Identifying non-Abelian anyons with upstream noise

Abstract

Non-Abelian phases are among the most highly-sought states of matter, with those whose anyons permit universal quantum gates constituting the ultimate prize. The most promising candidate of such a phase is the fractional quantum Hall plateau at filling factors $\nu=\frac{12}{5}$, which putatively facilitates Fibonacci anyons. Experimental validation of this assertion poses a major challenge and remains elusive. We present a measurement protocol that could achieve this goal with already-demonstrated experimental techniques. Interfacing the $\nu=\frac{12}{5}$ state with any readily-available Abelian state yields a binary outcome of upstream noise or no noise. Judicious choices of the Abelian states can produce a sequence of yes--no outcomes that fingerprint the possible non-Abelian phase by ruling out its competitors. Crucially, this identification is insensitive to the precise value of the measured noise and can uniquely identify the anyon type at filling factors $\nu=\frac{12}{5}$. In addition, it can distinguish any non-Abelian candidates at half-filling in graphene and semiconductor heterostructures.