Quantum computers prove geometry theorems from olympiad problems
Proving olympiad geometry theorems on a superconducting quantum processor
Artificial Intelligence
Summary
Proving mathematical theorems automatically is a challenge that usually relies on classical computers. The authors demonstrate that a quantum computer can carry out such proofs in geometry by encoding mathematical expressions as quantum states and performing symbolic reasoning. They used a superconducting quantum processor to prove the diagonals of a square are perpendicular and to solve a geometry problem from the International Mathematical Olympiad. This shows quantum machines can support logical reasoning tasks in new ways.
What this means in practice
- •For quantum software developers: Develop algorithms that perform symbolic mathematical reasoning on quantum hardware using algebraic elimination and guided proof search approaches.
- •For automated reasoning engineers: Integrate quantum processors to accelerate structured symbolic deduction tasks in theorem proving workflows.
Authors
Ning Wang, Zheng-Zhi Sun, Zhengyi Cui, Yiren Zou, Aosai Zhang, Fanhao Shen, Jiarun Zhong, Zehang Bao, Zitian Zhu, Han Wang, Jia-Nan Yang, Jiayuan Shen, Gongyu Liu, Yanzhe Wang, Yihang Han, Yiyang He, Jiahua Huang, Sailang Zhou, Xinrong Zhang, Yaozu Wu, Zixuan Song, Jinfeng Deng, Hang Dong, Qi Ye, Weikang Li, Si Jiang, Yixuan Ma, Shuangyue Geng, Zhide Lu, Chao Song, Hekang Li, Pengfei Zhang, Qiujiang Guo, H. Wang, Dong-Ling Deng
Abstract
Automated theorem proving seeks to use computational systems to prove or disprove mathematical and logical statements [1, 2]. It underpins a wide range of applications, and enhancing theorem-proving capabilities remains a central objective in artificial intelligence [3]. Although recent neuro-symbolic systems have achieved remarkable progress [4-7], their operation is ultimately constrained by classical computational architectures. Quantum computing [8], by contrast, enables information encoding and coherent parallelism beyond classical limits [9-14], raising the possibility of accelerating structured symbolic deduction [15]. Here we report the experimental realization of automated geometry theorem proving on a fully programmable superconducting quantum processor. We develop two complementary quantum proving frameworks. The first implements Wu's algebraic elimination method using quantum pseudo-division, with multivariate polynomials represented in superposition states, enabling quantum algebraic theorem proving. The second implements the full-angle method as backward symbolic reasoning through a hybrid quantum strategy-guided architecture, demonstrating a general route toward quantum symbolic proof search. 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. 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.