Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems · HackerPapers discussions

Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems — mentioned by SyzygyRhythm

Wed, 17 Jun 2026 20:35:34 GMT

Doh! You are correct. I had been looking at a previous paper (which this new paper references). The previous paper showed that you can use any non-linearity in QM to solve NP-complete problems, and the new one shows that semi-classical gravity + QM has such a non-linearity. The earlier paper: https://arxiv.org/pdf/quant-ph/9801041

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Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems — mentioned by tromp

Wed, 17 Jun 2026 07:44:47 GMT

Shor doesn't solve an NP hard problem. It's even possible that factoring and discrete log are in P, while P != NP. The paper builds on the results of "Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems" by Abrams and Loyd [1], from which I quote: > The last qubit now contains all the information that we need; however, for small s, a measurement of the last qubit will almost always return |0>, yielding no information. > We wish to distinguish between the cases s=0 and s>0. > Step 4. Repeatedly apply the nonlinear operation to drive the states…

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Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems — mentioned by foobar2020

Mon, 14 Sep 2015 21:24:41 GMT

Quantum mechanics does not permit parallel states to "communicate" in any way. The theory is purely linear (i.e. acts somewhat independently on all states), except for the wavefunction collapse phenomena. Any non-linenarity would, for instance, immediately imply that we can easily solve NP-complete problems using quantum computing: http://arxiv.org/abs/quant-ph/9801041 So QM is probably a poor model for explaining human indecisiveness and irrationality. Much better is that it is simply the thing that evolution has come up with that can a) fit in our brains and b) yields proper results.

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Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems — mentioned by michael_nielsen

Wed, 02 Feb 2011 21:34:23 GMT

If you change the underlying physics, computational power can change quite a bit. The best-known example of this is that quantum computers are widely believed to be more powerful than classical computers. An even more striking example, though less well known, is that certain non-linear variants of quantum mechanics allow NP-complete problems to be solved in polynomial time. This result was written up here: http://arxiv.org/abs/quant-ph/9801041 We could imagine, then, that what's going on is that the Universe really runs according to the laws of one of these non-linear variants of quantum…

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Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems — mentioned by Dn_Ab

Mon, 09 Aug 2010 02:53:55 GMT

P = NP would touch almost every field known to man: maths (e.g. it would only be matter of search to take down the remaining Clay Problems), philosophy, engineering, biology, physics. The tie to physics is particularly interesting: for example if Quantum mechanics was a nonlinear theory then we could physically solve NP complete problems [1]. Note the implication, this is not to say p = np => QM nonlinear. The utopian consequences of p = np are discussed very engagingly by Scott Aaronson here [2]. I suggest you also check out his blog as well - his writing style is clear and fun. Plus there…

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Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems — mentioned by michael_nielsen

Sun, 23 May 2010 00:23:28 GMT

If you work in quantum computing -- which I did, full time for 13 years, and part time for a few years prior to that -- it's VERY common to run into people outside the field who believe that quantum computers can solve NP-complete problems in polynomial time. Dozens of wrong papers have been written claiming just that, and the claim also appears frequently (often implicitly) in popular journalism. The blog's subtitle is just acknowledgment of that fact. Incidentally, P and NP certainly do have to do with the hardware. There are nonlinear variants on quantum mechanics in which all the problems…

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