Gravitational twists help theoretical physicists shed light on quantum complexity

September 27, 2017
Artistic impression of a space-time twist in a crystal. Credit: Oxford University

Are we are living in a computer simulation? Intriguingly, the crux of this question may be hiding in an exotic quantum phenomenon which shows up in metals as a response to twists of space-time geometry.

A recurring theme in science fiction, most famously popularised by the "Matrix' film trilogy, is whether our physical reality is a computer . While this seems to be a rather philosophical idea, in theoretical physics it has an interesting twist when applied to computer simulations of complex quantum systems.

How can one even attempt to give an answer to this question? In new research published in Science Advances magazine, a team of theoretical physicists from the University of Oxford and the Hebrew University, may have found a way to approach this answer.

While trying to address a computer simulation of a quantum phenomenon occurring in metals, the researchers, Zohar Ringel and Dmitry Kovrizhin, found proof that such a simulation is impossible as a matter of principle. More precisely, they showed how the complexity of this simulation, - that can be measured in a number of processor hours, memory size, and electricity bills, - increases in line with the number of particles one would have to simulate.

If the amount of computational resources required for a quantum simulation increases slowly (e.g. linearly) with the number of particles in the system, then one has to double a number of processors, memory, etc. in order to be able to simulate a system twice as large in the same amount of time. But if the growth is exponential, or in other words if for every extra particle one has to double the number of processors, memory, etc., then this task becomes intractable. Note, that even just to store the information about a few hundred electrons on a computer one would require a memory built from more atoms than there are in the Universe.

The researchers identified a particular physical phenomenon that cannot be captured by any local quantum: Monte-Carlo simulation. It is a curious effect, which has been known for decades, but has only ever been measured indirectly. In the field of condensed matter physics, it is called the "thermal Hall conductance" and in high-energy physics it is known as a "gravitational anomaly".

In plain words, thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time. Many physical systems in high magnetic fields and at very low temperatures are believed to exhibit this effect. Interestingly such quantum systems have been evading efficient numerical simulation algorithms for decades.

In their work, the theorists showed that for systems exhibiting gravitational anomalies the quantities which are involved in quantum Monte-Carlo simulations will acquire a negative sign or become complex. This ruins the effectiveness of the Monte-Carlo approach through what is known as "the sign-problem". Finding a solution to "the sign problem" would make large-scale quantum simulations possible, so that the proof that this problem cannot be solved for some systems, is an important one.

'Our work provides an intriguing link between two seemingly unrelated topics: gravitational anomalies and computational complexity. It also shows that the thermal Hall conductance is a genuine : one for which no local classical analogue exists', says Zohar Ringel, a professor at Hebrew University, and a co-author of the paper.

This work also brings a reassuring message to theoretical physicists. It is often said in society that machines are taking the place of people, and will eventually takeover human jobs. For example, in the event that someone, for instance, creates a computer powerful enough to simulate all the properties of large quantum systems, in the blink of an eye. Clearly the appeal of hiring a theoretical physicist to do exactly the same job (with the overhead considerations of office space, travel money, pension etc.) would be greatly diminished.

But, should theoretical physicists be alarmed by this possibility? On the bright side, there are many important and interesting quantum systems, some related to high-temperature superconductivity, and others related to topological quantum computation, for which no efficient simulation algorithms are known. On the other hand, perhaps such algorithms are just waiting to be discovered? Professor Ringel and Kovrizhin argue that, when it comes to a physically important subset of complex data, a class of algorithms as broad as Monte-Carlo algorithms, cannot outsmart us and are not likely to in the near future.

In the context of the original question of whether our perceived reality is really just a part of an advanced alien experiment, this work may provide extra reassurance to some of us.

Explore further: How to measure a molecule's energy using a quantum computer

More information: "Quantized gravitational responses, the sign problem, and quantum complexity" Science Advances (2017). advances.sciencemag.org/content/3/9/e1701758

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rogerdallas
not rated yet Sep 27, 2017
This brings up a problem: the physicists, and anyone else doing any thinking about some physical system, are using a simulation algorithm, the one that presumably underlies human intelligence in general. I'm reminded of Roger Penrose's question of whether any AI device can replicate all of known mathematics-- the AI device is of course going to use a simulation algorithm. Can such an algorithm be generated by another such algorithm, if human intelligence is the product of such an algorithm? This paper seems to prove that human intellect can't be modeled by any computational device, not even a quantum computer, since humans are somehow modeling quantum systems. Does that compute?
manfredparticleboard
5 / 5 (1) Sep 27, 2017
As far as the Turing problem goes, you need more processing of information to describe an event than the information contained in the event itself, which leads to a conclusion that a computer describing the universe would have to be bigger than the universe is one way of looking at this problem. But a mind- brain- AI that experiences a world only sees and recognises patterns of behaviour. We don't do numerical processing to represent a bird in flight by it's mass, it's physiology, it's cell biology - it's just moving colours that have attributes we recognise. The universe could be a simulation- but it can never fully describe all it's attributes at any one time because of processing limitations. We know that we know not.
Or: you can know something completely, but only at the expense of not knowing something else.
Da Schneib
4.2 / 5 (5) Sep 27, 2017
So much for the "quantum simulation" conjecture. Yes, reality is an irreducible construct not subject to simplified simulation. This has implications for Many Worlds and similar interpretations of QM.
Caliban
2.7 / 5 (7) Sep 27, 2017
So much for the "quantum simulation" conjecture. Yes, reality is an irreducible construct not subject to simplified simulation. This has implications for Many Worlds and similar interpretations of QM.


