Proposal for reading out anyon qubits in non-abelian $\nu =12\mathrm{/}5$ quantum Hall state

To detect non-abelian statistics in the $\nu =12\mathrm{/}5$ quantum Hall state through interferometry, we apply an analysis similar to the ones proposed for the non-abelian $\nu =5\mathrm{/}2$ quantum Hall state. The result is that the amplitude of the Aharonov-Bohm oscillation of this interference is dependent on the internal states of quasiholes, but, in contrast to the $\nu =5\mathrm{/}2$ quantum Hall state, independent of the number of quasiholes. However, if the quasiholes are in a superposition state, it is necessary for the interferometer to have certain additional features to obtain the coefficients.