Researchers at the Department of Energy’s Oak Ridge National Laboratory have tested a quantum computing approach to an old challenge: solving classical fluid dynamics problems.

The work is published in the journal Physics of Fluids. The results highlight avenues for further study of quantum computing’s potential to aid scientific discovery.

For the test problem, the research team used the Hele-Shaw flow problem—a scenario of two flat, parallel plates extremely close to each other and the flow of liquids and gases between them. The problem, although idealized, offers important applications in real-world problems such as microfluidics, groundwater flow, porous media flow, oil recovery and bioengineering.

The research team wanted to test whether a quantum algorithm running on a quantum computer could solve the flow equations more quickly than classical computers.

“Scalability and accuracy are the key issues here,” said Murali Gopalakrishnan Meena, the study’s lead author and an ORNL computational scientist. “We showed error suppression and mitigation techniques can help, but more research is needed.”

Modeling fluid flow plays a vital role across industrial design in fields from aerodynamics to oil refining. The unsteady flow of air, other gases and liquids over machinery parts can lead to turbulence that can impede performance.

Current approaches rely on a combination of physical testing and complex sets of approximated equations that offer a kind of shortcut to predicting flow. But physical experiments can be expensive and time-consuming, and traditional formulas often fail to account for all relevant physics. Digitally simulating flow captures more of the physics but can require huge amounts of computing time.

“Theoretically there’s a quantum advantage to be achieved for this problem,” Gopalakrishnan Meena said. “That by itself wasn’t really our objective for this study. We wanted to establish some benchmarks for guidance on how quantum algorithms like this could fit into the overall approach of simulating fluid flows.”

Quantum computing relies on quantum bits, or qubits, to store information. Qubits, unlike the binary bits used in classical computing, can exist in more than one state simultaneously via quantum superposition, which allows combinations of physical values to be encoded on a single object. That dynamic allows for a wider range of possible values, more like a dial with a range of precise settings than a binary on-off switch.

Researchers have theorized that expanded range could open up new, faster, more efficient ways to solve complex problems such as predicting fluid flow.

“On paper, this approach should give us that quantum advantage,” Gopalakrishnan Meena said. “But we found much of the challenge lay in arranging the problem for a workable result.”

The team applied for and received computing time on two of IBM’s quantum computers via QCUP, which awards time on industry-partner quantum processors around the country to support research projects. They used the Harrow-Hassidim-Lloyd, or HHL, algorithm, a quantum algorithm for solving a set of linear equations, as the test approach.

The HHL algorithm’s usefulness for solving a problem like the Hele-Shaw scenario depends on the sensitivity of the system of equations to small numerical errors. The more approximations, the less room for error.

“The sensitivity of the equations grows exponentially with our problem size, so if there’s even a small numerical error then the whole solution can blow up and become unworkable, requiring more computational effort to solve the problem,” Gopalakrishnan Meena said. “We tried to set up the system to keep these numbers low.”

Current quantum systems tend to be plagued by high error rates, or noise, due to measurement errors, qubit degradation and other causes. The team used noise models and reduction algorithms that attempted to predict errors and compensate for them, with uneven results.

“We found the noise models didn’t mimic the circuits’ actual behavior in the quantum computer, so they didn’t really help,” Gopalakrishnan Meena said. “What helped was to simplify the circuits by reducing and streamlining the number of operations. We saw the overall accuracy increase then.”

The team ultimately recommended more sophisticated noise models, particularly for larger problems, and an increased focus on optimizing and streamlining circuits for future studies.

“Scalability of the quantum algorithm and amenability of the problem for the quantum algorithm are the key elements here,” Gopalakrishnan Meena said. “Recently, there have been various improvements to the HHL algorithm we used, which we are currently exploring to tackle fluid flows.

“If we can understand how to effectively apply this algorithm to solve fluid dynamics problems and take advantage of the potential quantum speedup, this algorithm could have a variety of real-world fluid dynamics applications such as in combustion and fusion.”