Researchers blur the line between classical and quantum physics by connecting chaos and entanglement

July 12, 2016 by Sonia Fernandez
 Experimental link between quantum entanglement (left) and classical chaos (right) found using a small quantum computer. Credit: University of California - Santa Barbara

Using a small quantum system consisting of three superconducting qubits, researchers at UC Santa Barbara and Google have uncovered a link between aspects of classical and quantum physics thought to be unrelated: classical chaos and quantum entanglement. Their findings suggest that it would be possible to use controllable quantum systems to investigate certain fundamental aspects of nature.

"It's kind of surprising because chaos is this totally classical concept—there's no idea of chaos in a quantum system," Charles Neill, a researcher in the UCSB Department of Physics and lead author of a paper that appears in Nature Physics. "Similarly, there's no concept of entanglement within classical systems. And yet it turns out that chaos and entanglement are really very strongly and clearly related."

Initiated in the 15th century, generally examines and describes systems larger than atoms and molecules. It consists of hundreds of years' worth of study including Newton's laws of motion, electrodynamics, relativity, thermodynamics as well as chaos theory—the field that studies the behavior of highly sensitive and unpredictable systems. One classic example of chaos theory is the weather, in which a relatively small change in one part of the system is enough to foil predictions—and vacation plans—anywhere on the globe.

At smaller size and length scales in nature, however, such as those involving atoms and photons and their behaviors, classical physics falls short. In the early 20th century quantum physics emerged, with its seemingly counterintuitive and sometimes controversial science, including the notions of superposition (the theory that a particle can be located in several places at once) and entanglement (particles that are deeply linked behave as such despite physical distance from one another).

And so began the continuing search for connections between the two fields.

All systems are fundamentally , according Neill, but the means of describing in a quantum sense the chaotic behavior of, say, in an evacuated room, remains limited.

Imagine taking a balloon full of air molecules, somehow tagging them so you could see them and then releasing them into a room with no air molecules, noted co-author and UCSB/Google researcher Pedram Roushan. One possible outcome is that the air molecules remain clumped together in a little cloud following the same trajectory around the room. And yet, he continued, as we can probably intuit, the molecules will more likely take off in a variety of velocities and directions, bouncing off walls and interacting with each other, resting after the room is sufficiently saturated with them.

"The underlying physics is chaos, essentially," he said. The molecules coming to rest—at least on the macroscopic level—is the result of thermalization, or of reaching equilibrium after they have achieved uniform saturation within the system. But in the infinitesimal world of , there is still little to describe that behavior. The mathematics of quantum mechanics, Roushan said, do not allow for the chaos described by Newtonian laws of motion.

To investigate, the researchers devised an experiment using three quantum bits, the basic computational units of the quantum computer. Unlike classical computer bits, which utilize a binary system of two possible states (e.g., zero/one), a qubit can also use a superposition of both states (zero and one) as a single state. Additionally, multiple qubits can entangle, or link so closely that their measurements will automatically correlate. By manipulating these qubits with electronic pulses, Neill caused them to interact, rotate and evolve in the quantum analog of a highly sensitive classical system.

The result is a map of entanglement entropy of a qubit that, over time, comes to strongly resemble that of classical dynamics—the regions of entanglement in the quantum map resemble the regions of chaos on the classical map. The islands of low entanglement in the quantum map are located in the places of low chaos on the classical map.

"There's a very clear connection between entanglement and chaos in these two pictures," said Neill. "And, it turns out that thermalization is the thing that connects chaos and . It turns out that they are actually the driving forces behind thermalization.

"What we realize is that in almost any quantum system, including on quantum computers, if you just let it evolve and you start to study what happens as a function of time, it's going to thermalize," added Neill, referring to the quantum-level equilibration. "And this really ties together the intuition between classical thermalization and and how it occurs in quantum systems that entangle."

The study's findings have fundamental implications for quantum computing. At the level of three qubits, the computation is relatively simple, said Roushan, but as researchers push to build increasingly sophisticated and powerful quantum computers that incorporate more qubits to study highly complex problems that are beyond the ability of classical computing—such as those in the realms of machine learning, artificial intelligence, fluid dynamics or chemistry—a processor optimized for such calculations will be a very powerful tool.

