Artificial Intelligence Reduces A 100,000 Equation to 4 Equations to Solve Quantum Physics Problems

Using artificial intelligence, physicists have solved daunting quantum physics problems. Studies show that new properties of complex quantum materials are much more manageable. This computational feat could help tackle one of quantum physics' most difficult problems, the 'many-electron' problem, which attempts to describe systems containing large numbers of interacting electrons.

The team believes that the "dimensionality reduction" approach could "revolutionize" research into quantum puzzles, resulting in innovations in highly efficient material design. New materials with practical features, like superconductivity, or materials with uses in industries as diverse as renewable energy and neuroscience are possible consequences.  It could also extend the Hubbard model, a genuinely venerable method for predicting electron behavior in solid-state materials and enhance our comprehension of how useful phases of matter, like superconductivity, emerge. The research shows that it is possible to extract compact representations of dynamical electrons using AI, which is of the utmost relevance to tackle.

Artificial intelligence has been utilized by physicists to reduce a challenging quantum problem that formerly required 100,000 equations into a simple task that only requires four equations, all without sacrificing accuracy. The work, which was published on September 23 in Physical Review Letters, may change how researchers approach investigating systems with lots of interacting electrons. If the technique can be applied to other problems, it might also aid in the creation of materials with desirable properties like superconductivity or be used to generate renewable energy.

Domenico Di Sante, an assistant professor at the University of Bologna in Italy and the study's lead author, is a visiting research fellow at the Center for Computational Quantum Physics (CCQ) at the Flatiron Institute in New York City. "We start with this huge object of all these coupled-together differential equations, and then we're using machine learning to turn it into something so small you can count it on your fingers," he says.

The challenging issue relates to the motion of electrons on a lattice that resembles a grid. Interaction occurs when two electrons are present at the same lattice location. Scientists can study how electron behavior leads to desired phases of matter, such as superconductivity, in which electrons flow through a material without resistance, using this configuration, known as the Hubbard model, which idealizes several significant classes of materials. Additionally, the model acts as a proving ground for fresh approaches before they are applied to more intricate quantum systems.

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 with 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. The computing problem becomes increasingly more difficult as there are more electrons present because more entanglements form.

Renormalization groups are a tool that can be used to examine a quantum system. This mathematical tool is used by physicists to examine how the behavior of a system, such as the Hubbard model, varies as researchers alter certain parameters, like temperature, or consider the properties on other scales. Unfortunately, there may be tens of thousands, hundreds of thousands, or even millions of individual equations in a renormalization group that must be solved to maintain track of all potential couplings between electrons without making any sacrifices. The equations themselves are challenging since each one depicts the interaction of two electrons.

Di Sante describes it as "basically a machine with the ability to find hidden patterns." "Wow, this is more than we anticipated, we exclaimed as soon as we saw the outcome. We successfully captured the pertinent physics."

It took weeks for the machine learning algorithm to train, which required a lot of computer power. The good news, according to Di Sante, is that they can modify their curriculum to address additional issues without having to start from scratch now that it has been coached. To gain extra insights that could otherwise be challenging for physicists to understand, he and his partners are also looking into what machine learning is "learning" about the system.

The main unanswered question is how well the novel method applies to more complicated quantum systems, such as materials with long-range electron interactions. According to Di Sante, there is also intriguing potential for applying the method to other disciplines that work with renormalization groups, such as cosmology and neurology.