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Fibonacci anyon, an exotic quasi-particle excitation, plays a pivotal role inrealization of a quantum computer. Starting from a $SU(2)_4$ topological phase,in this paper we demonstrate a way to construct a Fibonacci topological phasewhich has only one non-trivial excitation described by the Fibonacci anyon. Weshow that arrays of anyonic chains created by excitations of the $SU(2)_4$phase leads to the Fibonacci phase. We further demonstrate that our theoreticalpropositions can be extended to other topological phases.

Fibonacci topological phase in arrays of anyonic chains