By using artificial intelligence (AI), American physicists compressed a daunting quantum problem involving 100000 equations into a small task with only four equations, without sacrificing accuracy. The research, published in the Physical Review Letters, may completely change the way scientists study systems containing many interacting electrons. If extended to other problems, the method can also help to design materials with desirable properties such as superconductivity or clean energy power generation utility. The way electrons behave as they move across the lattice is daunting. When two electrons occupy the same lattice position, they will interact. Hubbard's model is an ideal model for understanding strongly correlated electronic systems, enabling scientists to understand how electronic behavior produces material phases, such as superconductivity, where electrons flow through materials without resistance. Before the new method is applied to more complex quantum systems, the model can also be used as a test framework for the new method. However, Hubbard model seems simple, but even if it is used to solve problems involving only a few electrons, it also requires strong computing power. This is because when electrons interact, they will become entangled in quantum mechanics: even if they are far apart in different lattice positions, these two electrons cannot be treated separately, so physicists must treat all electrons at the same time, rather than one at a time. The more electrons there are, the more entanglements there will be, which will multiply the amount of computation. One way to study quantum systems is to use so-called renormalization groups. This is a mathematical tool used by physicists to observe how system behavior (such as Hubbard model) changes when modifying properties such as temperature. Unfortunately, a renormalization group that tracks all possible couplings between electrons without sacrificing anything may contain tens of thousands, hundreds of thousands or even millions of equations to be solved. Each equation represents a pair of interacting electrons and is therefore very tricky. Researchers at the Center for Computational Quantum Physics (CCQ) of the Iron Institute in New York use neural network tools to make renormalization groups easier to manage. First, the machine learning program creates a connection within a full-size renormalization group. Then, the neural network adjusts the strength of these connections until it finds a group of equations that generate the same solution as the original oversize renormalization group. Even if there are only four equations, the output of the program can capture the physical properties of Hubbard model. Training machine learning programs requires a lot of computing power, so the program ran for several weeks. Dominic Sant, a researcher at CCQ, said that they had adjusted the program to solve other problems without starting from scratch. In the future, researchers will explore the effects of new methods on more complex quantum systems, such as the long-distance interaction of electrons in materials. (Liu Xinshe)