I realize this is likely a translation error, but the amount of space required to keep the state of 300 up/down spins is 300 bits, or 38 bytes. What you're thi

I realize this is likely a translation error, but the amount of space required to keep the state of 300 up/down spins is 300 bits, or 38 bytes. What you're thinking of is a a single basis state. The state of a 300 spin system can, in general, have any superposition of the 2^300 basis states available. These superpositions also mean that even in the single spin case, you're not representing states exactly, but truncating the representation at some point that is good enough.