There isn't a special Matlab library for using the Quarto with Matlab. Generally, the way to connect the Quarto to Matlab (or LabView, python, etc) is via the USB comm port. Take a look at Read Streaming Data from Arduino Using Serial Port Communication from MathWorks for an outline of how to do that.
If you can tell me more specifically what you are trying to do, I can try to give a more detailed answer.