Yeah, Quantum theory isn't the word you are looking for...
In computer science, we have a technique called Memoization (NOT memorization).
http://en.wikipedia.org/wiki/Memoization
Lookup tables are quite popular too. It's pretty common to see sine and cosine tables saved as textures. You can precompute any problem space and store the values for reference. (linearly interpolated)
Now, you'll run into the memory/speed issue. Assuming that a lookup in a table is faster than the given operation (
not always the case, see 'Page thrashing' 2nd paragraph of the Overview section) then there is a direct trade off in memory for speed. Precomputing the problem space could exhaust the memory of the machine.
Now, this isn't to say that there isn't a place for precomputing, or offline rendering. Back in the day, Quake Maps had to have a BSP tree generated and light maps precomputed. This process took a couple hours (at least on my old 500mhz machine). Now-a-days this is done load time! A lot of lighting is done in real-time!
Precomputing AI decision trees isn't a bad idea. In fact, it's easier to precompute the search space and compose it into a tree for faster searching/navigation.
Now, exhausting the search space for moving a box (I'm thinking physics simulation) probably wouldn't be my first choice for a lookup table.
I have a game that uses natural cubic splines, which are great for approximating complex curves (think Zuma). However, the acceleration of the curve (2nd derivative) is pretty erratic, especially at sharp curves. I needed to normalize the curve by stepping and substepping to a set of points exactly 1 pixel in distance apart. On my fastest machine, it takes 30 seconds to generate. So I rendered the curve offline and loaded the data into memory.