Agreed.

This holographic universe nonsense is -and has always been- nothing more than a backdoor for the "intelligent design' and "creationist" buffoons.
Da Schneib
5 / 5 (2) Sep 27, 2017
I'd be careful @Caliban, irreducible doesn't mean irreplicable. Remember AdS/CFT.
Caliban
5 / 5 (2) Sep 27, 2017
I'd be careful @Caliban, irreducible doesn't mean irreplicable. Remember AdS/CFT.


Understood.

My point is that, if the amount of information represented by the Universe approaches infinity, then it takes an amount of energy and computational power to represent any fraction of it that is, itself, approaching infinite.

Where does this energy come from?
Da Schneib
5 / 5 (3) Sep 27, 2017
Mmmm, I'd be a little careful there too. I'm pretty cautious when talking about infinite anything to do with the visible universe, which is not infinite. The information implicit in the visible universe is certainly large, and I mean that in a scientific way where "large" means in excess of 10⁵⁰. That's incredibly huge, beyond our understanding of enormous by so much that we can barely imagine it. But it's still not infinite.

Certainly the visible universe implies a minimum universe many times what we can or will ever see. But we have to constrain our expectations to what we can ever know.
Parsec
5 / 5 (2) Sep 27, 2017
This brings up a problem: the physicists, and anyone else doing any thinking about some physical system, are using a simulation algorithm, the one that presumably underlies human intelligence in general. I'm reminded of Roger Penrose's question of whether any AI device can replicate all of known mathematics-- the AI device is of course going to use a simulation algorithm. Can such an algorithm be generated by another such algorithm, if human intelligence is the product of such an algorithm? This paper seems to prove that human intellect can't be modeled by any computational device, not even a quantum computer, since humans are somehow modeling quantum systems. Does that compute?


Of course it does. On the other hand, a mathematical proof of the nature presented here is not limited to what can be imagined. If the axioms (assumptions) underlying the proof are true, then the proof is true, no matter whose intellectual space one sits in.

Period.
NeutronicallyRepulsive
not rated yet Sep 27, 2017
"Infinity" (most likely just a very large number) in our simulated Universe might be just a small number in Universe that is simulating us. You can't really disprove simulation "hypothesis", you can just determine its apparent limits. It is similar to a concept of God, you can always postulate that whatever evidence is explainable inside Universe (or whatever) that simulates our. That's why I don't consider it a thing. It can't be proved or disproved, replicated and any evidence for/against it doesn't really change anything in our life. Just like an idea of God. It's a good plot device though.
Da Schneib
5 / 5 (2) Sep 27, 2017
That's not the point @Neutronic. The point is, if there's a simulation it can't be simpler than what we see. So why propose it? It's a WYSIWYG universe.
Mimath224
5 / 5 (2) Sep 27, 2017
As a layman, this is a bit over my head, although nonetheless interesting to say the least. So I'll take a 'general' point of view with the '...context of the original question...'. If our reality were a simulation then we might, though not necessarily, be talking of extra higher dimensions. Rather than talking of the Matrix Trilogy it might be then like the movie Men Black (1) where at the end it's shown that a (giant) alien is playing marbles, which is our universe. So here, if we want to get a look at the simulation builder we would need to poke our 'heads' into the next higher dim. Think we need to be careful just in case the 'alien' decides the simulation had then gone wrong and so switch it off (Ha!). By the same idea the builder might decide the experiment was successful, the simulation (us) was showing signs of probing its origins.
However, we then have to ask the question is it 'turtles all the way down'?. Is the simulation builder also the result of another simulation?
howhot3
5 / 5 (2) Sep 27, 2017
And it all comes down to this;
In plain words, thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time.

Ok... I'm pretty QM savvy, but what the hell does this mean?
axemaster
5 / 5 (2) Sep 28, 2017
In plain words, thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time.

I'm a physicist, and I can't make heads or tails of this sentence.

