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arXiv · 2610.30216

Lean-QuantumAlg: A Framework for AI Agents to Produce Quantum Algorithms that Humans Can Trust

Lei Zhang·Mingrui Jing·Yusheng Zhao·Jiahong Liu·Xin Wang
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Abstract

AI agents are increasingly capable of constructing quantum algorithms and proofs, yet machine-checked proofs alone cannot guarantee that the intended problem is solved or that resource claims match the verified computation.Here we introduce Lean-QuantumAlg, a Lean 4 framework for trustworthy AI-assisted development of quantum algorithms.Its Algorithm-Solves-Problem contract binds correctness, success probability, borrowed-state restoration and quantum and classical resource bounds to a single execution, while separating the guarantees that Lean checks from the problem specifications and execution models that humans review. We demonstrate the framework on nine AI-formalized quantum algorithms, from Grover search to quantum attacks on RSA-2048 and P-256, with less than 1% of each algorithm's imported source code requiring statement-level human review once the shared framework has been audited. By integrating reusable mathematical foundations, certified algorithmic primitives and execution-grounded verification, Lean-QuantumAlg provides a basis for AI agents to construct and certify quantum algorithms, opening a path toward scalable AI-driven discovery of quantum algorithms.

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Lei Zhang, Mingrui Jing, Yusheng Zhao, Jiahong Liu, Xin Wang. 2026-10-21. Lean-QuantumAlg: A Framework for AI Agents to Produce Quantum Algorithms that Humans Can Trust. https://arxiv.org/abs/2610.30216

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