Fast, self-correcting non-Clifford gates in driven, dissipative circuits

In a recent work (Nathan et al, arXiv:2405.05671), we proposed a circuit architecture and protocol for stabilizing a GKP qubit and doing Clifford gates in a driven, dissipative superconducting circuit. We extend this architecture by proposing a protocol for non-Clifford (T) gates, based on the inclusion of a potential that is quartic in the flux. We show that such a gate is topologically robust with exponentially suppressed infidelity down to sub-microsecond gate times. We discuss a circuit architecture which realizes the desired quartic potential, and analyze the resilience of the gate protocol to noise, imperfect control, and imperfect targeting of circuit parameters. With this new gate protocol, our architecture provides a potential platform for realizing universal, self-correcting single-qubit quantum computation, presenting exciting new opportunities in the field of superconducting quantum computing.