In a small saucepan over medium heat, combine the water and sugar, and boil until the sugar dissolves, stirring constantly. Remove from heat and allow to cool.

Stir in the pomegranate juice.

Transfer to ice cream maker and churn according to manufacturer instructions. When the sorbet has frozen (it will still seem quite soft), transfer to a storage container, cover tightly and freeze until ready to serve. The sorbet will solidify in the freezer.