cmap does't work to quit command line

I try to make <C-q> always mean 'make the current thing go away' but
this doesn't work for making the command line go away with cmap.

Pushing Esc does so I don't see why the map in the subject doesn't.
It does do something though, it changes from just putting a carrot
on the command line and flickering the cursor to giving an error:

E492: Not an editor command: (whatever was on command line)

Any ideas?

Thanks,
Britton

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