Magic teleportation with generalized lattice surgery

Abstract: We propose a novel, distillation-free scheme for the fault-tolerant implementation of non-Clifford gates at the logical level, thereby completing the universal gate set. Our approach exploits generalized lattice surgery to integrate two quantum error-correcting (QEC) codes. Specifically, non-Clifford gates are executed transversally on one QEC code and then teleported to the main circuit via a logical-level joint measurement that connects two distinct QEC codes. In contrast to conventional magic state distillation (MSD) combined with gate teleportation, our method obviates the need for concatenating separate codes for distillation and logical qubits, thus reducing the total overhead from multiplicative to additive scaling. We illustrate our approach by explicitly demonstrating its implementation for a 3D color code interfaced with a surface code of the same code distance, and comment on its potential advantage over the conventional MSD-teleportation scheme.