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The following paper provides a protocol to physically generate a $2$-qutritentangling gate in the Kauffman-Jones version of $SU(2)$ Chern-Simons theory atlevel $4$. The protocol uses elementary operations on anyons consisting ofbraids, interferometric measurements, fusions and unfusions and ancilla paircreation.

Protocol for making a $2$-qutrit entangling gate in the Kauffman-Jones version of $SU(2)_4$