"It means we can study things that are completely impossible to study right now, once we get to bigger systems," said Neill.

Explore further: Researchers refine method for detecting quantum entanglement

More information: Nature Physics, DOI: 10.1038/nphys3830 , http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3830.html

Related Stories

Doubling down on Schrödinger's cat

May 26, 2016

Yale physicists have given Schrödinger's famous cat a second box to play in, and the result may help further the quest for reliable quantum computing.

Worldwide quantum web may be possible with help from graphs

June 8, 2016

(Phys.org)—One of the most ambitious endeavors in quantum physics right now is to build a large-scale quantum network that could one day span the entire globe. In a new study, physicists have shown that describing quantum ...

Recommended for you

Inventing a new kind of matter

March 24, 2017

Imagine a liquid that could move on its own. No need for human effort or the pull of gravity. You could put it in a container flat on a table, not touch it in any way, and it would still flow.

Physicist develops drip-free wine bottle

March 23, 2017

Drips are the bane of every wine drinker's existence. He or she uncorks a bottle of wine, tips it toward the glass, and a drop, or even a stream, runs down the side of the bottle. Sure, you could do what sommeliers in restaurants ...

20 comments

Adjust slider to filter visible comments by rank

Display comments: newest first

Steelwolf
1 / 5 (3) Jul 12, 2016
This fits right along with the Astronomical type observations being found, how the fractal iterations are connected and using those finer-grade forces will allow us to see how atoms and neutrons, electrons, protons, all the various families of quarks, matched particles and forces can be found in the sky if one matches the right energy regime to it. Connecting chaos and entanglement is a huge thing as this bridges a gap that has left many baffled as to how these things could possibly exist, and yet both of them have been long accepted tenent in their fields.
Sina
5 / 5 (8) Jul 12, 2016
We had indeed predicted and simulated such phenomenon in Cavity QED (as a part of a Nationally Funded project) a few years ago:

IEEE Journal of Quantum Electronics, vol. 49, no. 12, pp. 1066-1079 (2013).

Applied Physics A, vol. 115, no. 2, pp. 595-603 (2014).

Quite recently, a closely related effect has been observed in Cavity Optomechanics (doi:10.1038/nphoton.2016.73), which is almost the mathematicsl dual of our studied Cavity QED system. However, the authors of this work also have totally dismissed our earlier published research, setting forth the excuse that they were unaware of our papers.
Da Schneib
5 / 5 (5) Jul 12, 2016
Actually, there is chaos, in the sense of stochastic behavior of exactly the kind seen in thermodynamics, in QM. Radioactivity is a great example of this. We can say in a sample of radioactive material how many nuclei will decay in a given time, but we can't say which ones. Similarly, in the gedankenexperiment from the article above, we can say that the gas molecules released into the empty room will wind up fairly evenly distributed, but we can't say which ones will go where.
vidyunmaya
1 / 5 (4) Jul 12, 2016
Sub; Spirit f Scientific Research- edge on Culture
researchers must draw a line between Knowledge base at the Milky-way float structure to ignorance .
the science of philosophy dictates to look at the foot of Cosmic Dance of lord Siva for control and regulation.
creation, Dissolution and stability are Continuing functions through space-Time Energy concepts provided by divine nature.
Modern science interpretation: Plasma Regulated Electromagnetic phenomena in Magnetic Field environment holds he key at milky Way reflecting Mirror Base Frame.
in search of origins, Cosmology Vedas interlinks help in this direction. Illustrations with log-scale light year cover Three tier cosmic pOt energy of the Universe. Energy regulation come within heart and center of the Universe -at 10^5 LY.15 Books at LULU. http://www.lulu.c...jnani108
Protoplasmix
5 / 5 (5) Jul 12, 2016
Quite recently, a closely related effect has been observed in Cavity Optomechanics (doi:10.1038/nphoton.2016.73), which is almost the mathematicsl dual of our studied Cavity QED system. However, the authors of this work also have totally dismissed our earlier published research, setting forth the excuse that they were unaware of our papers.
If you look at the list of references for the paper from the above article ( it's on arXiv: https://arxiv.org...01.00600 ), there are 10 out of 33 that were published after yours, but there are 23 out of 33 that are (obviously) related and were published before yours, a few over two decades before yours.
torbjorn_b_g_larsson
5 / 5 (4) Jul 13, 2016
Interesting! "Our work illustrates how controllable quantum systems can investigate fundamental questions in non-equilibrium thermodynamics."

