# What's the largest system we can study based on “fundamental limits to computation”?

If we have a (classical) computer about the size of a room and if its computational power is only limited by fundamental limits to computation, what is the largest system we can study using different approximations/methods in a reasonable amount of time?

The question is out of curiosity and hence we need some assumptions. Please be free to edit the question if the following asssumptions are not reasonable or if we need more assumptions.

Let's assume:

1. Size of the room is 5m x 5m
2. Reasonable time = 1 month
3. Property to be calculated = ground state energy of the system
4. Accuracy - milli-Hartree
5. Type of the system - Alkenes of length $$n$$
• +1. But as I mentioned earlier, you will need to give the accuracy you want for that energy (even for the H atom, if you want the electronic energy accurate to 10^50 digits, it won't happen even if a computer the size of Earth). Also as I mentioned earlier, you'll have to choose what system you're applying this to (ex. uniform electron gas, alkenes of length n, etc.). Organic compounds containing only single-bonded C's and H's, are easier than actinide-containing heavy metals, for example. – Nike Dattani Jul 27 at 17:24
• Added some more details as mentioned by you – Thomas Jul 27 at 18:05