Can AIs dream of Schrödinger’s cat? Art Box Images/Getty

The same type of artificial intelligence that mastered the ancient game of Go could help wrestle with the amazing complexity of quantum systems containing billions of particles.

Google’s AlphaGo artificial neural network made headlines last year when it bested a world champion at Go. After marvelling at this feat, Giuseppe Carleo of ETH Zurich in Switzerland thought it might be possible to build a similar machine-learning tool to crack one of the knottiest problems in quantum physics.

Now, he has built just such a neural network – which could turn out to be a game changer in understanding quantum systems.


Go is far more complex than chess, in that the number of possible positions on a Go board could exceed the number of atoms in the universe. That’s why an approach based on brute-force calculation, while effective for chess, just doesn’t work for Go.

In that sense, Go resembles a classic problem in quantum physics: how to describe a quantum system that consists of many billions of atoms, all of which interact with each other according to complicated equations.

Material improvement

Even ordinary matter, like a lump of gold or coal, is a quantum system, so cracking this problem is crucial for understanding materials and even designing new ones.

But the weird rules of quantum mechanics mean we can’t know a quantum particle’s precise location at every point in time. Many quantum particles also have a property called “spin”, which can be either up or down. The number of spin-based states that a group of just 100 such particles could inhabit is almost a million trillion trillion (1030).

The current record for simulating such a system, using our most powerful supercomputers, is 48 spins. Carleo estimates that even if we could turn the entire planet into a giant hard drive, we would still only be able to do these calculations for 100 spins at most.

That’s where artificial neural networks can help. Give such a network the rules of Go and it will figure out the optimal strategy to win the game. So perhaps it could do the same for quantum systems.

Dream machine

“Neural networks are very good at generalising, so they typically only need a limited amount of information to infer much more from that,” says Carleo. Feed a neural network a few pictures of Carleo, for example, and it will soon be able to recognise him in new pictures it has never “seen” before.

To assess the idea, Carleo and co-author Matthias Troyer, now at Microsoft, built a simple neural network designed to reconstruct the wave function of a multi-body quantum system, or the set of probabilities describing how all the states could be arranged. They also calculated its lowest energy or “ground” state, a standard problem in quantum mechanics.

They tested it on a few sample problems with known solutions and found that it performed better than other tools that have been applied to many-body systems. That’s sufficient proof of principle of the technique’s promise. Building a more-complicated deep neural net should be even more effective.

“It’s like having a machine learning how to crack quantum mechanics, all by itself,” Carleo says. “I like saying that we have a machine dreaming of Schrödinger’s cat.”

“It’s incredibly cool,” says Scott Aaronson of the University of Texas in Austin. “Given the success of deep learning… in pretty much every imaginable application domain, it’s a natural idea to try it for quantum many-body physics, but as far as I know this is the first time someone did. I expect to see a lot more of this in the future.”

Journal reference: Science, DOI: 10.1126/science.aag2302