How could working quantum computers test if nonlinear quantum mechanics or another nonlinear theory is at work at deeper levels or fundamental level?
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$\begingroup$ Purely in terms of the Question, why might nonlinear quantum mechanics being found by future quantum computers be a problem? How working quantum computers might test if nonlinear quantum mechanics or another nonlinear theory was at work is a wholly different Question and how could that matter? $\endgroup$– Robbie GoodwinCommented Feb 13, 2023 at 23:15
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4 Answers
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This is hard to say. Given that nonlinearities would be interpreted at first as a broken computer, presumably the answer would require many different quantum computers based on different technologies running into similar barriers vis-a-vis their quantum coherence times and the delicacy of their operations. By collecting many different physical systems with apparently the same boundary, you would start to get the idea that it's not just one physical realization of quantum mechanics that needs a more complicated model, but rather that you have found a deeper mystery which has an effective theory that is linear for typical quantum regimes, but becomes nonlinear in some corner case.
Fortunately there are lots of different proposals for quantum computers, unfortunately they're all kind of mediocre. When quantum computing breaks out it will probably be just one of these technologies passing a certain cost-benefit threshold and edging all of the others out of the market within a few decades. So we're speculating on something that would have to be a century or two off or so, even if quantum computing really “lands” in the next few decades. Maybe that is pessimistic, but given that we're 70 or 80 years into the silicon revolution and everyone is still talking the silicon silicon silicon, I think it's realistic.
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$\begingroup$ This answer doesn't consider the possibility that the Schrodinger equation might fail at level still practically simulable by a classical computer which would be much more convenient than the scenario you're describing. It will be very hard to debug a quantum computer that's not working because Schrodinger's equation is broken :( Another way we may realize quantum computers are broken is if their answers don't work. For example, suppose a computer generates a protein that should 100% behave a certain way according to the computer but then it doesn't behave that way. (1/2) $\endgroup$ Commented Feb 13, 2023 at 1:15
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$\begingroup$ It's not at all obvious that one should suspect the computer/Schrodinger's equation, but if you are certain enough in the computer's model and solution you may be led to that conclusion. (2/2) $\endgroup$ Commented Feb 13, 2023 at 1:16
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No. Models are not fundamental. A quantum computer can, in the end, tell you only about the properties of the model it computes. It cannot tell you whether that corresponds to reality. You need an experiment.
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1$\begingroup$ A quantum computer is an experiment. It is an experiment testing Schrodinger's equation. $\endgroup$ Commented Feb 13, 2023 at 1:13
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2$\begingroup$ @Jagerber48 True, but if it exhibited nonlinearity, we would attribute that to the computer, not to the physics being modeled. So, that would not count as using it as a computer. $\endgroup$ Commented Feb 13, 2023 at 1:18
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$\begingroup$ but, it is a theoretical possibility that quantum computers might be the first physical experiments to explore system scales large enough to probe such hypothetical non-linearities of the Schrodinger equation. Quantum computers are built assuming 100% that Schrodinger's equation is correct. The interesting assumption is if that assumption is wrong, how would we know? If the Schrodinger equation breaks down (in this hypothetical scenario) at a scale small enough that classical computers can simulate the quantum program which exposes the problem then we will see a divergence (1/2) $\endgroup$ Commented Feb 13, 2023 at 1:48
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$\begingroup$ quantum and classical results and after a few years or decades of double checking everything we may eventually suspect Schrodinger's equation. But what if the breakdown happens at a quantum computation scale larger than what we can classically simulate? The quantum computer would give answers, but how would we know they are the right or wrong answers? It's a very interesting question. The answer by CR Drosts adopts clock methodology of testing quantum computers based on different physical systems against each other. This is an interesting answer. I'm curious if there are others. (2/2) $\endgroup$ Commented Feb 13, 2023 at 1:50
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$\begingroup$ @Jagerber48 All true, but only in the sense that operation of any piece of machinery is a physics experiment. $\endgroup$ Commented Feb 13, 2023 at 14:12
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In principle yes. If the computer relies on a given linear model to work as expected, and we find it behaves strangely, then the computer has found nonlinear quantum behaviour.
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The computational model used in a quantum computer has no bearing to how quantum mechanics work, just like a computer made from solid state transistors is no tool for exploring solid state states and transitions.
It may be suited better for juggling the kind of computational tasks required to model quantum mechanical processes, but that does not provide insights into quantum mechanical processes.
The only means to discover quantum mechanical novelties is when the computer is regularly returning results inconsistent with the expectations of its implementation, just like randomly flipped bits in a classic computer may tell of its susceptibility to cosmic radiation.