"We have found a surprisingly simple solution to an important problem in physics," says Prof. Jens Eisert, a theoretical physicist at Freie Universitat 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 Physics is 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.

Research Report: "Linear growth of quantum circuit complexity"

Related Links
Helmholtz-Zentrum Berlin fur Materialien und Energie
Understanding Time and Space

Thanks for being there; We need your help. The SpaceDaily news network continues to grow but revenues have never been harder to maintain. With the rise of Ad Blockers, and Facebook - our traditional revenue sources via quality network advertising continues to decline. And unlike so many other news sites, we don't have a paywall - with those annoying usernames and passwords. Our news coverage takes time and effort to publish 365 days a year. If you find our news sites informative and useful then please consider becoming a regular supporter or for now make a one off contribution.
SpaceDaily Monthly Supporter $5+ Billed Monthly		SpaceDaily Contributor $5 Billed Once credit card or paypal

Visualizing the invisible
Tokyo, Japan (SPX) Mar 29, 2022
There are multiple ways to create two- and three-dimensional models of atoms and molecules. With the advent of cutting-edge apparatus that can image samples at the atomic scale, scientists found that traditional molecular models did not fit the images they saw. Researchers have devised a better way to visualize molecules building on these traditional methods. Their models fit the imaging data they acquire well, and they hope the models can therefore help chemists with their intuition for interpret ... read more

Read more from original source...