Could rocks from Earth have reached the Kuiper belt, or Neptune at least? If so, how? This answer  (currently edit 3) to How certain are we that we have not sent life to other planets/moons? begins:

First of all, rocks from Earth are probably just about everywhere in the Solar System. One simple example is this rock found on the Moon. A number of pieces of Mars have been found on Earth, and if that has happened, no doubt there are Earth rocks on Mars. If Earth life can survive a vacuum it has probably gotten to everywhere in the Solar System anyways. (emphasis added)

I started to write the following as a comment:

&quot;...rocks from Earth are probably just about everywhere in the Solar System&quot; is quite a statement, and  ...from which point they will travel throughout the solar system. requires energy. What mechanism accelerates a rock from Earth to the outer solar-system? Mars is not really a distant object compared to the size of the solar system. New Horizons is in the Kuiper belt already. Is it even remotely plausible to suggest that Earth rocks can become KBOs?

Question: Can rocks from Earth have reached the Kuiper belt or Neptune at least? If so, how?
I'll even allow a solid particle of proper space-dust to serve as proxy for the rock for the purposes of this question, even sub-micron in size if necessary, but not simply an atom or a molecule. We know from answers to What is the origin of the dust near the sun? that dust is surprisingly (to me at least) mobile in the solar system due in part to its large surface to mass ratio and interaction with static EM fields and photons for example.
(I have tracked down the reference that I made in my comment on the question.)
Presumably earth rocks once blasted into space (by volcanism or meteorite impact) gain or lose energy primarily by orbital interactions with planets or moons. Since these interactions will occasionally give enough energy to escape the solar system entirely, presumably anything short of that (Neptune's orbit, the Kuiper belt) is also possible. The questions is if this will happen often enough to create a reasonable expectation that an Earth rock could have collided with any given solar system body.
Various attempts to identify the odds have been made.  In one, researchers simulated the path of fragments from the Chixculub impact, and found that many may have made it to the outer Solar System within 10 million years.
This is the paper in Astrobiology