Fault tolerant non Clifford gate for GKP magic state distillation

Bosonic codes recently emerged as a promising approach for fault tolerant quantum computing. Among them, microwave Gottesman-Kitaev-Preskill (GKP) codes are appealing due to their enhanced lifetimes and high-fidelity Clifford operations. However, in microwave platforms, they lack a realistic fault tolerant non Clifford gate in order to complete the set for universal computation. We therefore study a new logical non Clifford gate √H, implemented by a Kerr interaction. Using the small-Big-small (sBs) protocol to correct errors, we demonstrate that we can use this gate to prepare GKP magic states and that it could lead to significant improvements in distillation protocols, therefore getting closer the goal of universal fault tolerant computation.