Post

arxiv.org/abs/2606.13521 claims a "new S gate in the rotated surface code". To me the protocol is quite the same as the one described in Ismail et al. 2025 arxiv.org/abs/2509.18294, see Fig. 12 !

In the text there, they discuss that "it reduces the code distance by 1", so they stick to the intra-SE implementation for performance reason. It does not jump at me why exactly.

Section IV. A. Theorem 1 of Holmes paper seems to leave room for it.