There's no rock officially recognized as "blue quartz". Quartz, in its pure form, is clear or white. However, there are a few possibilities for what you might be thinking of:

1. Blue Chalcedony: This is a variety of chalcedony, a type of microcrystalline quartz, that appears blue due to inclusions of various minerals like crocidolite, goethite, or other blue minerals.

2. Blue Topaz: While not technically quartz, blue topaz is a popular gem that is often mistaken for "blue quartz" due to its similar appearance.

3. "Blue Quartz" as a Trade Term: Some retailers might use the term "blue quartz" loosely to describe other blue gemstones or even dyed quartz. It's important to be cautious about this term and inquire about the specific mineral involved.

If you're looking for a specific blue stone, be sure to ask for its proper name to avoid confusion.