Hybrid Lattice Surgery

In universal fault-tolerant quantum computing, implementing logical non-Clifford gates often demands substantial spacetime resources for many error-correcting codes, including the high-threshold surface code. In this talk, we propose a novel way of implementing non-Clifford operations in the standard surface code based on hybrid lattice surgery. First we generalize the standard lattice surgery to hybrid lattice surgery, where operations of rough merge and rough split happen across different topological codes. Then we apply such procedures between Abelian and non-Abelian codes and show that this can provide non-Clifford operations in the standard surface code, in the form of a magic state or a non-Clifford gate teleportation.