Well, a real experimental system is a quantum computer that 'calculates' the emerging behavior in real time. Sorry, that was needlessly sarcastic---actually, you have a good point there: it's ironic that we used digital computers to simulate quantum systems, and now we're beginning to use quantum computers to calculate digital properties (like decryption, etc), whereas it would be interesting to actually use quantum computers to calculate quantum systems such as electronic structure of many body systems. It's just that we're nowhere near that yet.