Artificial intelligence reduces a 100,000-equation quantum physics problem to only four equations


With the use of artificial intelligence, physicists have been able 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.

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

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 behaviour 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 idealises 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 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. The Hubbard model is one example of a system that physicists use this mathematical tool to examine how the behaviour of a system varies as scientists alter properties like temperature or consider the properties on various 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 in order to maintain track of all potential couplings between electrons without making any sacrifices. Additionally, the equations are challenging: Each one symbolises the interaction of two electrons.

Di Sante and his coworkers questioned whether they could utilise a neural network, a machine learning technology, to simplify the renormalization group. The neural network resembles a cross between an anxious switchboard operator and evolution according to the principle of the strongest. The full-size renormalization group is first connected within the machine learning algorithm. In order to locate a smaller set of equations that yield the same result as the original, jumbo-size renormalization group, the neural network adjusts the strengths of those connections. Even with only four equations, the program's output was able to reproduce the physics of the Hubbard model.

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. In order to gain extra insights that could otherwise be challenging for physicists to understand, he and his partners are also looking into what the 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 are also intriguing potential for applying the method to other disciplines that work with renormalization groups, such cosmology and neurology.

Reference:  Physical Review Letters

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