Researchers from an international collaboration, including Professor Chris Heunen from the School of Informatics, have developed a new way to think about quantum computing — one that makes the field a bit less enigmatic and represents 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 (and edited by Peter Shor, whose seminal algorithm, ‘Shor’s algorithm’ launched the modern field of quantum computing) 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. To make real progress in quantum computing, we have to understand exactly what it is that makes a computation quantum, that cannot be reduced to classical behaviour. Only when we strip away classical structure hiding inside familiar models can we isolate the truly quantum ingredients, giving us clarity in both theory and design. Prof. Chris Heunen School of Informatics, University of Edinburgh Quantum computing researchers have spent decades searching for the essential ingredients that make quantum computing unique. This paper identifies two computational pieces that help bridge a gap in understanding from classical to quantum. Dr Jacques Carette, co-author Professor in Computing and Software, McMaster University 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 behaviour algebraically before it ever runs. Dr Jacques Carette, co-author Professor in Computing and Software, McMaster University 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. In the long term, this framework could change how we reason about quantum computing. By expressing quantum ideas in a clearer, more structured way, it becomes easier to verify results, prove that systems behave correctly, and teach the subject more effectively. That kind of clarity will be essential for building reliable, scalable quantum technologies. Prof. Chris Heunen School of Informatics, University of Edinburgh The researchers 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 including the University of Edinburgh, McMaster University, University of Southern Denmark, Dalhousie University and Indiana University — 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. This article is adapted from news posted on the McMaster website Related links Read the full paper | ‘Free Quantum Computing’ Publication date 19 Feb, 2026
