Peel and roughly chop quince; do not core. Combine with cardamom, clove, and rum in a clean, wide-mouthed 1-quart jar. Cover with plastic, then cap tightly.
Let stand in a dark place for a month or more, shaking the jar whenever you think of it.
Boil sugar and water for 3 minutes; cool completely. Strain out and discard solids from the liqueur. Strain