Actually, it’s explicitly not all in between. The quantum state is a super position, not a smear. It is (ideally) both 1 and 0, but nothing in between.
It’s power comes when you have a multi bit number. 16 bits give 65536 possibilities. A classical computer would have to check each one individually to process them all. A quantum computer does them all in 1 go.
While it gets very messy in the implementation, quantum computers are still binary, just quantum binary. No infinities needed