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The possibility of realizing non-Abelian statistics and utilizing it fortopological quantum computation (TQC) has generated widespread interest.However, the non-Abelian statistics that can be realized in most accessibleproposals is not powerful enough for universal TQC. In this paper, we considera simple bilayer fractional quantum Hall (FQH) system with the $1/3$ Laughlinstate in each layer. We show that interlayer tunneling can drive a transitionto an exotic non-Abelian state that contains the famous `Fibonacci'anyon, whosenon-Abelian statistics is powerful enough for universal TQC. Our analysis restson startling agreements from a variety of distinct methods, including thintorus limits, effective field theories, and coupled wire constructions. Weprovide evidence that the transition can be continuous, at which point thecharge gap remains open while the neutral gap closes. This raises the questionof whether these exotic phases may have already been realized at $\nu = 2/3$ inbilayers, as past experiments may not have definitively ruled them out.

Fibonacci Anyons From Abelian Bilayer Quantum Hall States