Fault-tolerant gates on a logical qubit*

A fault-tolerant architecture based on error-corrected qubits requires the implementation of logical gates that do not induce uncorrectable errors. Here, we present a fault-tolerant construction for a gate on a cavity-encoded logical qubit. The scheme uses the multilevel structure of a transmon ancilla, along with RF-tunable transmon-cavity interaction, to apply arbitrary phases to the cavity Fock states. This enables a broad range of gates on a variety of encodings, while protecting the logical qubit against photon loss, as well as ancilla decay and dephasing. Together with the previously demonstrated fault-tolerant syndrome measurements [1], this result further expands the toolbox towards fully fault-tolerant processing of logical qubits.

[1] S. Rosenblum, P. Reinhold, M. Mirrahimi, L. Jiang, L. Frunzio, and R. Schoelkopf, Science 361, 266-270 (2018).