AI Reduces 100,000-equation Quantum Physics Problem to 4 Equations

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. 

Domenico Di Sante, study lead author and a visiting research fellow at the Flatiron Institute's Center for Computational Quantum Physics (CCQ), New York, says, "We started with this huge object of all these coupled-together differential equations. Then we used machine learning to turn it into something so small you can count it on your fingers." 

Moreover, the problem concerns the behavior of the electrons as they move on a grid-like lattice. The two electrons would interact when they occupy the same lattice site. The team of researchers also wondered if they could use neural networks to make the renormalization group more efficient. Initially, the ML program would create connections within the enormalization group in full-size. Later, the neural network would tweak the strengths of the same connections until it locates a small set of equations generating solutions similar to the original renormalization group. 

The scientist claimed that the program's output captured the Hubbard model's physics with just four equations. "It's essentially a machine that has the power to discover hidden patterns," says Di Sante. "When we saw the result, we said, 'wow, this is more than what we expected’. We were really able to capture the relevant physics."

The biggest question lies in how well the new approach works on more complex quantum systems. Di Sante further notes that the model opens doors for exciting possibilities in fields such as cosmology and neuroscience.