I note that both chaos and entanglement are non-linear effects (of exponential sensitivity and phase space folding, respectively non-local correlations). The entanglement entropy map would show where trajectories in phase space tends to end up as thermalization progresses, which is what a classical phase space map (of, say, a chaotic system) shows too.

From the arxiv article (thanks, Protplasmix!): "It is interesting to note that chaos and entanglement are each exclusive to their respective classical and quantum domains and any connection is counterintuitive."

"Numerical results suggest that ergodic behavior breaks down only when the evolution is
highly constrained by conservation laws, such systems are referred to as integrable and represent models that are fine tuned and consequently rare [3]."

[tbctd]
torbjorn_b_g_larsson
5 / 5 (4) Jul 13, 2016
[ctd]

Sina's massive paper seems to agree: "It is surprisingly observed that by the increasing the coupling constant the entering into ultrastrong regime the coupled system not only exhibits a very chaotic and disordered behavior in the three-dimensional parametric plot, but also the corresponding phase changes abruptly. This behavior is also seen in nearly all other complex expectation values of all ultrastrongly coupled multipartite systems we have studied so far, and is yet to be understood."

[But I am browsing at breakneck speed, so I may have misunderstood. Any suggestions for the analogous behavior would be *very* welcome!]

So NET strikes again, becoming even more pervasive and hard to grok. Fun!

@vidunmaya: We have already grokked that EU substitutes for (other) religious magic. But thanks for making it explicit, and for showing that EU adherents has no business parading their occultism on science sites!
Protoplasmix
5 / 5 (4) Jul 13, 2016
I was able to find links for the other articles mentioned by Sina that aren't behind a paywall:
IEEE Journal of Quantum Electronics, vol. 49, no. 12, pp. 1066-1079 (2013) (reference #64)
Applied Physics A, vol. 115, no. 2, pp. 595-603 (2014) (same site, reference #63)
doi:10.1038/nphoton.2016.73 (different site, reference #29)

They're all related (representative of 'analogous behavior'), and all are interesting, but it doesn't appear that anyone has refuted or "dismissed" anything.
BackBurner
not rated yet Jul 14, 2016

the science of philosophy dictates to look at the foot of Cosmic Dance of lord Siva for control and regulation


I have some difficulty with this explanation.
BackBurner
not rated yet Jul 14, 2016
"It is interesting to note that chaos and entanglement are each exclusive to their respective classical and quantum domains and any connection is counterintuitive."


Humans have difficulties with counter-relationships in general. More important I think is the specious nature of "entanglement" which is, by its nature, a statistical phenomenon. It's a large inference to assume there is such a thing as quantum entanglement, or that it's in any way a reliable means to exchange information. Now we would add to this?
BackBurner
not rated yet Jul 14, 2016
This behavior is also seen in nearly all other complex expectation values of all ultrastrongly coupled multipartite systems we have studied so far, and is yet to be understood."


Well, perhaps we should spend more time determining the probability two photons will exhibit exactly the same phase change at exactly the same time without being "entangled". Now that would actually add something to the conversation.
Da Schneib
5 / 5 (2) Jul 14, 2016
I was able to find links for the other articles mentioned by Sina that aren't behind a paywall:
http://sina.shari...0009.htm (different site, reference #29)
Good stuff, @Proto, thanks for the links.

They're all related (representative of 'analogous behavior'), and all are interesting, but it doesn't appear that anyone has refuted or "dismissed" anything.
Yeah, more like they discovered some more compelling evidence to think that we might find a general solution for the Navier-Stokes equations in quantum computing. Which is actually a pretty big deal in and of itself.

