# Quantum Mechanics Meets Artificial Intelligence

Columbia Physics PhD student Matija Medvidović shares why he uses AI to tackle quantum problems.

Quantum mechanics is all about probabilities: What are the chances that, say, an electron or photon will be *here* versus *somewhere* else? It’s one thing to calculate the odds for a single quantum particle, but most often quantum particles don’t exist in isolation. They interact with other particles and objects, and their collective states and behaviors will change over time. Determining the properties and behaviors of increasingly large quantum systems is a key consideration in the development of emerging technologies like quantum computers and sensors. To physicists, this area of research is known as quantum many-body physics.

“Basically, quantum many-body physics is about keeping track of a lot of things at once,” said Matija Medvidović, a Columbia Physics PhD student and Flatiron Institute Center for Computational Quantum Physics graduate scholar. Medvidović started his career studying questions about complex physics at the University of Zagreb in Croatia, the country where he was born, before moving west to the Perimeter Institute in Toronto for his master’s degree.

Now a fifth-year PhD candidate, Medvidović is working with Columbia’s Andrew Millis and NYU’s Dries Sels, who are also researchers at the Flatiron Institute. Their research concerns the complicated calculations needed to solve quantum many-body physics problems.

Medvidović has been looking for a computational advantage; his latest work, published recently in *PRX Quantum* with Sels, combines quantum mechanics with artificial intelligence. Here, Medvidović explains that work, and why we need to keep track of so many pieces to begin with.

## Why is quantum many-body physics important?

Everything in our world contains more than one particle, or what physicists call a “body.” If you want to calculate anything useful using quantum mechanics, you have to work on many-body problems. For example, to describe the conductivity or thermal properties of a metal, you need to understand how many electrons it has, how fast each of them is moving, how they interact, and how all these things change over time. There can be 10 to the power of 23 particles to begin with in a sample, so the total number of variables to keep track of is huge.

It becomes exponentially more difficult when you start including quantum mechanical probabilities. There’s not enough computing power in the universe to perform these kinds of calculations. Instead, theoretical physicists have to be in the business of making good approximations, but we need better tools to make better approximations.

## And that’s where AI comes in?

We might not be very good at keeping track of so many variables, but AI is, and it’s very good at extracting important information from irrelevant information. We can use AI to distill an enormous number of variables into the ones that are relevant for a particular problem.

## What problem were you working on in your recent paper?

The time-evolution of rotor models. Imagine little arrows that spin in a plane in quantum states that change over time. These rotors don’t exist in nature, but the model captures some interesting physics of quantum bits, the basic unit of information in quantum computers.

We designed a neural network that could make predictions about how the rotors will change further into the future than previous methods. Each step forward in time is less computationally expensive as well, thanks to this new algorithm. In the future, we want to develop algorithms that are even more efficient at solving time-evolution problems.

We have some new work out on quantum dynamics! The question is what happens to quantum matter when you leave it on its own? We show that neural-networks can compress dynamics in cases of practical interest. You can read about our results in PRX Quantum.https://t.co/DVl1YqZMPx

— Matija Medvidović (@Matemagija) October 13, 2023

## Where is this work heading?

Apart from predicting material properties, many of the researchers at Columbia and at Flatiron are interested in controlling the quantum properties of materials. A roadblock to that is developing a robust quantum simulator. If you look at self-driving cars for example, the AI used for those is initially trained in a virtual environment—essentially, the AI learns from a video game. We need to develop a quantum video game for AI to learn how to control the quantum properties of a material.

## So what’s harder: Quantum mechanics or AI?

Quantum mechanics.

AI is a tool that works amazingly well. And when we don’t understand why it’s working, we at least have ways to investigate it. Sometimes quantum mechanics works, sometimes it doesn’t. But when it doesn’t work, it’s hard to even ask why not. It’s not apples-to-apples, but I feel quantum mechanics is more difficult to learn. There’s so much to it, but I think we can use AI to help us understand it better. AI is like a hammer, and we are using it to build a house.

## What’s next for you?

I recently started exploring how AI techniques for quantum problems can be applied to chemistry. I should be finishing up my PhD next summer, so I’ve started job hunting. I’m looking for postdocs, and also industry positions. I see jobs in pure quantum computing or in pure AI, but I’m really hoping to find one where the two overlap.

## Any advice to leave others with?

Build your networks *before* you need them. I found a great environment at Columbia and Flatiron with colleagues who are really willing to share with me so it’s worked out so far, but I think the transition from Croatia could have been smoother.

The best ways I found to build a network is to go to conferences and use social media to advertise your work. To put it mildly, I am not a fan of social media and have only recently started to use it more. However, if you find the sub-community that overlaps with your interests, there is a lot to gain from those interactions. Scientists are nice people and love to talk about what they do. Often, if you just email them and ask questions, they will be happy to talk to you. The same goes for conference hallways—I found that spending time talking to people outside presentations is just as important as going to talks. Learning to make these things a part of your routine will almost certainly grow your network.