  We study the tidal deformability of bare quark stars and hybrid compact stars
composed of a quark matter core in general relativity, assuming that the
deconfined quark matter exists in a crystalline color superconducting phase. We
find that taking the elastic property of crystalline quark matter into account
in the calculation of the tidal deformability can break the universal I-Love
relation discovered for fluid compact stars, which connects the moment of
inertia and tidal deformability. Our result suggests that measurements of the
moment of inertia and tidal deformability can in principle be used to test the
existence of solid quark stars, despite our ignorance of the high density
equation of state (EOS). Assuming that the moment of inertia can be measured to
10% level, one can then distinguish a 1.4 (1) $M_\odot$ solid quark star
described by our quark matter EOS model with a gap parameter $\Delta=25$ MeV
from a fluid compact star if the tidal deformability can be measured to about
10% (45%) level. On the other hand, we find that the nuclear matter fluid
envelope of a hybrid star can screen out the effect of the solid core
significantly so that the resulting I-Love relation for hybrid stars still
agrees with the universal relation for fluid stars to about 1% level.
