Around the World with Quantum Mechanics An Interview with András Gilyén, Junior Prima Award-Winning Mathematician

You’ve appeared on television and frequently give presentations at conferences. Do you think the research career is appealing enough in Hungary today? Is it being promoted effectively?

This career is less recognized than other fields, both socially and financially. Most people have little understanding of what it means to do research. Nowadays, there aren’t many established platforms to showcase deeper mathematical results. In the past, there were far more public educational programs, such as "Ki miben tudós" (Who’s the Expert?), Professor Öveges’ lectures, or The University of All Knowledge.That said, there are many valuable scientific talks and videos available online. It’s also our responsibility to find ways to connect with young people, translating the wonders of science into their language so that pursuing a research career becomes more attractive.

As a high school student, you developed the Mobile Compass, which earned you first prize at the 15th National Youth Science and Innovation Competition organized by the Hungarian Association for Innovation in 2006. Did this innovation contribute to your later research?

Indirectly, it did contribute to my current research by sparking my experimental curiosity, which continues to drive me to create something new. Taking an idea and diligently transforming it into a functional solution was a significant lesson I gained from the compass project - it was downloaded by thousands of users, which validated the effort. It taught me that even if the practical applications of an idea aren’t immediately clear, it’s still worth pursuing a promising concept. Research inherently involves risk; your plan may not materialize as you envision. That’s why it’s essential for a researcher to have the instinct to identify a compelling problem that can actually be addressed with the tools at hand and holds relevance for others. It’s crucial to shape ideas into something that either benefits individuals or advances scientific understanding.

At the Rényi Institute, you are conducting research as a Marie Curie Fellow, focusing on quantum algorithms and computer science, particularly linear algebra procedures (efficient matrix operations), optimization, and quantum walks. What are the potential everyday applications of these fields?

In the realm of quantum information, the first applications are emerging in the development of highly precise sensors. These sensors rely on quantum mechanical measurements and can, for example, detect gravitational waves - achieving an extraordinary resolution possible only with light prepared in special quantum states. This represents the cutting edge of technology today, but once suitable manufacturing techniques are developed, quantum sensors will become increasingly accessible to broader audiences. Another area attracting growing attention is the development of motion-detection sensors, though practical applications are still some distance away. These sensors are crucial for aviation navigation, as planes currently rely heavily on GPS, which can be disrupted during military operations, potentially causing aircraft to lose their way.

In experimental trials, a quantum mechanical device utilizing ultracold atom clusters was mounted on an aircraft. This device measured accelerations with extremely high resolution, enabling precise calculations of both speed and position. Without quantum mechanical measurements, achieving the required accuracy is virtually impossible due to noise in conventional systems, which causes position calculations from acceleration data to become unreliable within minutes. However, the unparalleled resolution of quantum systems could enable reliable navigation over extended periods. Quantum computers, far more versatile than quantum sensors, are expected to find their first major applications in the simulation of quantum physical systems. These simulations will enable researchers to deepen their current understanding of complex chemical processes, which is particularly important in drug development. In the field of materials science, quantum simulations could lead to the discovery of new specialized materials, such as superconductors. By narrowing down the range of potential materials and compounds through simulations, researchers can focus on those most likely to be useful in real-world applications.

Back in 2011, news emerged about your idea to build an online Tree of Knowledge. The Mathematical Tree of Knowledge would be a specialized repository to store mathematical theorems, proofs, examples, and visualizations in a graph-based structure. More than a decade has passed since then. What happened to the project? Was the Knowledge Tree ever realized?

I was very passionate about this topic and even created a small prototype using material from a university course as part of my undergraduate thesis. However, I quickly realized that the scale and complexity of the task required resources I did not have at the time. It would have required a dedicated research team, scientific collaborators, and funding, none of which I had at the time. As a freshly graduated BSc student at ELTE, I lacked the strong support needed to continue planning, and ultimately, I abandoned the project. Interestingly, I recently watched a video featuring Terence Tao, the world-renowned mathematician, describing his team's efforts to formally document mathematical theorems and proofs. They’re breaking down mathematical papers into tiny steps, rewriting them in a formal proof language with the help of hundreds of volunteers and professionals, which are then solved in a fully formalized way within a specialized system. From this library of formalized mathematics, an encyclopedic collection is automatically generated, allowing users to explore proofs and connections at various levels of depth. At the time, I aimed to create something similar - a lexicon - and I succeeded in producing a small slice of it in a rudimentary form.

With your ideas, international connections, talent, and achievements, you could work anywhere in the world. Yet, you’ve chosen the Rényi Institute. Why?

I enjoy working at the Rényi Institute because, while it is home to many renowned researchers, it’s not an enormous institution - it’s a workplace on a human scale. The environment here is supportive, everyone cheers for each other’s success, and the Institute maintains meaningful relationships with universities.

You’ve loved mathematics since you were a child. How did you become a researcher?

At the end of primary school, I was drawn to carpentry because I enjoyed assembling things. Later, I thought about becoming a mechanical engineer, but deep down, I always wanted to be an inventor.

My desire for deep understanding developed during high school, thanks to my brilliant math and physics teachers, Marianna Ábrahám and Katalin Gambár, who had a profound influence on me.

During my undergraduate studies, I worked on a student research project under the supervision of Tamás Kiss at the Wigner Research Centre for Physics, where I became fascinated by the world of quantum computers. This field combines the principles of mathematics, physics, and computer science, which captivated me.

With the László Sólyom Presidential Scholarship, I completed a one-year master's program in mathematics at the University of Cambridge. There, I deepened my knowledge of quantum computing theory through the lectures of Richárd Józsa, a renowned scientist of Hungarian origin.