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A method, termed controlled-injection, is proposed for compiling three-qubitcontrolled gates within the non-abelian Fibonacci anyon model. Building onsingle-qubit compilation techniques with three Fibonacci anyons, the approachshowcases enhanced accuracy and reduced braid length compared to theconventional decomposition method for the controlled three-qubit gates. Thismethod necessitates only four two-qubit gates for decomposition, a notablereduction from the conventional five. In conjunction, the study introduces anovel class of controlled three-qubit gates and conducts a numerical simulationof the topological iToffoli gate to validate the approach. In addition, wepropose an optimization method for single-qubit gate approximation using novelalgebraic relations and numerical methods, including distributed computing.

Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach