Entanglement : Chaos

Researchers at UCSB blur the line between classical and

quantum physics by connecting chaos and entanglement

By Sonia Fernandez,University of California
Santa Barbara

“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.”

Researchers at UCSB blur the line between classical and

quantum physics by connecting chaos and entanglement

By Sonia Fernandez,

Monday, July 11, 2016 -- 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
a chaotic system 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 at UCSB physics professor
John Martinis' lab 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.

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