# Professor Giuseppe Carleo brings expertise in quantum computing methods to NCCR MARVEL's phase III

Giuseppe Carleo arrived at EPFL in September 2020 as assistant professor and is head of the Computational Quantum Science Laboratory in the School of Basic Sciences. He has joined NCCR MARVEL in phase III as project leader of the Bonus project Leveraging Quantum Computers and Algorithms for Materials Discovery.

*Interviewed by Carey Sargent, EPFL, NCCR MARVEL*

Professor Giuseppe Carleo did his undergraduate studies in physics at Sapienza University in Rome before earning a PhD in theoretical physics at the International School for Advanced Studies (SISSA) in Trieste. He then set off to discover the world beyond Italy’s borders, starting with postdocs at the Institut d’Optique in Paris and ETH Zurich, where he was also a lecturer, and then moving to work as a research scientist for three years at the Flatiron Institute of the Simons Foundation in New York. As Carleo explains it, this is a place where computational scientists, in their different incarnations, from physics to mathematics to biology, come together and try to combine their expertise to study the different fields of science with computational methods. As much as he enjoyed the experience, he missed the pure university environment and decided to move back to Europe. He joined EPFL in 2020, starting up his Computational Quantum Science Laboratory, which has now grown to almost 20 people. In his free time, Carleo, who comes from the Cilento Coast, in the south of Italy, enjoys cooking and is “relatively skilled” at pizza making, spending at least one day a week preparing his homemade pizza to share with friends. Making do with a pizza stone for the time being, he plans to acquire a proper oven once he has a sufficiently large garden. He also enjoys hiking…“like everyone else in Switzerland”.

**Why are you a scientist? **

Because of curiosity about how things work, wanting to understand and to develop models to explain things in simple terms. Those are the main motivations that have driven my curiosity in the field—that and the challenge of solving hard problems. I like a challenge and clearly science is full of them.

**Have you always been interested in science? **

Actually, I was hesitating between a career in philosophy or science, that’s the usual dilemma, at least for a few people I know, especially since I studied a lot of humanities during high school. I did classical studies where I studied ancient Greek for five years and could translate from Greek and Latin, for example. Clearly this had an influence on me, I was always fascinated by classical culture. For me though, I eventually found that the challenges were, maybe not more interesting, but I can say that I found more challenges in the sciences. I’m still interested in the humanities though.

**What’s the aim of your research? **

In my group, we develop new computational methods, or more broadly theoretical methods, but mostly computational methods, to study what we call strongly interacting quantum systems. These are all those systems where interactions among electrons, for example, mean that you cannot neglect the fact that the atoms are strongly entangled with one another. Describing their properties is extremely challenging because of these strong interactions and we do our best to develop new methods to do that. The new methods that we develop in my lab are, broadly speaking, from two families of techniques.

The first is deeply rooted in machine learning approaches. For this, we use a description of these many-body quantum systems in terms of artificial neural networks. This is a technique that I developed a few years back, in 2017, when I was in Zurich. The technique, which we call neural quantum states—a term that’s pretty telling about the marriage between quantum and neural, you have everything in the name—is now popular and widely used worldwide.

What we do here is develop it to special applications where other existing computational techniques are not accurate enough. For example, there are two interesting problems that we don’t know how to solve.

One is the dynamics of these interacting quantum systems. Imagine that we have these electrons, or other strongly interacting particles, and put them in a box, so to speak, and let them evolve over time. We want to understand how their physical properties, like density for example, will evolve over time. Studying this is extremely hard, it’s probably one of the hardest problems we face in classical computing. What we do here is develop new approaches to solving these dynamical properties using neural quantum states.

Other problems concern, for example, the equilibrium problem. What happens at equilibrium, when the system has settled down, is especially interesting. What we’re doing, along with many other groups worldwide, is working on extending in the most efficient way possible these neural network approaches to studying the wavefunctions to ultimately study the properties of these electronic systems. This is an open challenge and a research theme that is very interesting and exciting—it should lead to an understanding of what molecules and materials do in an intrinsically electronic system.

The second family of techniques that we develop is using quantum computers to study the physical properties of matter and this is the area directly related to MARVEL. What we had started doing in my group, before joining MARVEL, is trying to understand how we can use quantum computers to do something useful. It’s important to say this because there have already been a few demonstrations of quantum computing, some of which gained a lot of popular attention, and this gave rise to a controversial notion of quantum supremacy.

**What motivates you?**

There’s again the “challenge thing” in the sense that we really have no idea of what happens when you take these strongly interacting electrons or matter and let them, for example, evolve over time. Even experimentally we are limited in understanding what happens and so having tools to answer these questions and tackle these hard problems is really crucial and it motivates me, as does the idea of extending the frontiers of what can be simulated or accessed or studied.

**What paper are you most proud of? **

It would be the one on neural quantum states, which was published in *Science*. (Solving the quantum many-body problem with artificial neural networks). It is certainly the most important paper in my career because it opened the entire research field. There was also the excitement of doing something truly new. That doesn’t happen very often in somebody’s career, maybe a couple of times if you’re lucky. In this case it was one of the early applications of machine learning to quantum physics and it came from just randomly discussing other things with people in the group. I had an intuition that turned out to be not so bad. It went from a stage of crazy idea to working in six months and that was just really exciting.

**What is the appeal of working with NCCR MARVEL?**

NCCR MARVEL is a great opportunity for the group to integrate with the Swiss eco system in the broader sense, in that it brings together almost all the people in Switzerland working on computational materials science methods to simulate quantum properties. I am happy to be part of this family, especially since my group has a strong, full interest in computational methods. It’s clear that there’s a lot of shared interest with the other PIs in MARVEL.

What we do essentially is solve Schrödinger’s equation. As highlighted by the great physicist Dirac in the 1920s, at this point, we know most of the basic, fundamental equations of matter around us, especially at the scales relevant for human life. While we do have the fundamental equations, we don’t know how to solve them when there are interactions. This is the core of the problem that is somehow central to all of MARVEL activity in one way or another. What we work on is solving these equations on the most fundamental level, which means solving for the “wavefunction”, the fundamental object describing the properties of quantum matter. What we do in my group is try to approximate solutions to these equations, that is, finding wavefunctions in the form of neural networks.

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