillary qubit, such as a transmon. However, decoherence of the ancillary qubit can propagate to uncorrectable errors on the bosonic modes. In principle, use of a biased-noise ancillary qubit can prevent this damaging error propagation, but in practice simultaneously realizing large noise bias and high-fidelity control interactions has so far proven challenging. In this talk, we present a practical scheme to simultaneously realize exponential noise bias and high-fidelity control by combining together a dissipative cat qubit with a standard transmon. The resulting hybrid cat-transmon ancilla inherits exponential noise bias from the dissipative cat, and high-fidelity control schemes from the transmon, which is repeatedly reset to prevent damaging error propagation. We discuss several applications of this approach, including implementations of bias-preserving CX and Toffoli gates between dissipative cat qubits, and stabilization of GKP qubits.