Put the water and sugar into a small pot over medium heat, and stir it constantly with a spatula until the sugar has dissolved (less than a minute).
Then let it heat until just starting to simmer, set a timer for three minutes of simmering, and turn off the heat when the timer goes off. Immediately pour in the yuzu juice concentrate and stir well, then let it get to room temperature on a cool burner (about 30 minutes). Don't cover it or the syrup will end up too thin; the cooling time also lets more of the water evaporate out.
Once cooled, pour your yuzu simple syrup into a glass jar, close the jar and store it in the fridge for up to 2 weeks or the freezer for up to 6 months. Makes ¾ cup of syrup.