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I'm a computer science major who's really keen on physics and quantum mechanics. I have started learning about Q# and D-Wave, but I just wanted to know if it's possible to test quantum mechanical theories using quantum computers.

If so, then what all different things should I look into? For example, Q# allows us about 30 qubits for free developing. What kind of simulations can I do with that many qubits?

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What do you mean by "Quantum Mechanical Simulations" ?

One of the primary motivations in the early history of quantum computing was a statement from Richard Feynman that a quantum computer would be able to effectively simulate quantum systems. To that end, a lot of the nearest term quantum programs people are trying to run (and have run) are simulations of ground states of atoms and molecules. These are very classically resource intensive, but IBM has done this to good success on smaller highly symmetric molecules using their current quantum computers.

On the other hand, if you are wondering if we can test Quantum Mechanics as a theory using a Quantum Computer things like Bell's Inequalities can be tested. This is a proof that a system is Quantum Mechanical, as there is an inequality which can only be broken if using entanglement. The article linked has a good explanation, and goes into some of the experimental verifications which have already been done, but such a test is one of the ways to ensure that a given Black Box Computer is quantum is nature.

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  • $\begingroup$ Yess this is exactly what I meant by quantum simulations, perhaps I shouldve used Quantum Mechanics as a theory like you mentioned :) $\endgroup$ – Yashank Varshney Aug 2 '18 at 3:00
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    $\begingroup$ The problem with Bell tests on a quantum computer is that most architectures are not set up to be able to close the loopholes, particularly the locality loophole, because qubits are placed close to each other so that they can interact. Perhaps contextualise would be a better suggestion? $\endgroup$ – DaftWullie Aug 2 '18 at 5:34
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    $\begingroup$ @DaftWullie That's a fair point, I'm not sure I have a better example which still stays within the realm of somewhat simple quantum theory. I'm sure there's some form of a coin-flipping game which would work, but I can't think of one. $\endgroup$ – Dripto Debroy Aug 2 '18 at 13:37
  • $\begingroup$ @DaftWullie For a recent experimental result that tries to avoid the locality loophole, see arxiv.org/pdf/1603.05705.pdf. $\endgroup$ – Mariia Mykhailova Aug 2 '18 at 18:49
  • $\begingroup$ @MariiaMykhailova i’m Familiar with Bell tests. The point that I was making is that those are distinct experiments from quantum computers, and that the quantum computer experiments are not designed to close the loopholes. $\endgroup$ – DaftWullie Aug 3 '18 at 5:12
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A separate note on using simulators for this (as opposed to using an actual quantum computer).

Simulators, like the one that ships with Q#, are built to simulate quantum mechanical theories as we understand them now. This means that any experiment you run on a simulator will behave exactly as the theory says (well, unless the simulator has a bug in the code), but it doesn't mean that this experiment confirms the theory - it only means that it's a good simulation/illustration of the theory.

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  • $\begingroup$ So are you saying that if there is something different from the proposed theory, we practically will not be able to test them out using simulators like Q#? Just because they're essentially supposed to do exactly what the current theory states? $\endgroup$ – Yashank Varshney Aug 3 '18 at 13:32
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    $\begingroup$ Yes, exactly. (Except Q# is not a simulator but a programming language which can invoke a simulator shipped as part of Quantum Development Kit... But I nitpick) $\endgroup$ – Mariia Mykhailova Aug 3 '18 at 14:35

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