Researchers have developed a novel protocol for creating reusable logical catalyst states, enabling the implementation of precise dyadic phase gates through phase kickback. This breakthrough utilizes a surface-code cultivation approach, leveraging a high-period Clifford circuit to construct the catalyst state, which can be supported on a relatively small number of logical qubits, specifically O(2^b). The catalyst state is an eigenstate of the circuit, allowing for the implementation of exact fine dyadic phase gates $Z^{2^{-b}}$. Once created, the catalyst can be invoked multiple times to apply the target phase gate, making it a significant advancement in quantum computing. The controlled-$U$ gadget is used to remove the catalyst after each invocation, ensuring reusability. This development has important implications for fault-tolerant quantum computing, as it enables more efficient and precise control over quantum states, so it matters to practitioners seeking to improve the reliability and scalability of quantum systems1.