Most people think of bumpy airplane rides when they hear the word “turbulence.” For Xiangyu Li, an Earth scientist at Pacific Northwest National Laboratory (PNNL), turbulence means so much more.

“Turbulence is everywhere, from eddies in a stream to the irregular motion of molecules in a cell,” said Li. “But modeling turbulence is very complex. Not many scientists are pursuing problems involving turbulence.”

The sheer complexity of turbulence problems represents a major challenge: even exascale computers—the most powerful supercomputers in the world—cannot solve some of these problems. 

To find a solution, Li teamed up with PNNL scientists Johannes Mülmenstädt, Margaret Cheung, Gregory Schenter, and Jaehun Chun as well as Xiaolong Yin from the Colorado School of Mines and PNNL joint appointee and University of Toronto professor Nathan Wiebe. Together, they devised a mathematical solution to simulate fluid dynamics—including turbulence—using quantum computing. Their results, published in Physical Review Research, could be used to clarify some of the most prominent uncertainties in atmospheric science and beyond. 

Modeling turbulence across scales: from molecules to clouds

The randomness in turbulence makes simulating the motion of fluids—including air and water—incredibly difficult. Currently, scientists must choose between performing an extremely computationally expensive calculation to resolve motion at the smallest scales or approximating the motion and accepting large uncertainties in the calculation. There is currently no way to simulate fluid dynamics with both precision and computational efficiency. 

“One of the grand challenges in physics, chemistry, and engineering is to connect molecular details to the continuum models, like the ones that Earth scientists use,” said Schenter. 

With their combined expertise, which encompasses the fields of physics, quantum computing, biology, chemistry, and atmospheric science, the team developed a potential quantum speedup for simulating turbulence. Specifically, they applied a quantum algorithm to the current equation used to understand turbulence by reformulating it based on the Boltzmann form. Though current quantum computers aren’t sufficiently developed to successfully carry out the simulation, the team provided evidence that their new quantum formulation could provide a quantum advantage over classical computing methods for the simulation of fluid dynamics. 

“This formulation will allow us to cross so many scales where complex transport phenomena occur. This includes the native size of turbulence all the way up to the size of clouds,” said Schenter.

Indeed, the team’s expertise reflects knowledge of these different scales. Schenter and Chun are interested in fluid dynamics at the molecular scale, whereas Li and Mülmenstädt study them on an atmospheric level.

“In climate projections, cloud physics—including turbulence—is the largest source of uncertainty,” said Mülmenstädt, who serves as principal investigator of the project. “If we want to solve climate problems, we need to resolve cloud processes.”

Clouds and precipitation affect the transfer of energy and water across the globe. Understanding and representing how environmental conditions alter cloud system formation and evolution, which in turn influence atmospheric radiation and precipitation processes, remains a challenge. PNNL combines field measurements, modeling, and experimentation when studying clouds and aerosol particles across scale.

Scale is also important when considering biological systems. As a biological physicist and computational scientist, Cheung’s interests land her squarely in the middle—the intermediate scale at the cellular level. 

“One aspect of microbial research focuses on the coupled changes in the chemical reactions through the metabolic networks in time and space,” said Cheung. “With our formulation, quantum computing may provide speedup in advancing the simulations of this complex system. This provides a basis and motivation for creating quantum algorithms of complex systems to increase society’s predictive power relevant to health and environmental queries, ultimately leading to a better bioeconomy for addressing energy and environmental problems.”

These findings pave the way to harnessing the advantages of quantum computers for the study of turbulence. Many challenging and exciting questions are now accessible for study by quantum computing methods. 

“We are thrilled to extend our work to multiphase turbulence with complex boundary conditions and to a wide class of nonlinear transport problems across fields such as biophysics and plasma physics,” said Li. “With this new method, we can achieve an end-to-end quantum advantage for these challenges.”

Cross-disciplinary collaboration

This diverse research team came together by chance, despite working in different divisions across PNNL. Schenter, a physicist, and Chun, a chemical engineer, attended a talk by Li on cloud properties in turbulence. 

As it turns out, Li knew Chun by reputation. Over a decade earlier, Chun published a seminal paper on turbulence in aerosols while he was a graduate student at Cornell University. 

“I’ve always been fascinated by turbulence,” said Chun. “Though my work has shifted from the gas phase to liquid, and into smaller scales, like nanoscale and molecular scale, the problems are essentially the same.”

Following Li’s seminar, Chun and Schenter approached Li about investigating a problem in turbulence. Around the same time, Mülmenstädt, an Earth scientist, was recruited to PNNL. On the basis of their shared interest, they formed a group along with Cheung to share papers and commentary via email.

They discussed applying quantum computing to classical problems and found that very little research on the topic existed. Nevertheless, they remained intrigued by the idea of using quantum computing to solve turbulence problems.

“I'd been dreaming about working on quantum computing for turbulence or even quantum turbulence since 2016,” said Li. 

Despite their extensively varied backgrounds, no one in the group at the time had any expertise in quantum computing. The team decided to take advantage of PNNL’s annual Quantum Bootcamp, a lecture series covering fundamental topics in quantum computing. There, they met Wiebe, who immediately became interested in applying his quantum computing expertise to the turbulence problem the team had identified.

High risk, high reward

Li credits PNNL’s leadership and support for their research through Laboratory Directed Research and Development funds to make this work possible.

“In many places, it would be extremely difficult to get support for such high-risk work,” said Li. “I’d been wanting to pursue this project for years; it wasn’t until I came to PNNL that I actually could.”

“When I first came to PNNL, I decided I would use my honeymoon period with the lab management to see how willing they were to entertain some crazy ideas,” said Mülmenstädt. “And it turns out they were very interested because I think they recognize that we need some blue sky–type projects.”

This research was primarily supported by the Laboratory Directed Research and Development Program at PNNL. Code development, simulations, and the main quantum algorithm complexity analysis were supported by the Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage. Domain applications to chemical physics and biophysics were supported by the Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Bioscience, Chemical Physics and Interfacial Sciences Program as well as the National Science Foundation.