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


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. 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.

Link to the rest at

PG notes that this is the first quantum physics post he remembers making. He doesn’t think he was in two places at once when he decided to post this item.

3 thoughts on “Artificial intelligence reduces a 100,000-equation quantum physics problem to only four equations”

  1. This kind of scientific progress is a very good reason to use AI.

    Computers have made most science more scientific, more useful – it’s just the next step. My happiest moments from a former life all had to do with computational physics.

  2. Materials Science is one of the unsung pillars of modern tech and one ripe for both AI and Quantum physics analysis, especially in the area of superatoms.

    Which aren’t kryptonian but might as well be. They are clusters of atome that behave like one giant atom, but with different and/or stronger properties.

    Making them isn’t easy but once made, they are stable.
    They are the product of quantum effects at the atomic level which makes them a perfe t targetfor tbe AI in the OP.

    We may yet find a room temperature/low pressure superconductor. 😉

  3. All this “advance” does is enable one to more-quickly open the box and inspect the cat.

    I’m always skeptical of these sorts of efforts until I see the math (and work through it, slowly and rustily). There’s a regrettable and ironic history in physics and chemistry of glossing over boundary condition failures† in intermediate calculations — and the irony is that Schrödinger’s thought experiment arose because he was trying to resolve a boundary-condition failure. By their natures, both Bessel functions and Hermitians (the core classes of functions at issue in statistical mechanics) have lots of internal and external boundary conditions to potentially violate, especially regarding intermediate results.

    So this might be an exciting advance regarding nonexcited states. But don’t get too excited yet — and especially not until this method is successfully applied to excited states (like systems of overall nonzero charges) and systems of dissimilar atoms (like, say, a gallium-doped silicon substrate, or anything organic… and that’s before considering isotopes). OK, OK, those are all really bad puns that only the nerdliest among us will appreciate.

    And even then, the universe will find a way to test our patience with anomalous experimental data.

    † One example of a “boundary condition failure” is the divide-by-zero error familar from basic arithmetic; another is treatment of calculations that have intermediate results below the Planck limit, and that is going to be at issue.

Comments are closed.