Using artificial intelligence, physicists have compressed a daunting quantum problem that hitherto required 100,000 equations into a small task of no more than four equations — all without sacrificing accuracy. The work was published in the September 23 issue of physical review messages, could revolutionize how scientists research systems with many interacting electrons. Moreover, if this approach is scalable to other problems, it could potentially help design materials with desirable properties such as superconductivity or utility for clean energy generation.
“We start with this massive object of all these paired differential equations; then we use machine learning To turn it into something so small that you can count on your fingers,” says lead author of the study Domenico De Santi, a visiting research fellow at the Flatiron Institute’s Center for Computational Quantum Physics (CCQ) in New York City and assistant professor at the University of Bologna, Italy.
The formidable problem is how electrons behave as they move along a lattice. When two electrons occupy the same lattice site, they interact. This setup, known as the Hubbard model, is an ideal model for several important classes of materials and enables scientists to learn how electron behavior gives rise to required phases of matter, such as superconductivity, where electrons flow through a material without resistance. The model also serves as a testing ground for new methods before they are launched on more complex quantum systems.
However, Hubbard’s model is deceptively simple. Even for a modest number of electrons and sophisticated computational methods, the problem requires serious computing power. This is because when electrons interact, their fates can become mechanically entangled: even once they are spaced out at different lattice sites, the two electrons cannot be manipulated individually, so physicists must deal with all the electrons at once rather than one at the same time. time. With more electrons, more entanglements arise, making the computational challenge even more challenging.
One way to study a quantum system is to use the so-called renormalization set. This is a mathematical device that physicists use to look at how the behavior of a system – such as the Hubbard model – changes when scientists adjust properties such as temperature or look at properties at different scales. Unfortunately, a renormalization array that tracks all possible electron pairings and sacrifices nothing can contain tens of thousands, hundreds of thousands, or even millions of individual equations that need to be solved. Moreover, the equations are tricky: each represents a pair of interacting electrons.
De Santi and his colleagues wondered if they could use a machine learning tool known as a neural network to make the renormalization array more manageable. The neural network is like a cross between a frantic switchboard operator and the evolution of survival of the fittest. First, the machine learning software establishes connections within the full-size rematch group. The neural network Then it adjusts the strengths of those connections until it finds a small set of equations that generates the same solution as the original jumbo-sized rematch set. The program’s output captured the physics of the Hubbard model even with just four equations.
“It’s basically a machine that has the ability to detect subtle patterns,” says de Santi. “When we saw the result, we said, ‘Wow, that’s more than we expected.’ We were really able to pick up on the relevant physics.”
Training the machine learning program required a lot of computational muscle, and the program went on for whole weeks. The good news, De Santi says, is that after their program has been trained, they can adapt it to work on other problems without having to start from scratch. He and his colleagues are also investigating what machine learning “learns” about the system, which can provide additional insights that may be difficult for physicists to solve.
Ultimately, the bigger question is how well the new approach works in more complex quantum systems such as materials in which electrons interact over long distances. In addition, there are exciting possibilities for this technique to be used in other fields dealing with renormalization groups, says de Santi, such as cosmology and neuroscience.
Domenico De Santi et al., Deep Learning for the Functional Regeneration Group, physical review messages (2022). DOI: 10.1103/ PhysRevLett.129.136402
Provided by Simons . Foundation
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