Bring sugar and water to a boil in a saucepan, stirring until sugar dissolves. Add zucchini. Reduce heat to medium. Simmer, with a round of parchment placed directly on the surface, until zucchini are translucent, 15 to 20 minutes. Let zucchini cool in syrup.
Arrange zucchini in a single layer on a wire rack set over a baking sheet. Let dry for 1 hour. Use immediately.
Use a mandoline to slice the zucchini into thin, even strips that are less than 1/8 inch thick but not paper thin (or they'll fall apart). The syrup infuses the ribbons, making them translucent and shiny. Have a piece of parchment ready to place directly on the surface of the syrup -- it will keep the zucchini submerged.