Rethinking how data meets the atom

Quantum computing is often framed as a hardware race with attention fixed on machines that promise amazing speed. But a foundational mathematical problem remains unresolved.

No complete framework yet exists for converting massive amounts of data generated by fields such as healthcare, disease surveillance, financial transactions and climate monitoring into units a quantum machine can process.

“What exactly we are proposing is this: data is continuous,” said Arni S.R. Srinivasa Rao, PhD, professor and director of the Laboratory for Theory and Mathematical Modeling, Division of Infectious Diseases, Medical College of Georgia at Augusta University. “That means the generation of the data is continuously happening. And how to slice it down into pieces, that is what it is about. The slicing down of the data into smaller pieces, not too small pieces, but smaller enough for the computers to handle them in a meaningful way.”

Rao and Steven G. Krantz, a professor of mathematics at Washington University in St. Louis, published their findings on “The Role of Quantization in Quantum Computing” in the July/August 2026 issue of SIAM News, published by the Society for Industrial and Applied Mathematics.

“Quantization is a mathematical method, nothing to do with quantum computing,” Rao said. “But these two we are trying to mix together.”

The problem with just chopping it up

Classical computers store information as bits, switches that are either off or on, zero or one. Quantum computers use qubits, which can hold combinations of both states simultaneously, which is why they can theoretically process vastly more information at once.

But qubits operate at the atomic level. Getting that data into a quantum machine requires breaking it down into atomic-scale pieces first. The math for doing that well, Rao and Krantz argue, does not yet exist in any complete form.

The hard part is “slicing” it right.

“Not slicing in a random, arbitrary way,” Rao said. “If you slice it in a way which is arbitrary, then you might miss, you might necessarily slice it where no information is required. Information is broken into pieces rather than combining the information. That’s what the mathematics is playing a role here.”

Their research proposes using an ensemble of quantization techniques rather than a single method, with different mathematical tools matched to the different layers inside a dataset. A disease surveillance file might bundle together demographic data, income levels, infection status and housing type, for example. Each layer has its own structure. The partitioning, they argue, should flex to fit the problem rather than forcing every dataset through the same process.

Mixing two worlds that don’t quite line up

The second major contribution is a formally defined measure the authors call “atomic uncertainty.” It quantifies the mismatch between quantized data and the atomic structure that data is supposed to travel through inside a quantum processor.

The mismatch exists because atomic models, the diagrams of electrons and nuclei that physics students study, are approximations. The actual behavior of electrons inside an atom follows probability distributions. There is inherent randomness in there that scientists have not resolved.

Planets are called spheres, and textbooks draw them as smooth perfect balls, Rao explained, but their surfaces are cratered and irregular. The sphere is a useful model, not an accurate description. Atomic structure works the same way.

When quantized data does not fit cleanly into that imperfectly understood atomic structure, the gap becomes computational error. At small scale, manageable. At the scale of real-world data inputs, those errors can compound into results that are simply wrong.

“We are not trying to fix the error. We are trying to see how big the error is,” Rao said.

This study illustrates the concept with a disease-modeling example, building a dataset that layers population age, income bracket, infection status and housing type. When the data is quantized and compared against a model atomic structure, the spaces do not fully align. That leftover mismatch is the atomic uncertainty. In a real quantum system processing actual disease data, it does not disappear but shows up as wrong answers about how a disease spreads.

The next step, Rao said, requires industry partners to take the framework and build hardware around it.

“Designing a computer is different from the actual making a computer,” Rao said. “We designed the method of slicing the larger, huge continuous data into smaller digestible computer bits, that’s called qubits. The industrialists have to build it. Like designing a mobile phone is different from actually making a mobile phone.”