Hello.
You’ll need a device that will act as a MIDI host between the CQ and your midi controller.
Hardware boxes like BOME BomeBox midiHub or CME U4Midi will allow dialogue between the 2.
You can also use an IPAD between the CQ and your controller. The IPAD, with the help of a little IOS app like Midimittr will act as a midi hub also.
Then you need to be sure that your midi controller speak the same language than the CQ.
CQ uses mostly NRPN midi.
Some midi controller natively handle NRPN, some don’t.
For those last ones, the hardware boxes above have extra features that can translate normal midi from your controller to NRPM understandable by the CQ.
There must be also IOS app that can do that (I don’t know).
And at the end, you have also DIY solution like mine: