Simulating the world of quantum mechanics

Expertise in both computational and computer science

What comes to mind when you hear the term “computer simulation”? For example, can a certain skyscraper design withstand an earthquake? What kind of flooding would heavy rain induce? Or, what shape should a car be to minimize air resistance? To put it more generally, computer simulation is the process of using computers to create realistic representations of things that are impossible to experiment within the real world and test them. In the modern era, computer simulations play a crucial role in advancing the boundaries of numerous scientific fields, collectively known as “computational science.”

On the other hand, there is a field called “computer science.” Computational science involves the use of computers to perform simulations for scientific purposes, whereas computer science is the study of computers themselves. It is easy to confuse the two.

Yoshimoto is exploring the microscopic world governed by quantum mechanics using both computational and computer science. However, it is an incredibly complex, challenging, and daunting endeavor.

“I originally studied condensed matter physics and joined a research lab specializing in surface physics in graduate school. One of the major research topics there was the surface of the semiconductors. The first electronic computers were made by connecting vacuum tubes with wires. However, modern semiconductors are made by printing circuits onto the surface of materials, much like printing a photograph. Therefore, to create stable circuits at the nanoscale that are both extremely fine and highly dense, a thorough understanding of the properties of material surfaces is essential. However, when dealing with the atomic scale, it becomes increasingly difficult to investigate experimentally what is happening at the surface. This is where computer simulations became crucial.”

During his doctoral studies, Yoshimoto devoted himself to investigating the state and properties of materials using supercomputers. This was the computational science aspect of his research. After completing his doctoral program, in addition to pursuing this research area at the Institute for Solid State Physics, he joined projects to set up a supercomputer dedicated to solid state physics. Simultaneously, he developed and operated simulation programs designed for supercomputers, actively engaging in computer science as well. He was drawn to this field because he had loved computers since his childhood.

“When I was in an upper elementary grade, I was given an MSX (an inexpensive 8-bit computer) that was barely more than a toy. It was almost like a game console, and I used it to learn the basics of programming. At that time, I gradually began to understand the various parts, such as memory, and how they worked. Of course, I also played games (laughs). When I was in high school, I was allowed to use my father's PC-98 (16-bit personal computer manufactured by NEC).”

Given how familiar he had been with computers from a young age, Yoshimoto faced a major dilemma in his second year of college: should he pursue physics or computer science?

“I was genuinely torn. In the end, I chose physics because I thought it would offer more opportunities to encounter the unknown.”

Simulation should be realistic

Now, how exactly does one simulate the world of atoms?

The properties of semiconductors, metals, dielectrics, and magnetic materials that Yoshimoto studies change significantly depending on the state of electrons governed by quantum mechanics. Therefore, simulations must be run using the equations of quantum mechanics. In other words, the state of electrons is calculated based on the Schrödinger equation, a fundamental equation of quantum mechanics. This method is called “first-principles electronic structure simulation,” and Yoshimoto says it is extremely challenging.

“There are a lot of tedious things involved (laughs). To perform simulations, we need to be able to represent the position of an object. In the atomic world, we need to specify the position of each particle (electron). However, in quantum mechanics, the position of a particle cannot be definitely determined. This is because, in quantum mechanics, the position of a particle is probabilistically represented by a wave function. In other words, it might be at position A or position B. That is the world we are dealing with.”

Simulating something like a skyscraper this way, with beams and columns without fixed positions, is impossible. Of course, nobody attempts to simulate skyscrapers this way, but in the world of quantum mechanics, this is the norm.

“Moreover, if there is only one particle, a single three-dimensional function is sufficient, but with three particles, a nine-dimensional function is required, and with four particles, a twelve-dimensional function is needed, and so on. The biggest problem is how to control these functions whose dimensions keep increasing. The solution is not to use a function whose dimension increases multiplicatively but to use a set of three-dimensional functions whose number corresponds to that of electrons. In this way, the rapid increase of required information is suppressed to an additive increase following the number of electrons. In practical simulations, the number of particles can reach hundreds.”

Yoshimoto states that simulations should be as “realistic” as possible.

“Just as you cannot tell whether a car is a van, a sedan, or a truck if it is like a child’s drawing of a box with four wheels, the state of electrons must be realistic enough to show the details. This is the principle behind first-principles electornic structure simulation, and we develop our programs following it. However, there is a major challenge. Solving problems realistically requires writing the function as carefully as possible. For example, there is a strong, attractive force in the atomic nucleus that makes its behavior “sharp,” so to speak. If its behavior were smooth, we could represent it with a single curve, but to simulate behavior that is “sharp” and “turbulent,” we need a lot more information. We incorporate various programming techniques to address this challenge, but it is a very complex and difficult process.”

Leveraging knowledge from both physics and computer science

Let us now review the steps of computer simulation.

