The rules are based purely off the description supplied on Quantum Gothic's website. There, it is stated that the cannon can be operated in two modes: a blast of "quantum energy" that causes instantaneous aging in the area of effect, or as a regular shell/projectile artillery piece.
I suggest treating the cannon as an objective that is placed at least 12" from any unit at the start of the game. If a player controls it (in an uncontested sense) at the start of his/her turn, then they may fire it provided that the controlling squad undertakes no other movement.
As an alternative, treat it is as a BS=3, AV=12 all-round static vehicle that costs 125 points.
Before shooting, the controlling player must select which mode the cannon will fire in this turn.
Type: Apocalyptic Barrage 1
Quantum Energy Blast mode.
Type: Small blast 1