Semiclassical Gravity Efficiently Solves NP-Complete Problems

(arxiv.org)

32 points by ascarshen7 hours ago

5 comments

SyzygyRhythm1 hour ago
I was skimming the paper and came to this: > This transformation is like an AND gate - it ignores the index qubit and places the flag qubit in the state |1> if and only if either of the original components had the state |1> for the flag qubit.Shouldn't that be an OR gate? Not only does the description above say "if and only if either of the original components had the state |1>", which is an OR, but the truth table listed above shows the same thing for the flag qubit.Of course, one could say it's an AND on the |0> states, which is just De Morgan's law, but that's pretty awkward phrasing.
aix14 hours ago
Anyone care to ELI5 the novelty or significance of this?
- tancop3 hours ago
 if the PECTT (Physical Extended Church-Turing Thesis) is true then the current standard way of connecting classical gravity with quantum mechanics is wrong. the authors take it as evidence for full quantum gravity because the alternative is changing the Einstein equations in some arbitrary complex way. im not a physicist so this might be a bad explanation.the extended thesis it depends on is "No physical procedure can decide an NP-complete problem in polynomially many steps." imo thats a very strong and controversial assumption when we still dont know the limits of what quantum computers can do.
 - red75prime9 minutes ago
 > we still dont know the limits of what quantum computers can do.Well, we don't know the limits of what classical computers can do too (P!=NP is not proven).While not directly related to P!=NP, historical claims of quantum superiority were occasionally taken down by finding an efficient classical algorithm.
 - bawolff1 hour ago
 > the extended thesis it depends on is "No physical procedure can decide an NP-complete problem in polynomially many steps."I think part of the confusion here, is that usually the extended church turing thesis means that any physical computation can be efficiently (in polynomial time) simulated by a deterministic turing machine. (And thus if quantum computers exist and BQP is a superset of P, the proposition is false). I've never seen it defined before as above. But im definitely not a complexity theorists.
 - misja1113 hours ago
 But isn't PECTT already challenged by quantum algorithms such as Shor and Grover?
 - xdertz2 hours ago
 Prime factorisation is not proven to be NP-hard so the existence of a quantum polynomial algorithm (Shor) has no bearing on complexity classes other than showing that prime factorisation is in BQP (quantum polynomial). So it does challenge PECTT on 'vibes' as most experts think it is not in P, but there is no mathematical proof for it.Grover gives an at most quadratic speedup for NP-hard problems, it does not turn a non-polynomial algorithm into a polynomial one.
 - tromp2 hours ago
 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 representing these two cases apart at an exponential rate: eventually, at a time determined by a polynomial function of the number of qubits n, the number of solutions s, and the rate of spreading (Lyapunov exponent) λ, the two cases will become macroscopically distinguishable.[1] <a href="https://arxiv.org/abs/quant-ph/9801041" rel="nofollow">https://arxiv.org/abs/quant-ph/9801041</a>
 - mofeing2 hours ago
 No. As far as we know, no realization of a quantum algorithm can solve NP-complete problems in polynomial many steps.Some people that worked on this topic told me that there seems to be some improvements on the quasi-optimal solution found, but that due to the scale of current quantum computers, it just have been tried out on small-sized problems.Theoretically, there are some papers suggesting that there are problems in BQP (the computational model of quantum computers) outside of NP [1] and even, the PH [2] (Polynomial Hierarchy, the infinite hierarchy of composition of NP and co-NP problems), which is why we cannot still satisfactorily say whether quantum computers can or cannot solve NP-complete problems.The Wikipedia page for BQP [3] does a good job showing what is currently known.[1] <a href="https://arxiv.org/abs/2209.10398" rel="nofollow">https://arxiv.org/abs/2209.10398</a> [2] <a href="https://eccc.weizmann.ac.il/report/2018/107/" rel="nofollow">https://eccc.weizmann.ac.il/report/2018/107/</a> [3] <a href="https://en.wikipedia.org/wiki/BQP#Relationship_to_other_complexity_classes" rel="nofollow">https://en.wikipedia.org/wiki/BQP#Relationship_to_other_comp...</a>
 - IsTom1 hour ago
 As to the PH result, arguments on relativized classes can be pretty inconclusive. There's both oracles for P^A = NP^A and P^B != NP^B.
- casey231 minutes ago
 They essentially are saying semiclassical gravity (a broader theory subsuming classical) is theoretically incorrect. Like doing the konami code IRL and getting infinite money.
einpoklum2 hours ago
From the abstract:"Assuming [assumptions] we show that ... can in principle solve..."Yeah, well, you know... that doesn't sound as promising as the title.
- Garlef2 minutes ago
 That's the whole point of the article:"We show [Assuming {competing physics theory} then {P = NP}]"(or something along the lines)"But we actually think P != NP... so [Assuming {P != NP} then {competing physics theory} cant be true]"
- bawolff1 hour ago
 Assuming X is true, that implies Y. We don't think Y is true therefore we now doubt that X is true, is a very standard thing to do in math.
- greenbit24 minutes ago
 Shocking..