Quantum

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

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Briefings

Lean-QuantumAlg is a Lean 4 framework designed to help AI agents build and certify quantum algorithms by binding correctness, success probability, and resource bounds to a single execution. The framework was tested on nine AI-formalized quantum algorithms, including Grover search and quantum attacks on RSA-2048 and P-256, achieving less than 1% of imported source code requiring human review after audit. This represents a significant step toward scalable AI-driven discovery of quantum algorithms.

Key points

• Lean-QuantumAlg integrates reusable mathematical foundations and certified algorithmic primitives to support AI agents in constructing quantum algorithms.
• The framework separates Lean's verification guarantees from human review of problem specifications and execution models, reducing required human review to less than 1% of imported source code for nine tested algorithms.

Context

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. This framework addresses that gap by providing a systematic approach to algorithmic certification.

Limitations

The framework was demonstrated on nine AI-formalized quantum algorithms, with specific results for Grover search, RSA-2048, and P-256 attacks. The study does not provide results for all possible quantum algorithms, and the framework's scalability for production use remains unverified.

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