I own the HSM II version of this lens, which natively is a little soft wide open but sharpens up once you stop it down a bit.
When I initially tested it on the Q I was disappointed with the results.
The images were hazy and lacked contrast, almost like they were shot through smoke.
User Barondla suggested internal reflections might be causing the issues and I noticed that the HSM II has a lens element at the rearmost section near the mount.
The Fotodiox adapter also had a semi gloss finish internally so I decided to take a chance and coat the inside of the adapter with flat black paint to absorb any reflections.
The results after painting the adapter were drastically improved, the images no longer exhibited the smoky appearance, and I found that dialing the lens to 5.6 yielded very good results on the Q.
Once I acquired the Pentax adapter I was pleased to find that the design and finish of the adapter did not cause any reflections with this lens and it continues to be a usable choice with the Q.
The Sigma 70-200 is an excellent choice for the Q as long as you take the precautions mentioned regarding internal reflections on the third party adapters.
The lens exhibits no tendencies for CA, and gives sharp results at f5.6.
SInce I had previously only tested tele primes, it was nice to be able to have a good quality tele zoom that could allow me to widen the shot if needed, going from approx 350mm equivalent to 1100mm equivalent on the Q.