First, the target phenomenon, the behavior of atoms and electrons in Yoshimoto’s case, is expressed using equations. This is called “modeling.” At this stage, multiple equations are combined in various ways rather than using a single equation. The complexity is already overwhelming.

The modeled equations are then converted into mathematical expressions suitable for computer calculations, and these are written into programs that can efficiently perform calculations using various algorithms. Then, the programs are revised and optimized by distributing and parallelizing calculations (running many computers simultaneously and coupling their computations) to suit the computer system being used.

Finally, the calculations are performed. Afterward, the results are analyzed, and research into the phenomenon is conducted.

Yoshimoto, who is an expert in both relevant areas, is involved in every step of this process.

“As I mentioned earlier, the more atoms (particles) there are, the more difficult the calculations become. Therefore, we focus on the key points, extract the important parts, and perform calculations that determine the movement of atoms in specific areas. Atomic nuclei are “glued together” by electrons. So, we can determine where the nuclei will be positioned or where they might move by precisely calculating the properties of the “glue.” This is what I mean by realistic simulations, which have predictive power. We can compare the results of the simulation with those of experiments to understand what is happening.”

Calculating the behavior of the “glue,” which must be expressed by the Schrödinger equation, is precisely the challenge that quantum mechanics poses. Overcoming such difficulties requires leveraging both knowledge of physics and computer science.

“To calculate accurately, we must first address the issue of how to express physics as mathematical formulas, and then how to translate those formulas for the computer. Translating it properly for a computer means converting calculations into a flow of information. What makes modern computers complicated is that they have multiple processing units; even smartphones have 4 or 8 cores, meaning their CPU can perform 4 or 8 calculations simultaneously. A single core is not sufficient even for the tasks carried out by a smartphone. Therefore, when you scale up to larger computers, the number of cores becomes significantly large. For example, the supercomputer “Fugaku” has hundreds of thousands of cores. At that scale, the flow of information becomes extremely complex, and programming and controlling it become crucial factors. To calculate large and complex things, distributed parallel computing is unavoidable, and it is essential to recognize this and organize the data appropriately. This awareness is not easily gained by simply studying physics equations.”

Will there be a “computational revolution” in 10 years?

Computer simulations lead to new discoveries. According to Yoshimoto, this is not unusual. There are already many examples of new, unknown substances whose structures have been predicted by simulation. This means that with the advent of more powerful computers, more complex substances will be discovered, and more complex phenomena will be elucidated.

“Until now, computing resources have doubled every 1.5 years. This is called Moore’s Law. However, whether this continues is uncertain. Some say we have reached the limit. I believe there are two paths forward. One is to achieve a breakthrough in computational techniques without relying on the development of computers themselves. The other is to develop and commercialize “exotic” computers.”

By “exotic,” Yoshimoto means “different,” referring to computers that operate on principles different from existing computers.

“For example, there was a time when people tried to solve differential equations by directly mapping the changes in voltage and current in electrical circuits. That was analog computing. Such an approach might be taken again. If that happens, there will be significant changes in programming as we know it today. Or perhaps specialized computers will be built for each field of physics. Or computers with completely different computing principles may be created... I do not know how things will develop from here, but I feel that there is no doubt that we are at an important turning point in the structure of computers themselves.”

Yoshimoto anticipates that, much like the sudden appearance of diverse life forms in the Cambrian explosion, we might see the emergence of numerous exotic computers in the next 10 to 20 years.

“If you are a high school student reading this, by the time you enter the workforce, there might be a major transformation in the world of computers.”

Yoshimoto has the following message to young people who will witness the “computer revolution,”.

“Computers are indispensable for scientific work. This is true not only for the natural but also for the social sciences. Therefore, even if some researchers do not feel comfortable with computers, being able to process information effectively will enable them to do many things that are impossible with human power alone. I hope the research community will learn to work well with computers. Particularly, it is vital in programming to understand the computer mechanisms based on which it works. Just as it is important to understand the culture behind a foreign language when learning it, understanding what is happening inside a computer is critical.”

When asked about the joys of research, he replies as follows.

“I just feel good when I can implement a beautiful solution on a computer (laughs). I am more interested in the solution itself than the calculation results. Beautiful programming is natural to the computer: it does not go against the computer's structure and makes processing not only easy to understand for the computer but also fast. That is what I aim for.”

So, is that Yoshimoto’s greatest dream?

“Absolutely. I want to find beautiful computational solutions.”

※Year of interview:2025
Interview/Text: OTA Minoru
Photography: KAIZUKA Junichi

YOSHIMOTO Yoshihide

Associate Professor, Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo

2000, PhD in physics, University of Tokyo Graduate School of Science 2001- Research associate (jokyouju), Institute for Solid State Physics, The University of Tokyo, 2009-Associate Professor Tottori University 2014- Associate Professor, Graduate School of Information Science and Technology, The University of Tokyo.