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To your first question, two things. First it could be real, sure, and that's called an analog computer (not to be confused with an analog circuit). That subject
by daxfohl 6y ago
To your first question, two things. First it could be real, sure, and that's called an analog computer (not to be confused with an analog circuit). That subject has been studied too, but hasn't been terribly fruitful in terms of realizable improvements over classical. Second, complex because that's how physics works (we think). Scott Aaronson wrote up an article about what the alternatives might be. https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021
To your second question, the quantum system can represent all N states simultaneously (until you observe it) because of entanglement. The classical system can only represent one at a time.
- Sniffnoy 6y agoA quantum computer with real amplitudes is not an analog computer. The two are quite different. Note that a quantum computer with real amplitudes is actually just as powerful as one with complex amplitudes; the complex amplitudes are actually inessential. Also, your answer to the second question fails to distinguish a quantum computer from a classical probabilistic computer. The key here is really cancellation of amplitudes, not the larger state space.
- Green_man 6y agorepresentation of all N (where N = 2^n) states simultaneously is due to superposition, not entanglement.