10^12 qubits, though sounding impressively large, is actually rather low for a teleporter of everyday objects. Remember the Avogadro constant cup? If allocating just one qubit per molecule, a single mol requires on the magnitude of 10^24 qubits.

(Of course, if there were some sort of square-root-of N phenomenon going on here — as there are in a couple of quantum algorithms — then that would probably constitute one major clue on how the teleporter works for anyone seeking to reverse engineer it. Knowing that something really is possible makes it easier to repeat, and all that.)

[SPOILER]

Helen Narbon Sr. had already spent her whole budget on enough boxed wine to get her to concentrate on an invention made from someone elses blueprints.

Or enough boxed wine to survive 30 minutes.

You know, either way.

  “Oh, come on…”

“Just say it!”

“All right…”

We were stranded on an island,
But we made it back to dry land!
Dave, he teleported Helen away!
Trouble is, her life he saves,
But her genes got mixed with Dave’s;
Now we gotta clean her gene DNA!
It’s like splicing with a hatchet!
(Now we’re gonna quote Pratchett;
You people, don’t just sit there and lurk!
Come on, say it ev’ryone!)
“It’s a million-to-one,
It sounds crazy, but it maybe could work!”

Yeah, we’re
Teleporting Dave’s genes!
(In this strip!)
Teleporting Dave’s genes!
(What a trip!)
Teleporting Dave’s genes!
(Helen’s clean!)
Teleporting Dave’s genes!
(We built a cool machine!)

The seasoned reader might wonder if some sort of hideous causal loop is at work in Dave’s mind – having deconstructed a teleporter back on that lovely island, how much of that retained knowledge went into constructing this teleporter? Let’s quietly assume that, given half of the brainpower behind this invention being Helen’s, it wasn’t very much at all.

Nanobots tend to bring to mind artificially motivated metal powder, unlike than the gooey cellular life-infused mental imagery of gene-splicing, don’t they?