This work also brings a reassuring message to theoretical physicists. It is often said in society that machines are taking the place of people, and will eventually takeover human jobs. For example, in the event that someone, for instance, creates a computer powerful enough to simulate all the properties of large quantum systems, in the blink of an eye. Clearly the appeal of hiring a theoretical physicist to do exactly the same job (with the overhead considerations of office space, travel money, pension etc.) would be greatly diminished.

I think someone looked too hard at this article and caused it to decohere...
Da Schneib
not rated yet Sep 28, 2017
@axe, first you have to understand the thermal Hall effect. I don't think you'll have any trouble once you do, and it's not very hard to understand. I have confidence in you.
antialias_physorg
5 / 5 (2) Sep 28, 2017
Yes, reality is an irreducible construct not subject to simplified simulation

Caveat: ..at least by classical computers.

We don't know whether any reality in which such a 'simulatior' resides has the same set of physical laws as the ones it simulates - which could well give it the ability to overcome the complexity problem.
So there's a number of (increasingly weird) loopholes before we have definite proof either.

In plain words, thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time.


I'm a physicist, and I can't make heads or tails of this sentence.


The way I read it it means:
"Thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or - if no such energy current is evident - a twist in the underlying geometry of space-time."
Spaced out Engineer
not rated yet Sep 28, 2017
This line of thought is conditional on gravitation not being emergent(also require this to be a variant paradigm) and the mapping account of computation not holding up. Dualities and the holographic principle may be able to get close enough. Who needs all, when the Bloch Sphere is so useful. There exist means of getting certain calculations utilizing uncertainty.
I agree with this article however. Unity defined as everything but the electron mass and charge or as ℏ (Wheeler), still does not commensurate the spectral gap being undecidable. I would leave computationalism, mathematical realism, or radical mathematical Platonism as tribes like symbolism, connectionist, genetic algorithms, Bayseian, analogizer. Different contexts grant each modality as optimal. If we must have Betti numbers, what happens to potential infinitesimal Ricci curvature? Without geometric ontology we still have useful principles. ℏ =0, charge=1 for the ground state, the bridge is patience. Both and neither.
Da Schneib
not rated yet Sep 28, 2017
@anti and @Spaced, it appears that there has been a paper published that equates thermal Hall effect to gravitational effects. You may find this interesting: https://arxiv.org...9463.pdf It is the arXiv version of a paper published in Physical Review B. It says:
From the perspective of chiral gapless boundary theories, the thermal Hall effect has been studied in terms of the chiral Luttinger liquid, the conformal field theory, the gravitational Chern-Simons theory, and the equilibrium partition function.
Note the presence of CFT. This implies that AdS/CFT correspondence may be what is bringing gravity studies into this.
Spaced out Engineer
not rated yet Oct 02, 2017
It is just so too weird. Reality might be slightly new via electrodynamics interaction with gravity.

1+1 formulations fail, yet (2,0) +(2,0) is no problem, hell 2+1. No problem. With B-modes (6,0) and a slight Ricci curvature maybe permitted. It is as though the electron is fated. As though partitions work evenly but oddly require error correction, though there may exist a "replacement".

Either way the simulation argument is not out if Quibism holds. Truths approach conditional. So whose map is best?
https://arxiv.org...12.09592
eachus
5 / 5 (1) Oct 02, 2017
Speaking as a computer scientist specializing in complexity not a physicist, I don't see how this particular issue rules out a holographic universe. Certainly a (quantum) hybrid or analog computer can be constructed with subsystems that model the quantum Hall effect. Such a model should require fewer resources than the system being simulated, but even if it didn't, it should not be necessary to have one model for each possible appearance of the quantum Hall effect, just those that might be measured. In other words, a global model should be able to limit the number of points where the quantum Hall effect needs to be simulated exactly.

Or to cut right to the point, does a simulation have to worry about modelling any value which is subject to the uncertainty principle more accurately than the value can be measured? It seems to me that any "realistic" simulation if run from the same starting conditions will soon be in different states. The same will happen to real universes...
Colbourne
not rated yet Oct 03, 2017
You do not need to simulate the whole universe accurately. All you need to do is simulate for one observer. What ever they do or look at is simulated to as near perfection as possible. That observer is you.
bcbg
not rated yet Oct 04, 2017
Doesn't this just say that at least some quantum processes cannot be simulated objectively by classical computers using reasonable amounts of resources. However, couldn't quantum computers accomplish this still allowing for a simulated universe?
idjyit
not rated yet Oct 05, 2017
Short answer is no, a qubit is information encoded into an electron or a photon, it is not all the quantum probabilities by any stretch of the imagination.

Quantum computers still need to be cooled to .015 degrees kelvin before they can be used reliably and I believe the biggest quantum computer is only around the 1000 qubit range at the moment.

Quantum computers are good for a specific range of calculations because of the way they encode data they are particularly good for problems like calculating the modulus period part of Shor's algorithm, which is used to crack https encryption, but they are not faster than classical silicon CPU's they are in fact considerably slower.

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