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 !
Quantum Logic Codes: Complete Transversal Logical Clifford Instruction Sets for High-Rate Stabilizer Quantum Error Correcting Codes
We study the structure and transversal logical capabilities of stabilizer quantum error correcting codes. Among our results, we identify universal lower bounds on circuit depth to generate a full logi...
arxiv.org