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, classical physics 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 quantum systems, according Neill, but the means of describing in a quantum sense the chaotic behavior of, say, air molecules 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 quantum physics, 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 entanglement. 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 chaos 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 quantum 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

## Steelwolf

## Sina

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

## vidyunmaya

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

## torbjorn_b_g_larsson

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

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

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

I have some difficulty with this explanation.

## BackBurner

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

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

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

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

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

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.

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

## Steelwolf

## Steelwolf

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

"All systems are fundamentally quantum systems, according Neill,"

They should reverse that and correct it.

## kpvats