As for the encoding a table base on a single atom, what would this premise be based on? If you go to the quark level, you are adding what, 1 order of magnitude to just storing on electrons? So, for even the most unstable atoms, still less storage for a single atom than a QR code.
Blueemu brought up what in computer/hardware parlance would be called "destructive reads" i.e. when the process of reading the data destroys the usable data. Just because particles have N properties does not mean we can store N bits of data thereby, nor read them back without disrupting the data.
Like trying to use the Bat Thermos to store a Riddler's riddle left in alphabet soup and feed it into the bat computer later, there are serious issues involved. I'll be surprised if anyone knows that reference
.
If unlimited levels of smaller particles (heretofore undiscovered) useful for storage is the notion, then I would consider anything much past quarks currently to be in the realm of positing magic.
another question is does the chess world really want to solve chess. I feel like so many of the people who have the most competence to try solving chess dont actually want to solve for their own good. Not to mention its extremely difficult to do anyways