Using artificial intelligence, an international team of physicists has shown that the thousands of equations needed to model a complex system of interacting electrons can be reduced to just four. This was done by using machine learning to identify patterns previously hidden within the system of equations. The technique could be used to vastly reduce the effort required to calculate electronic properties, says the team, which was led by Domenico Di Sante at the University of Bologna, who is also a visiting research fellow at the Flatiron Institute in New York City. Quantum interactions between electrons underly the properties of matter, and over the past century physicists have developed mathematical and computational tools to boost our understanding of systems ranging from individual atoms to solid materials. These models must consider entanglement, a quantum phenomenon that allows stronger correlations between electrons than exists in classical physics.

Scientists have reduced a vastly complex quantum physics problem requiring 100,000 equations to just four equations using artificial intelligence. The team hope that the "dimensionality reduction" method could "revolutionise" scientific investigation into quantum problems, leading to breakthroughs in ultra-efficient materal design. Potential outcomes could include new materials that have useful properties, like superconductivity, or have applications in fields ranging from neuroscience to renewable energy. "We start with this huge object of all these coupled-together differential equations; then we're using machine learning to turn it into something so small you can count it on your fingers," said Domenico Di Sante, an assistant professor at the University of Bologna in Italy, and a visiting research fellow at the Center for Computational Quantum Physics in New York. "It is essentiall a machine that has the power to discover hidden patterns."

"We start with this huge object of all these coupled-together differential equations; then we're using machine learning to turn it into something so small you can count it on your fingers," says study lead author Domenico Di Sante, a visiting research fellow at the Flatiron Institute's Center for Computational Quantum Physics (CCQ) in New York City and an assistant professor at the University of Bologna in Italy. The formidable problem concerns how electrons behave as they move on a gridlike lattice. When two electrons occupy the same lattice site, they interact. This setup, known as the Hubbard model, is an idealization of several important classes of materials and enables scientists to learn how electron behavior gives rise to sought-after phases of matter, such as superconductivity, in which electrons flow through a material without resistance. The model also serves as a testing ground for new methods before they're unleashed on more complex quantum systems.

With AI's help, physicists have now compressed a daunting quantum problem that until now required 100,000 equations to as few as four equations – all without sacrificing accuracy. The work'Deep Learning the Functional Renormalization Group' was published last week in Physical Review Letters revolutionizing how scientists investigate systems containing various interacting electrons. The setup is based on the Hubbard model – an idealization of several important classes of materials – enabling scientists to learn how electron behavior gives rise to sought-after phases of matter. The model would serve as a testing ground for new methods before they are utilized on more complex quantum systems. The new approach could potentially aid in the designing of materials with properties that are most sought-after, such as utility for clean energy generation and superconductivity.

Using artificial intelligence, physicists have compressed a daunting quantum problem that until now required 100,000 equations into a bite-size task of as few as four equations--all without sacrificing accuracy. The work, published in the September 23 issue of Physical Review Letters, could revolutionize how scientists investigate systems containing many interacting electrons. Moreover, if scalable to other problems, the approach could potentially aid in the design of materials with sought-after properties such as superconductivity or utility for clean energy generation. "We start with this huge object of all these coupled-together differential equations; then we're using machine learning to turn it into something so small you can count it on your fingers," says study lead author Domenico Di Sante, a visiting research fellow at the Flatiron Institute's Center for Computational Quantum Physics (CCQ) in New York City and an assistant professor at the University of Bologna in Italy. The formidable problem concerns how electrons behave as they move on a gridlike lattice.

Using artificial intelligence, physicists have compressed a daunting quantum problem that until now required 100,000 equations into a bite-size task of as few as four equations--all without sacrificing accuracy. The work, published in the September 23 issue of Physical Review Letters, could revolutionize how scientists investigate systems containing many interacting electrons. Moreover, if scalable to other problems, the approach could potentially aid in the design of materials with sought-after properties such as superconductivity or utility for clean energy generation. "We start with this huge object of all these coupled-together differential equations; then we're using machine learning to turn it into something so small you can count it on your fingers," says study lead author Domenico Di Sante, a visiting research fellow at the Flatiron Institute's Center for Computational Quantum Physics (CCQ) in New York City and an assistant professor at the University of Bologna in Italy. The formidable problem concerns how electrons behave as they move on a gridlike lattice.