1. Prepare the syrup: In a small saucepan, combine water and sugar. Bring to a boil and cook until sugar dissolves, five to seven minutes. Cool completely.
2. Puree the passion fruit in a food processor until smooth.
3. Add pomegranate juice and syrup and pulse until combined and smooth. Pour through a sieve to remove seeds.
4. Pour mixture into an ice cream machine and churn until frozen. Alternately, pour into a shallow dish and freeze, stirring every half hour or so, until frozen and scoopable. Best eaten within a few days. If frozen too hard, thaw for five to 10 minutes before serving.