Recently, scientists have demonstrated that quantum complexity grows exponentially linearly over a long period of time, which will help understand the physical properties of chaotic quantum systems ranging from black holes to complex many bodies.
In recent years, scientists have used theoretical physics to propose some conjectures to bridge the gap between quantum physics and gravitational theory, and hope to describe complex quantum The behavior of many-body systems, such as black holes and wormholes in the universe. 
Complex quantum many-body systems can pass qubits circuit to prepare. But how many basic operations are needed to prepare the desired state? On the surface, the complexity of the system appears to be increasing all the time. Stanford physicists Adam Brown and Leonard Susskind formulate this as a mathematical conjecture that the quantum complexity of many-particle systems first grows linearly over astronomical lengths of time and then maintains maximum complexity for longer periods of time. status. Their conjecture came from the theoretical behavior of wormholes, where the volume of wormholes appears to grow linearly over long periods of time.
This time, a theoretical group composed of researchers from the Free University of Berlin, the Helmholtz Institute Berlin (HZB) and Harvard University in the United States, using only paper Pen analysis has successfully proved the aforementioned mathematical conjecture about the behavior of complex quantum many-body systems. The results were recently published in Nature Physics. 
Geometric methods provide the physical basis for proving the complexity growth conjecture, image from the paper
“We have found a very simple way to solve this important physical problem ,” said Jens Eisert, a theoretical physicist at the Free University of Berlin, Germany. “Our findings lay the foundation for understanding the physical properties of chaotic quantum systems ranging from black holes to complex many-bodies.”
Based on the mathematical conjectures of Adam Brown and Leonard Susskind, the researchers further speculated that from two different perspectives, the complexity and volume of a wormhole arean equal amount. “This redundancy in description, also known as the holographic principle, is an important approach to unifying quantum theory and gravity,” said Jonas Haferkamp, first author of the paper. “Brown and Susskind’s conjecture about complexity growth can be viewed as A plausibility test of the holographic principle.”
The aforementioned research team, by combining geometric methods and quantum information theory methods, proved that the quantum complexity of random circuits does increase linearly with time, Saturation is not reached until a point in time that is exponentially related to the size of the system. Such stochastic circuits are powerful models of many-body system dynamics. “This new approach makes it possible to solve conjectures for the vast majority of systems,” Haferkamp said.