*November 25, 2015 - by Simone Ulmer*

**Professor Troyer, what does this award mean to you?**

The prize is a wonderful acknowledgement of my group’s achievements in this area of physics, which is still very much in its infancy. In physics, it is traditionally new discoveries in theory and experimentation that are honoured. The Rahman Prize is one of the few prizes in computational physics. It recognises achievements in the development of new methods to solve physical problems and the simulation of difficult problems on computers. The award shows that we are one of the world’s leading groups in this field.

**How did you end up in computational physics?**

Through my interest in supercomputing and physics. Even at high school I was interested in both science and computing. Back then, I thought “I know how to program but I don’t understand science well enough” and that is why I studied physics. For my diploma thesis I had the opportunity to do a project on a Cray X-MP supercomputer – and that’s how I got to do physics with state-of-the-art supercomputers like we have at CSCS today.

**So, what is many-body quantum physics, and why is it so hard to solve?**

We’ve known the Schrödinger equation, which describes how materials behave, for nearly a century. While it is a simple equation, a macroscopic solid state is composed of many particles, electrons and atomic nuclei. The problem is not finding the equations that describe a solid state, but solving them. For one particle, the Schrödinger equation is a partial differential equation in three dimensions, which is much simpler than similar equations for fluid flows as they appear in simulations of climate and weather. To describe the behaviour of many electrons, however, one needs to solve equations in 3N dimensions. For a million particles, this is a differential equation in three million dimensions. Due to the curse of dimensionality, this is an enormous task.

**What are the “seemingly intractable areas of quantum many-body physics” that the Selection Committee touched upon?**

Because of the huge number of dimensions, it is difficult to solve these many-particle problems. It isn’t enough to simply wait for faster and larger supercomputers but one needs to have new ideas and new approaches to this problem. The power of supercomputers has grown exponentially in the last twenty or thirty years, but we have made even greater progress in the development of new algorithms.

**The software algorithms you use to solve particular problems?**

Exactly. But you can’t afford to limit yourself to just developing algorithms. We develop algorithms, implement them in software, optimise them for supercomputers and finally use them to solve problems. By combining new algorithms, good software and supercomputers, we can make progress and solve problems that nobody could solve before. While we cannot solve every problem, we have made a lot of progress in certain areas.

**Can you give an example?**

We studied phase transitions in quantum systems, ultra-cold quantum gases and so-called supersolids – materials that are simultaneously perfect crystals and liquids that flow without friction. Moreover, we developed new methods for simulations of correlated electrons, where we managed to improve the performance of the algorithms by a factor of 100,000. These kinds of improvements enable one to tackle new problems that wouldn’t have been possible in the past.

**The Prize Committee explicitly mentions your work on increasing the efficiency of software.**

We publish much of our software within the scope of the ALPS project, which stands for “Algorithms and Libraries for Physics Simulations”, and make it open source, so that everyone can use it.

**But you don’t just optimise software; you also use it to research the aforementioned phenomena.**

Indeed. And besides that, we also test and simulate a new class of computers known as quantum computers, and develop algorithms for future such systems. We are already thinking about the types of problems that we might be able to solve with state-of-the-art algorithms when quantum computers become available. We are most interested in problems that we can’t solve classically, not even with the fastest supercomputer that we’ll have in twenty years.

**Are you already cooperating with manufacturers in this regard?**

Yes, we are collaborating with various companies that are interested in quantum computers, especially Microsoft. We currently simulate materials for quantum bits and develop new applications for quantum computers.

**Did this motivation come through D-Wave, which launched the first apparent quantum computer?**

Our interest in quantum computing predates D-Wave. The fact that D-Wave built a quantum annealer heightened the interest of companies and government organisations and as a result more resources are now available. Half of my group is working on topics related to quantum computing. However, the devices built by D-Wave are not the quantum computers we are thinking of but are rather special purpose devices for solving particular optimization problems.

**When will we have a “real” quantum computer?**

In the next five years we will be able to produce devices that can outperform conventional supercomputers for specific physics problems. While this might not be able to solve problems of general interest, it will still demonstrate that one can compute something that is regarded as difficult. Within twenty years I expect that we can build quantum computers that will solve certain applications of wider interest more quickly and effectively than a classic supercomputer.

**But that doesn’t mean that this quantum computer will be suitable for all applications, does it?**

A quantum computer will always be a special purpose high-performance computer. Even conventional supercomputers are already niche products that are only needed for certain applications. For most people, a smartphone or PC is sufficient. While quantum computers are able to calculate anything that classic computers can, they will demonstrate their specific strength in a narrow range of really difficult problems. We want to find out for which problems this is the case and what we can solve better than with a classic computer.

**Does that mean we don’t really know which problems we hope to be able to solve with a quantum computer yet?**

There are lots of ideas of how to apply them to fundamental science problems. However, given the considerable resources that the development of a quantum computer will require, companies investing in quantum computing naturally ask about their application potential. Consequently, we are already developing and optimising algorithms for quantum computers in order to demonstrate that it will be possible to solve certain problems on quantum computers better than on classical ones. We already know several applications in the field of cryptography, quantum chemistry and materials science and are on the lookout for others in new areas.

**Is it easy to find people who are working in this field?**

That is not a problem at all! Many excellent students are interested in quantum computing. Even if D-Wave’s products are controversial, the company made the field of quantum computing extremely popular and inspired businesses and students to do it better.

**Will you invest your prize money in the development of quantum computing?**

That would be less than a drop in the ocean, but of course the prize will help further our research in the field both directly and indirectly.

### Matthias Troyer

Matthias Troyer studied in Linz, Austria and ETH Zurich, Switzerland where he received his diploma in physics in 1991 and his doctorate in 1994. After a postdoctoral year at ETHZ he spent three years as postdoc at the University of Tokyo before returning to ETHZ initially as lecturer and since 2005 as full professor of computational physics. Working at the interface between physics and computational science he has made contributions to quantum phase transitions in quantum magnets, supersolidity of bosons, strongly correlated electrons, ultracold quantum gases and the development of simulation algorithms for quantum many-body systems. To make modern simulation methods accessible to a broader community he initiated the open-source ALPS project. His interest in advanced high-performance computing systems has recently led him towards the testing and development of quantum devices and on the optimization of quantum algorithms. Troyer won a gold medal at the International Chemistry Olympiad in 1986, received the ETH Medal for his doctoral thesis in 1994, and was awarded an ERC Advanced Grant in 2012. He is a Fellow of the American Physical Society and currently serves as Member and Trustee of the Aspen Center for Physics.

### Aneesur Rahman Prize

The prize is presented annually to recognize and encourage outstanding achievement in computational physics research. It consists of $10,000, an allowance for travel to the meeting of the Society at which the prize is awarded and at which the recipient will deliver the Rahman Lecture, and a certificate citing the contributions made by the recipient.