  We investigate the response of a model gravitational wave detector consisting
of two particles to the quantized cylindrical gravitational waves and obtain a
relation between the standard deviation of the distance between two particles
and the distance from the source to the detector. It is found that the quantum
effect carried by the cylindrical gravitational wave can be observed above
Planck scale even though the source is as far as the cosmological horizon. The
equation of motion for the change of the distance between two particles is
obtained when the cylindrical gravitational waves pass. It is surprising that
the dissipative term does not exist up to the first order approximation due to
cylindrical symmetry of the gravitational wave.
