An international team of five professors has developed a new way to think about quantum computing — one that makes the field a bit less enigmatic. The work, co‑authored by Jacques Carette, Professor in McMaster University’s Department of Computing and Software, represents what he calls a “shift in viewpoint” on how to approach quantum computation.
Published in the Proceedings of the National Academy of Sciences (PNAS), one of the world’s leading multidisciplinary journals, the study introduces a framework that avoids unnecessary mathematical complexity and clearly separates what is truly quantum from what is just classical computing in disguise.
The team’s key insight is that adding only two components to ordinary reversible classical computing — a long‑known V‑gate and a small complex‑phase rotation — is enough to produce full quantum behaviour to any desirable degree of accuracy. “Quantum computing researchers have spent decades searching for the essential ingredients that make quantum computing unique,” says Carette. “This paper identifies two computational pieces that help bridge a gap in understanding from classical to quantum.”
The new framework also replaces continuous mathematics with a small set of discrete, symbolic building blocks directly inspired by how real quantum devices work. This allows researchers to use familiar tools from classical computer science, such as algebraic equations and step‑by‑step rewrites, to check and improve quantum circuits. In many cases, this means a circuit’s behaviour can be proven correct outright, rather than tested through repeated, probabilistic runs.
The immediate win is certainty. Quantum hardware measurement is probabilistic, but with our symbolic equations we can certify a design’s behavior algebraically before it ever runs.
“The immediate win is certainty,” says Carette. “Quantum hardware measurement is probabilistic, but with our symbolic equations we can certify a design’s behavior algebraically before it ever runs.”
The paper, titled “Free Quantum Computing,” also introduces a clean, programming‑language‑style model built from these basic parts. It is just as powerful as the standard mathematical model used across the field today, but it enables checking and reasoning, which could help people who design and test quantum circuits.
Carette and his co‑authors emphasize that the work is not a way to simulate quantum computers efficiently on classical ones. Instead, it provides a clearer foundation and a new set of reasoning tools for teams working in quantum algorithms, quantum compilers, post‑quantum cryptography and quantum chemistry.
The project took shape over three years of weekly online meetings, during which the five professors — each working at a different institution — debated, refined and challenged each other’s ideas. Their insight was inspired partly by optical quantum computing and ultimately distilled into a simpler, high‑level model.
“If I were an applied person, this research would be frustrating,” says Carette, “but as a theoretician, the elegance of the results appeal to me.” As for what the new framework will reveal next, Carette says it’s too early to know, and that is part of the excitement. “It has a lot of promise, but now we need other researchers to take a look, try it out and really kick the tires,” he says. “It makes sense to us. Now we want to see if it makes sense to everyone else.”