While I'm thinking of it, it's very much worth mentioning that the NS equations are a very important part of climate modeling. So once quantum computing is up we should have some very much faster and more precise climate models available.
BackBurner
4 / 5 (1) Jul 15, 2016
We have solutions to the Navier-Stokes equations now! They aren't predictive. They aren't economical but they work.

What you really want is a generalized algorithm to repeatably solve multiple dependent problems simultaneously. And here's the ticket; you can do it, but only once. The answer will be different the next time you ask.

And that my friend is the universe.
torbjorn_b_g_larsson
5 / 5 (1) Jul 15, 2016
@Backburner: The usual sense of "repeatably" is to produce the same result. Climate is predictive (seasons, climate zones, AGW), it is weather that is more of a problem. So DS is making an interesting observation. IMO of course.

On another matter, you note that quantum mechanics is statistical in nature (states propagate deterministically, however observations on them have stochastic outcomes). That doesn't mean QM properties can't be tested, any less than we can determine properties of statistical distributions. Specifically, entanglement can be observed in particles.

Nitpick: entanglement carries non-causal (non-local!) correlations, not causal information.
Da Schneib
5 / 5 (1) Jul 16, 2016
We have solutions to the Navier-Stokes equations now!
No, we have numerical simulations which must be tailored to the precise environment in which we wish to solve them; we do not have a general solution to them. In fact such a general solution (or a proof that one cannot exist) is a Millenium Problem and there is a large cash prize for solving it.

They aren't predictive. They aren't economical but they work.
I don't see how we can resolve the tension between these two sentences. If they work they're predictive; if they're not predictive they don't work.

What you really want is a generalized algorithm to repeatably solve multiple dependent problems simultaneously. And here's the ticket; you can do it, but only once. The answer will be different the next time you ask.
Sure, but if you run it many times you can develop a stochastic answer by averaging the outcomes. The point is that you can do this in a single run with a quantum computer.
jwhite
not rated yet Jul 16, 2016
Fascinating article - you should check out the novel Quantumnition by Benjamin Owen -it's a great exploration of some if these ideas about quantum physics
Steelwolf
not rated yet Jul 16, 2016
Backburner, while we have "Some" equations and answers for them, they presently work for a very limited number of parameter inputs. Even though there will be, on higher level processing situations, more than one correct answer, there will be a Range of answers, or maybe a set of bands where the answer is correct. Just like here on this planet there happened to be the right combinations for water-based life, first using iron and sulfur and moving their hydrogen atoms around for energy, and working up the scale to using Oxygen for energy now, in SOME life forms. Some life forms still produce Oxygen as a Waste Product here and now. And how many different directions did that life form go, those original ones, along with surviving mutations which we have learned to call chains of beneficial mutations to be Evolution. But, we can still compute where on the tree many things come from, and see places that did not work due to changing conditions (continued)
Steelwolf
not rated yet Jul 16, 2016
And while every answer will be different, there are ranges of difference, we can see that in Geology itself just on THIS Planet. Imagine that a billion times over just for THIS Galaxy, and then for the Billions of Galaxies that we know about, and similar sets of galaxies, in their billions of billions, Beyond what we can see due to redshift. And no two stars are going to be exactly the same along the way either, but they will all act within their different ranges, just as with radioactive materials having half-lives, it changes at a set rate, but you cannot pin down the exact order and timing of each atom in that mass, but you still have a good gauge of it's properties vs a different radioactive.

So, yes, different each time, but enough to be able to see patterns and then once we have Those patterns, further matches to known fractal iterations and parameters become easier and more possible, much easier to see the Real Data vs Noise.
crusher
not rated yet Jul 17, 2016
The article has typographical error;
"All systems are fundamentally quantum systems, according Neill,"
They should reverse that and correct it.
kpvats
not rated yet Jul 30, 2016
I can bet 100 USD that some of QM is correct (like probability wave) and some of it is just a mathematical brain wash (like superposition, to be specific, having all possibilities at all times, like a cat is dead and alive both.). I challenge that if experiments are done as I specify, the quantum entanglement mystery will be resolved quickly. Otherwise, I will pay 100 dollars from my pocket. 100 is just symbolic, I do not think one can put a price on these things.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.