  We analyze the interior controllability problem for a nonlocal Schr\"odinger
equation involving the fractional Laplace operator $(-\Delta)^s$, $s\in(0,1)$,
on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The controllability
from a neighborhood of the boundary of the domain is obtained for exponents $s$
in the interval $[1/2,1)$, while for $s<1/2$ the equation is shown to be not
controllable. The results follow applying the multiplier method, joint with a
Pohozaev-type identity for the fractional Laplacian, and from an explicit
computation of the spectrum of the operator in the one-dimensional case.
