There is a caveat: Because the ground states are effectively found through trial and error rather than explicit calculations, they are only approximations. But this is also why the approach could make progress on what has looked like an intractable problem, says Juan Carrasquilla, a researcher at ETH Zurich, and another coauthor on the Science benchmarking paper.
If you want to precisely track all the interactions in a strongly correlated system, the number of calculations you need to do rises exponentially with the system’s size. But if you’re happy with an answer that is just good enough, there’s plenty of scope for taking shortcuts.
“Perhaps there’s no hope to capture it exactly,” says Carrasquilla. “But there’s hope to capture enough information that we capture all the aspects that physicists care about. And if we do that, it’s basically indistinguishable from a true solution.”
And while strongly correlated systems are generally too hard to simulate classically, there are notable instances where this isn’t the case. That includes some systems that are relevant for modeling high-temperature superconductors, according to a 2023 paper in Nature Communications.
“Because of the exponential complexity, you can always find problems for which you can’t find a shortcut,” says Frank Noe, research manager at Microsoft Research, who has led much of the company’s work in this area. “But I think the number of systems for which you can’t find a good shortcut will just become much smaller.”
No magic bullets
However, Stefanie Czischek, an assistant professor of physics at the University of Ottawa, says it can be hard to predict what problems neural networks can feasibly solve. For some complex systems they do incredibly well, but then on other seemingly simple ones, computational costs balloon unexpectedly. “We don’t really know their limitations,” she says. “No one really knows yet what are the conditions that make it hard to represent systems using these neural networks.”
Meanwhile, there have also been significant advances in other classical quantum simulation techniques, says Antoine Georges, director of the Center for Computational Quantum Physics at the Flatiron Institute in New York, who also contributed to the recent Science benchmarking paper. “They are all successful in their own right, and they are also very complementary,” he says. “So I don’t think these machine-learning methods are just going to completely put all the other methods out of business.”
Quantum computers will also have their niche, says Martin Roetteler, senior director of quantum solutions at IonQ, which is developing quantum computers built from trapped ions. While he agrees that classical approaches will likely be sufficient for simulating weakly correlated systems, he’s confident that some large, strongly correlated systems will be beyond their reach. “The exponential is going to bite you,” he says. “There are cases with strongly correlated systems that we cannot treat classically. I’m strongly convinced that that’s the case.”
