There is one caveat: since ground states are effectively determined by trial and error rather than explicit calculations, they are only approximations. But this is also the reason why this approach could allow progress on what seemed to be an insoluble problem, explains Juan Carrasquilla, researcher at ETH Zurich and another co-author of the study. Science comparative analysis document.

If you want to accurately track all interactions in a highly correlated system, the number of calculations you need to perform increases exponentially with the size of the system. But if you’re happy with an answer that’s just good enough, you have plenty of opportunities to take shortcuts.

“There may be no hope of capturing it exactly,” Carrasquilla says. “But there is hope of capturing enough information to capture all the aspects that physicists are interested in.” And if we do that, it’s basically impossible to discern a real solution.”

And although highly correlated systems are generally too difficult to simulate classically, there are notable cases where this is not the case. This includes some systems relevant to modeling high-temperature superconductors, according to a 2023 report. paper in Natural communications.

“Because of exponential complexity, you can always find problems for which you can’t find a shortcut,” says Frank Noe, research director at Microsoft Research, who has led much of the company’s work in this domain. “But I think the number of systems where you can’t find a good shortcut is just going to decrease.”

No miracle solution

However, Stefanie Czischekassistant professor of physics at the University of Ottawa, says it can be difficult to predict which problems neural networks can realistically solve. For some complex systems they perform incredibly well, but for other, seemingly simple, computational costs increase unexpectedly. “We don’t really know their limits,” she says. “No one really knows yet what conditions make it difficult to represent systems using these neural networks.”

At the same time, other classical quantum simulation techniques have also seen significant progress. Antoine Georgesdirector of the Center for Computational Quantum Physics at the Flatiron Institute in New York, who also contributed to the recent Science comparative analysis document. “They are all successful in their own right, but they are also very complementary,” he says. “So I don’t think these machine learning methods are going to completely put all other methods out of business.”

Quantum computers will also have their place, according to Martin Roettelersenior director of quantum solutions at IonQ, which develops quantum computers built from trapped ions. While he acknowledges that classical approaches will probably be sufficient to simulate weakly correlated systems, he is convinced that some large, highly correlated systems will be beyond their reach. “The exponential will bite you,” he says. “There are cases with highly correlated systems that we cannot treat in a classical way. I firmly believe that this is the case.