image: Juan Jose Mendoza Arenas (center) with PhD students Hirad Alipanah (left) and Daniel Madrid (right)
Credit: Thomas Altany
Those who have searched for a pattern in the chaotic splatters of a Jackson Pollock painting may intuitively grasp turbulence and all its complexity. Now imagine Pollock’s swirls of paint in motion and extending into space at different length scales while interacting with different forces.
That’s the challenge of turbulence. While it shows up everywhere and affects everything from air travel to blood flow, it is extremely difficult to calculate. Indeed, as the physicist Richard Feynman once said, “Turbulence is the most important unsolved problem of classical physics.”
The University of Pittsburgh’s Juan Jose Mendoza Arenas and Pennsylvania State University’s Xiang Yang hope a new form of computing might change that.
Professors Mendoza Arenas and Yang have received a highly competitive New Initiative Grant from the Charles E. Kaufman Foundation to design algorithms and model turbulence using quantum computers. The collaborative, two-year project titled “Small-Scale Turbulence as a Quantum System” seeks to advance understanding of turbulence and the potential of quantum computers to model complex systems.
The challenge of modeling turbulence
Consider the smoke billowing from an extinguished candle. It starts in a smooth upward flow but soon breaks into eddies, which break into smaller eddies until each one dissipates. As they break apart, the eddies interact with other eddies, producing a random mix of length scales, where even a small change can alter flows.
Fully considering all these length scales leads to the vast complexity of dealing with turbulence. For instance, “to simulate the turbulent flow of air around an airplane wing under standard flight conditions could take a classical computer millions of years,” said Mendoza Arenas, an assistant professor in the Swanson School of Engineering’s Department of Mechanical Engineering and Materials Science.
Traditional models focus on the largest motions while approximating the smaller ones. That saves computational power, but it doesn’t tell the full story, which matters for fields like engineering and medicine.
Turning to quantum computing
Increasingly, researchers are turning to quantum computers to help solve complex problems. Unlike classical computer systems, which are constrained by the binary logic of ones and zeros, quantum systems use quantum bits, or qubits. A qubit can represent any normalized combination (or superposition) of one and zero.
“Quantum computers function under the laws of quantum mechanics and can represent many possibilities simultaneously,” said Mendoza Arenas. “That opens the door to modeling complex systems like turbulence more naturally.”
Rather than treating turbulent flows as a single, fixed outcome, their project will use quantum mechanics to represent the random nature of turbulence.
The team will design new algorithms to run on quantum computers. They will test these algorithms on a quantum simulator, which mimics an actual quantum computer. “When we’re confident with our algorithm, we’ll run it on the actual system,” Mendoza Arenas said of the expensive, sensitive computers.
By combining expertise in fluid dynamics and quantum computing, Mendoza Arenas and Yang hope to develop more accurate and efficient models of turbulence and other multiscale systems, where behavior at small scales can have a big impact.
As the committee awarding this New Initiative Grant noted, “this research opens a high-risk, high-reward pathway towards scalable, physically grounded models for multiscale systems.” Such models could profoundly improve how engineers design vehicles, predict environmental flows, and understand the dynamics of the human body.