Topological quantum computing (TQC) is a newer type of quantum computing that uses “braids” of particle tracks, rather than actual particles such as ions and electrons, as the qubits to implement computations. Using braids has one important advantage: it makes TQCs practically immune to the small perturbations in the environment that cause decoherence in particle-based qubits and often lead to high error rates. anyons tunneling in a double-layer system can transition to an exotic non-Abelian state that contains “Fibonacci” anyons that are powerful enough for universal TQC.
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous “Fibonacci” anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.
In the Supplemental Materials, they discuss a different “coupled wire” approach and show the remarkable agreement with the results presented. They provide additional details and generalizations of our analyses, and they discuss the duality between (nnl) bilayer state with interlayer pairing and (n, n, −l) state with interlayer tunneling.