Proving olympiad geometry theorems on a superconducting quantum processor

arXiv:2609.14533v1 Announce Type: cross 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.

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.

Quantum Physics (quant-ph); Artificial Intelligence (cs.AI)

arXiv:2609.14533 [quant-ph]

(or arXiv:2609.14533v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.14533 arXiv-issued DOI via DataCite (pending registration)

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Proving olympiad geometry theorems on a superconducting quantum processor

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