  We present a method for numerically building a vortex knot state in the
superfluid wave-function of a Bose-Einstein condensate. We integrate in time
the governing Gross-Pitaevskii equation to determine evolution and stability of
the two (topologically) simplest vortex knots which can be wrapped over a
torus. We find that the velocity of a vortex knot depends on the ratio of
poloidal and toroidal radius: for smaller ratio, the knot travels faster.
Finally, we show how unstable vortex knots break up into vortex rings.
