"swift thought" is correct and usable in written English.
You can use it to emphasize the quickness of someone's thoughts or decisions. For example, "When the thief was threatening them, he had a swift thought and decided to call the police."
Light is the ultimate velocity, light is gossamer nimbleness, light is the swift thought of God.
There is no better proof of the strong sympathies on which their friendship was founded than the brilliance with which Shelley can evoke it: "the swift thought, Winging itself with laughter, lingered not, But flew from brain to brain..."...
The first problems, Swift thought, seemed manageable.
The apartment had a rainy, musty smell that Ms. Swift thought the selling broker could have fixed by buying a dehumidifier.
If Swift thought for even just a second of how lucky she is not to know what that's like, then trap has done its job.
Regardless of what Swift thought of himself, the Cathedral was always crowded during his sermons.
In Not I, Dwan is a spotlit motormouth whose speech is swift as thought, if not swifter.
An artful flick of Khedira's heel slipped the ball between the defenders, Benzema was on it in a nanosecond, and, too swift for thought, he flicked the moving ball over the head of the opposing goalkeeper, into the net.
The visitors were everything the Celtic manager would wish his own side could be: swift of thought and movement, incisive, quick and precise in their passing, and capable of winning the ball back effectively.
Friedrich Nietzsche, the third member of the irrationalist triumvirate, was a prolific but unsystematic writer, presenting his patchwork of ideas in swift atoms of thought.
If that seems swift, spare a thought for two direct-to-DVD items that had lofty festival premieres under different titles last year.
