  On the two-dimensional unit sphere, we construct uniformly bounded spherical
harmonics of arbitrary degree, under a condition of point distribution on the
sphere. It extends the results on odd-dimensional spheres by Bourgain,
Shiffman, and Marzo-Ortega-Cerda. Moreover, we show that the spherical
harmonics constructed in this paper are equidistributed in the phase space,
i.e., they are quantum ergodic. It provides the first example of Laplacian
eigenfunctions which are both uniformly bounded and quantum ergodic.
