Without losing accuracy, researchers trained a machine learning technique to capture the physics of electrons travelling on a lattice using a far less number of equations than would ordinarily be necessary.

Scientists have used artificial intelligence to condense a difficult quantum problem that previously required 100,000 equations into a manageable assignment that only requires four equations, all while maintaining accuracy. The research, which appeared in Physical Review Letters on September 23, may completely alter how scientists approach studying systems with lots of interacting electrons. The method may also help in the development of materials with desirable qualities like superconductivity or use in the production of renewable energy if it is transferable to other issues.

Together differential equations; then we're using machine learning to reduce it to something so small you can count it on your fingers,' explains the study's lead author, Domenico Di Sante, a visiting research fellow at the Center for Computational Quantum Physics (CCQ) of the Flatiron Institute in New York City and an assistant professor at the University of Bologna in Italy.

How electrons move on a lattice-like structure and behave is a difficult topic. There is interaction when two electrons are present at the same lattice location.

But the Hubbard model appears to be rather straightforward. The problem demands a significant amount of computer power, even for a small number of electrons using state-of-the-art computational techniques. That's because interactions between electrons might induce quantum mechanical entanglements in their fates: The two electrons cannot be dealt separately, even when they are far apart on distinct lattice sites, therefore physicists must deal with all of the electrons at once rather than one at a time.