He apprenticed as an engraver under Jonas Haas and Odvardt Helmoldt von Lode.
Haas sued him for having left his workshop to set up his own without the Royal Art Academy's approval but the dispute seems ultimately to have been settled outside the courtroom.
[1] Qvist completed a substantial number of prospects for Johan Jacob Bruun's Novus Atlas Daniæ in 1761.
He created most of the engravings for Bruuns work as well as some of the leads for Danske Atlas.
He purchased the property at Ny Vestergade 9 in 1772 and sold it to royal gunsmith Christian Kyhl in 1797.