Quantum information theory: Quantum complexity grows linearly for an exponentially long time

Date:
March 28, 2022
Source:
Helmholtz-Zentrum Berlin fu"r Materialien und Energie
Summary:
Physicists know about the huge chasm between quantum physics and
the theory of gravity. However, in recent decades, theoretical
physics has provided some plausible conjecture to bridge this gap
and to describe the behavior of complex quantum many-body systems
-- for example, black holes and wormholes in the universe. Now,
researchers have proven a mathematical conjecture about the
behavior of complexity in such systems, increasing the viability
of this bridge.



FULL STORY ========================================================================== Physicists know about the huge chasm between quantum physics and the
theory of gravity. However, in recent decades, theoretical physics has
provided some plausible conjecture to bridge this gap and to describe
the behaviour of complex quantum many-body systems, for example black
holes and wormholes in the universe. Now, a theory group at Freie
Universita"t Berlin and HZB, together with Harvard University, USA,
has proven a mathematical conjecture about the behaviour of complexity
in such systems, increasing the viability of this bridge. The work is
published in Nature Physics.


==========================================================================
"We have found a surprisingly simple solution to an important problem
in physics," says Prof. Jens Eisert, a theoretical physicist at Freie Universita"t Berlin and HZB. "Our results provide a solid basis for understanding the physical properties of chaotic quantum systems, from
black holes to complex many-body systems," Eisert adds.

Using only pen and paper, i.e. purely analytically, the Berlin physicists
Jonas Haferkamp, Philippe Faist, Naga Kothakonda and Jens Eisert, together
with Nicole Yunger Halpern (Harvard, now Maryland), have succeeded in
proving a conjecture that has major implications for complex quantum
many-body systems.

"This plays a role, for example, when you want to describe the volume
of black holes or even wormholes," explains Jonas Haferkamp, PhD student
in the team of Eisert and first author of the paper.

Complex quantum many-body systems can be reconstructed by circuits of
so-called quantum bits. The question, however, is: how many elementary operations are needed to prepare the desired state? On the surface,
it seems that this minimum number of operations -- the complexity of
the system -- is always growing.

Physicists Adam Brown and Leonard Susskind from Stanford University
formulated this intuition as a mathematical conjecture: the quantum
complexity of a many- particle system should first grow linearly for astronomically long times and then -- for even longer -- remain in
a state of maximum complexity. Their conjecture was motivated by the
behaviour of theoretical wormholes, whose volume seems to grow linearly
for an eternally long time. In fact, it is further conjectured that
complexity and the volume of wormholes are one and the same quantity
from two different perspectives. "This redundancy in description is
also called the holographic principle and is an important approach to
unifying quantum theory and gravity. Brown and Susskind's conjecture on
the growth of complexity can be seen as a plausibility check for ideas
around the holographic principle," explains Haferkamp.

The group has now shown that the quantum complexity of random circuits
indeed increases linearly with time until it saturates at a point in
time that is exponential to the system size. Such random circuits are
a powerful model for the dynamics of many-body systems. The difficulty
in proving the conjecture arises from the fact that it can hardly be
ruled out that there are "shortcuts," i.e. random circuits with much
lower complexity than expected.

"Our proof is a surprising combination of methods from geometry and those
from quantum information theory. This new approach makes it possible to
solve the conjecture for the vast majority of systems without having
to tackle the notoriously difficult problem for individual states,"
says Haferkamp.

"The work in Nature Physicsis a nice highlight of my PhD," adds the
young physicist, who will take up a position at Harvard University at
the end of the year. As a postdoc, he can continue his research there, preferably in the classic way with pen and paper and in exchange with
the best minds in theoretical physics.


========================================================================== Story Source: Materials provided by Helmholtz-Zentrum_Berlin_fu"r_Materialien_und_Energie.

Note: Content may be edited for style and length.


========================================================================== Journal Reference:
1. Jonas Haferkamp, Philippe Faist, Naga B. T. Kothakonda, Jens Eisert,
Nicole Yunger Halpern. Linear growth of quantum circuit complexity.

Nature Physics, 2022; DOI: 10.1038/s41567-022-01539-6 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2022/03/220328150620.htm

--- up 4 weeks, 10 hours, 50 minutes
* Origin: -=> Castle Rock BBS <=- Now Husky HPT Powered! (1:317/3)