re: computational complexity, I am not informed enough to answer that, but I've wondered it too. But we've said things like that before about, say, factoring huge numbers, only to find out that quantum computers can solve it with a fraction of the energy ("orders of magnitude" doesn't even cut it here).

The other thing I've wondered is how could you have a detector for those particles without interfering with your measurement (heisenberg's)? Your measurement apparatus will give off heat or very slightly change the shape of spacetime, thus interfering where your particles are detected :(.