I would like to install a surge protector in my panel. I am limited on space and it calls for two 30 amp breakers. Is it possible to use a quad breaker? I included a photo of the breaker.
Unnecessary work. Surge suppressors don't need to take breaker spaces.
First, you can install a wire-on surge suppressor and have it share a large breaker with another appliance. The surge suppressor isn't really a load per se, so it doesn't have an ampacity. If the UL-approved instructions on yours says "don't do that", then send it back - there are plenty which allow it, and with wire-on surges, brand doesn't matter since bus stabs aren't involved.
Second, since "correct breaker for the panel" is in your vocabulary, I'll infer you have a Siemens lineage panel. Siemens makes a plug-on "surge protector that goes where breakers go" with 2 actual breakers in it. They took the quadplex form-factor, hollowed out the middle 2-pole breaker, and put a surge there. Since it has 1 breaker per space, it is a regular breaker (QP) not a tandem/quad (QT), CTL is not a factor, and it fits any panel where Siemens breakers belong.