  We present simulations of interferometric Sunyaev-Zel'dovich effect (SZE) and
optical weak lenisng observations for the forthcoming AMiBA experiment, aiming
at searching for high-redshift clusters of galaxies. On the basis of simulated
sky maps, we have derived theoretical halo number counts and redshift
distributions of selected halo samples for an AMiBA SZE survey and a weak
lensing follow-up survey. By utilizing the conditional number counts of weak
lensing halos with the faint SZE detection, we show that a combined SZE and
weak lensing survey can gain an additional fainter halo sample at a given false
positive rate, which cannot be obtained from either survey alone.
