Physicists are well aware of the enormous gap between quantum physics and gravity theory. Theoretical physics has presented some plausible speculation to bridge this gap and to characterise the behaviour of complicated quantum many-body systems, such as black holes and wormholes in the cosmos, in recent decades. Now, researchers from Freie Universität Berlin and the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), in collaboration with Harvard University in the United States, have verified a mathematical hypothesis regarding the behaviour of complexity in such systems, boosting the bridge's practicality. The research was published in the journal Nature Physics.
Prof.
Jens Eisert, a theoretical physicist at Freie Universität Berlin and HZB,
states, "We have found a very simple solution to an important problem in
physics." "Our findings lay a solid foundation for understanding the
physical features of chaotic quantum systems, ranging from black holes to
complicated many-body systems," says Eisert.
The
Berlin physicists Jonas Haferkamp, Philippe Faist, Naga Kothakonda, and Jens
Eisert, along with Nicole Yunger Halpern (formerly of Harvard, now in
Maryland), have proven a conjecture that has major implications for complex
quantum many-body systems using only pen and paper, i.e. purely analytically.
"For example, whether you wish to define the volume of black holes or even
wormholes," says Jonas Haferkamp, a Ph.D. student in Eisert's team and the
paper's first author.
Circuits
of so-called quantum bits can recreate complex quantum many-body systems. The
question is, how many basic operations are required to achieve the desired
state? On the surface, it appears that the system's minimum number of
operations—its complexity—is always increasing. Stanford University physicists
Adam Brown and Leonard Susskind formalised this perception as a mathematical
conjecture: A many-particle system's quantum complexity should initially grow
linearly for astronomically long times before remaining in a state of maximum
complexity for even longer. The behaviour of theoretical wormholes, whose
volume appears to develop linearly for an infinitely long time, prompted their
hypothesis. In fact, from two separate views, it is hypothesised that wormhole
complexity and volume are one and the same quantity. "The holographic
concept, which is a key approach to reconciling quantum theory and gravity, is
based on this redundancy in description. Brown and Susskind's evolution of
complexity conjecture can be viewed as a plausibility check for concepts
centred on the holographic principle "Haferkamp says.
The
team has now demonstrated that the quantum complexity of random circuits increases
linearly with time until it saturates at a time that is exponentially
proportional to the system size. Such random circuits are an effective model
for many-body system dynamics. The difficulty in proving the conjecture stems
from the fact that "shortcuts," or random circuits with significantly
lower complexity than expected, can't be ruled out. "Our proof combines
methods from geometry and quantum information theory in an unexpected way. This
novel method allows the great majority of systems to solve the hypothesis
without having to deal with the famously tough problem of individual states
"Haferkamp agrees.
"My
work in Nature Physics was a great highlight of my Ph.D.," says the young
scientist, who will join Harvard University at the end of the year. He can
continue his study as a postdoc there, preferably using pen and paper and in
exchange with some of the top brains in theoretical physics.
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