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Classical chaos and quantum entanglement are related

Using a small quantum system consisting of three superconducting qubits, researchers at the University of California, Santa Barbara (UCSB, USA) and Google have discovered a relationship between aspects of classical and quantum physics that were not believed to be there. related: classical chaos and quantum entanglement.


Their findings suggest that it would be possible to use controllable quantum systems to investigate some fundamental aspects of nature.


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


Beginning in the 15th century, classical physics generally examines and describes systems larger than atoms and molecules. It consists of hundreds of years 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.


A classic example of a chaotic system is the weather, in which a relatively small change in one part of the system is enough to thwart predictions - and vacation plans - anywhere in the world.


However, on smaller size and length scales, such as those related to atoms and photons and their behaviors, classical physics falls short. In the 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 they are deeply linked and behave as such despite the physical distance between one and the other). And so began the continuous search for connections between the two fields.


All systems are fundamentally quantum systems, says Neill in the UCSB press release, but the means of describing in a quantum sense the chaotic behavior of, say, air molecules in an empty room, remains limited.


Classical chaos and quantum entanglement are related

A balloon


Imagine picking up a balloon filled with air molecules, labeling them in some way so you can track them, and releasing them into a room without air molecules, as UCSB / Google co-author and researcher Pedram Roushan points out.


One possible result is that the air molecules remain clustered in a small cloud following the same path around the room. And yet, he continues, "as we can probably guess, molecules will be more likely to take off at a variety of speeds and directions, bouncing off walls and interacting with each other, resting when the room is sufficiently saturated with them."


"The underlying physics is chaos, in essence," says Rousham, in the UCSB briefing. The fact that the molecules stop - at least on the macroscopic level - is the result of thermalization , the equilibrium that occurs when they reach a uniform saturation within the system.


But in the infinitesimal world of quantum physics, there are still few tools to describe that behavior. The mathematics of quantum mechanics, Roushan says, does not allow for the chaos described by Newton's laws of motion.


To investigate, the team in the laboratory of physics professor John Martinis devised an experiment using three quantum bits, or qubits, the basic computational units of the quantum computer.


Unlike classical computer bits, which use a binary system of two possible states (for example, zero / one), a qubit can also use a superposition of two states (zero and one) as a single state.


Additionally, multiple qubits can become entangled, or linked so tightly that their measurements are automatically correlated. By manipulating these qubits with electronic pulses, Neill caused them to interact, rotate, and evolve into the quantum analog of a high-sensitivity classical system.


Entropy and entanglement


The result is a map of the entanglement entropy of a qubit that, over time, comes to closely resemble that of classical dynamics: the entanglement regions on the quantum map resemble the chaos regions on the classical map. The islands of low quantum entanglement on the map coincide with the places of low chaos on the classic map.


"There is a clear connection between intertwining and chaos in these two images," says Neill. And, it turns out, thermalization is what connects chaos and entanglement. It turns out that they are actually the driving forces behind thermalization. "

"What counts is that in almost any quantum system, including quantum computers, if we let it evolve and start studying what happens as a function of time, thermalization will occur," Neill adds.


The results of the study have fundamental implications for quantum computing. At the three-qubit level, the computation is relatively simple, Roushan says, but as researchers build increasingly sophisticated and powerful quantum computers that incorporate more qubits for studying very complex problems that are beyond the ability of the Classical computing - such as the fields of machine learning, artificial intelligence, fluid dynamics or quantum chemistry - a processor optimized for these calculations will be a very powerful tool.


"This means that we will be able to study things that are completely impossible to study right now, once we have larger systems," says Neill.


Bibliographic reference:


C. Neill, P. Roushan, M. Fang, Y. Chen, M. Kolodrubetz, Z. Chen, A. Megrant, R. Barends, B. Campbell, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, J. Mutus, PJJ O'Malley, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, TC White, A. Polkovnikov, JM Martinis: Ergodic dynamics and thermalization in an isolated quantum system . Nature Physics (2016). DOI: 10.1038 / nphys3830.

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