Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

In this work, we introduce building blocks of error-corrected gadgets for bosonic qubits by leveraging ancilla-assisted bosonic operations through a generalized variant of path-independent quantum control (GPI). With these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction only requires dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Using our scheme, each error-corrected bosonic qubit is only comprised of a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic error correction in the full fault-tolerant setting. These developed fault-tolerant schemes can also be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits.