A Quantum Computer Just Confirmed a 48-Year-Old Math Problem - ScienceAlert

Quantum computers already exist and are advancing quickly, but scientists predict there's much, much more to come from them – and a new study points the way to another significant step forward in the field of math. The study team, led by researchers from Zhejiang University and Tsinghua University in China, was able to get a 121-qubit superconducting quantum processor to prove two math theorems, including one set at the 1978 International Mathematical Olympiad, a prestigious mathematics competition for students. What's important here is not that the quantum computer got to the right answer (as this was largely dictated by the researchers), or the speed with which it worked (as classical computers can solve these problems very quickly) – but that these kinds of deductions were carried out on quantum hardware at all.A diagram of the quantum processor used in the research (left) and the first theorem it tackled (right). (Wang et al., arXiv, 2026)It suggests quantum computers can transition from being very advanced number crunchers to systems capable of executing logical mathematical reasoning: starting with an initial set of rules, and taking verifiable steps to an outcome. "Here we report the experimental realization of automated geometry theorem proving on a fully programmable superconducting quantum processor," write the researchers in their paper. "As illustrative examples, we prove two theorems on a superconducting quantum processor: the perpendicularity of the diagonals of a square and a 1978 International Mathematical Olympiad geometry problem." The first theorem mentioned there was a test of quantum algebra. The challenge was to take a square, draw both diagonals, and prove the diagonals cross at right angles. The researchers got their quantum system to do this using a hybrid implementation of a well-known approach called Wu's method.Over 100 countries compete in the International Mathematical Olympiad, with a past question from the event used in this research. (International Mathematical Olympiad)Next came the IMO theorem, a more complex geometry problem involving intersecting triangles and circles. Here the researchers turned to an approach called symbolic proof search, where the quantum circuits were used to propose, apply, and evaluate logical steps to reach the right deduction. Again, it's not the processes that are new – it's that these processes, known as automated theorem proving, can work on a quantum processor, with their abstract concepts, algebraic formulas, and chains of logical arguments. Researchers had not previously demonstrated experimentally whether quantum circuits could be encoded this way, given the noise and instability usually associated with qubits. "Our results establish, at the experimental level, automated logical reasoning as a viable task for near-term quantum processors and provide a concrete pathway toward quantum-enhanced symbolic intelligence," write the researchers. There are implications here for AI and math too. The researchers used some simplified machine learning techniques for the second theorem, to reinforce the correct steps as they were worked through. Further down the line, the researchers suggest that quantum computing could help AI solve math problems that its algorithms are currently unable to solve on classical computers – though it's worth emphasizing that none of that was tested here.Due to their superpositional capabilities, qubits can do exponentially more than conventional computer bits, and if this technology can be successfully scaled up, then new mathematical possibilities may be reachable for these quantum and AI systems. "These results show that structured mathematical reasoning can be formulated as an executable quantum process rather than merely verified through classical post-processing," write the researchers. No one has managed to prove theorems in this way before, so it's inevitably going to be a small and limited proof-of-concept, as this is just the beginning: relatively simple math problems, and a lot of guidance toward the answers. However, to take it further forward, the physical hardware of quantum computers available will need to get better – in part to accommodate larger geometry equations known as polynomial instances – and then these approaches can be tried again. Related: CERN Detects Quantum Entanglement in Particles Born From The Higgs Boson "The present experiments operate on polynomial instances of limited size and a restricted set of symbolic relations, with the proof state measured and re-prepared between successive reasoning rounds," write the researchers. "These restrictions arise from the available hardware resources rather than from the structure of the framework itself."The research has yet to be published in a peer-reviewed journal, but a preprint is available on arXiv. This article was fact-checked by Rebecca Dyer and edited by Rebecca Dyer. While we pride ourselves on our process, we are only human. If you spot a mistake, please let us know.