It's not a string quartet, nor is it classical music. A string quartet is comprised of four stringed instruments--two violins, a viola, and a cello. For example, here's a link to Maurice Ravel's String Quartet in F major,
The 6 second piece of music that you've posted has percussion and electronics & is possibly computer generated. So, I'd say it's relatively current music.
Michall writes, "This is classical music. I should add that it has been modified with electronic drums and maybe some other sounds. But definitely the base is classical music."
Well, okay, it's possible that it's a modified bit from some classical piece, but it's very difficult to say what it is based on, judging from only a 6 second clip. Do you have more than just 6 seconds? If you had more & it is based on a classical work, I think it's quite possible that people around here might recognize what it is. To my ears, I don't think it's based on a 4 part string quartet. But I could be wrong.