We investigate quantum phase transitions for the s=1/2 antiferromagnetic He
isenberg model on the pyrochlore lattice. By means of the series expansion
method starting from isolated tetrahedra, the ground-state phase diagram is
determined. When the ratio of the two competing exchange couplings is vari
ed, a first-order (second-order) quantum phase transition occurs between tw
o spin gap phases (the spin-gap and the antiferromagnetic phases). We also
discuss some properties expected for the s=1 pyrochlore spin system.