Stabilizer Formalism for Quantum Gate Teleportation

Quantum gate teleportation is a fundamental building block for realizing logical operations in fault-tolerant quantum computation. In particular, non-Clifford and certain Clifford gates are often executed via teleportation protocols that consume specific resource (magic) states. Although many such protocols have been proposed, their underlying structures have not been systematically understood. In this work, we develop a unified framework for quantum gate teleportation based on the stabilizer formalism. This framework reveals common structural features among different teleportation schemes and provides a clear way to quantify operational costs of implementing non-Clifford gates through various magic states. Furthermore, we demonstrate that our formalism naturally extends to describe addressable Clifford operations in high-rate stabilizer codes, offering new insights into efficient logical gate synthesis in fault-tolerant architectures.