When the American physicist Richard Feynman first proposed the idea of a “quantum computer” in the early 1980s, he wasn’t imagining a faster version of a laptop. He was posing a paradox: if the natural world runs on the strange rules of quantum mechanics, why not build machines that do too? At its core, quantum computing is an emerging approach to computation that uses the principles of quantum mechanics to solve certain problems far more efficiently than classical computers—potentially reshaping what kinds of problems machines can solve at all.
Four decades later, that idea has evolved into one of the most ambitious technological races of our time. Lehigh Professor Luis F. Zuluaga, a leading expert in the development of solution schemes and effective algorithms for optimization over polynomials, is helping advance the research that is shaping this new frontier through his work on quantum and quantum-inspired optimization methods.
Unlike traditional computers, which store information in bits—ones or zeros states—quantum computers use qubits, which can exist in a superposition of both states at once. This ability to represent many possibilities simultaneously transforms the scale of what’s possible.
“If I have three bits in a classical computer, I can store one single number between zero and seven,” Zuluaga explained. “But with three qubits, because each one is in superposition, they can hold all the numbers between zero and seven.” That’s where the exponential increase in memory comes from. Multiply that exponential leap across hundreds or thousands of qubits, and in principle it could result in staggering computational power.
Zuluaga’s research focuses on how these capabilities can be applied to hard optimization problems—questions that classical computers struggle to solve efficiently. As part of Lehigh’s Quantum Computing and Optimization Lab (QCOL), he studies how to translate complex, real-world questions—like how to make a system more efficient or a decision more reliable—into forms that quantum computers and advanced classical machines can tackle. Working with colleagues in engineering, he designs and analyzes new algorithms that could one day help quantum and “hybrid” quantum–classical computers solve these problems faster and more effectively than today’s machines. Examples of this promise have already appeared in the field.
One of the first breakthroughs in quantum computing came when mathematician Peter Shor devised a quantum algorithm capable of factoring large numbers—a task classical computers struggle with, and one that underpins nearly all modern cryptography. The result demonstrated that quantum computers could solve certain mathematical problems exponentially faster than classical machines, fundamentally challenging assumptions about digital security.
“The big revolution really started when Peter Shor came up with an algorithm for prime factorization,” Zuluaga said. “Classical machines are very bad at that, and modern cryptography depends on that difficulty.” So if a quantum computer can factor efficiently, it could, in theory, break today’s encryption. The revelation triggered a global race—not only to build quantum hardware, but to invent new cryptographic methods that can withstand it.
For now, that threat remains theoretical. The largest number successfully factored by a quantum computer is just 15 digits—tiny by cryptographic standards—but progress is accelerating. “Quantum computers are real,” he said. “They’re just very expensive.” Quantum computers themselves are tiny—processors the size of a coin—surrounded by elaborate refrigeration systems that cool them to near absolute zero.
At Lehigh, Zuluaga is part of a cross-disciplinary research group working to advance both the science and application of quantum computing. The team, which includes faculty from industrial and systems engineering, was initially funded by a DARPA ONISQ grant and is now supported by the National Science Foundation. Their work spans several major challenges: developing quantum algorithms for optimization and decision-making, modeling and mitigating noise in near-term quantum devices, and designing problem frameworks that can take advantage of emerging quantum architectures.
Major institutions like IBM and Google are betting big, expecting quantum technologies to account for a significant share of their business within the next two decades. Hospitals, such as the Cleveland Clinic, have already begun investing in quantum systems for medical modeling and pharmaceutical research. The excitement, Zuluaga said, stems from possibility: quantum computing could solve problems we can barely articulate today.
For Zuluaga, the field is exciting because it forces researchers to rethink the fundamentals of computation itself—what becomes possible when machines begin to operate according to the laws of nature at the quantum level.
This research was presented at the 2025 Lehigh University Research Symposium.
Generative AI was used to organize this story, based on data and information from a research presentation. It was reviewed for accuracy by the researchers and edited by university communications staff.
