76 Quantum Theorems Completed by AI in New Lean 4 Benchmarks

QudeLeap Research and The Hong Kong University of Science and Technology (Guangzhou) have achieved a new benchmark in automated reasoning by introducing benchmarks containing 76 theorem-completion tasks using an artificial intelligence system. The research team introduced two Lean 4 benchmarks, Lean-QuantumAlg-Bench and Lean-QIT-Bench, focused on quantum algorithms and quantum information theory. Every task underwent deterministic proof checking and semantic review, establishing a standardized evaluation process for AI agents in this complex field. This work demonstrates a move towards formal verification in quantum computing, a crucial step for building reliable systems, and measures, for the first time, an AI agent’s capability to construct machine-checkable proofs. The highest difficulty-weighted scores were 60.4 out of 100 on the quantum-algorithm benchmark and 59.6 out of 100 on the quantum-information benchmark. The results reveal recurring weaknesses in areas like quantum simulation and entanglement theory, while also highlighting important trade-offs between model capability and efficiency.

Lean-QuantumAlg-Bench and Lean-QIT-Bench Benchmark Suites

The ability of artificial intelligence to rigorously verify quantum computations has long been a theoretical goal. Recent work demonstrates a measurable advancement in this capacity with the introduction of two new benchmark suites, Lean-QuantumAlg-Bench and Lean-QIT-Bench. The suites contain a total of 76 tasks, 36 focused on quantum algorithms and 40 on quantum information, each designed to be evaluated through deterministic proof checking and semantic review. This approach moves beyond simply achieving a result to verifying the correctness of the process, a critical step toward building reliable quantum systems. Researchers evaluated four models, GPT-5.5, Kimi K3, DeepSeek V4-Pro, and MiniMax M3, under two conditions: a baseline task completion and a library-augmented deduction (LAD) setting, which provided access to verified domain libraries.

The highest difficulty-weighted score achieved was 60.4 out of 100 on the quantum-algorithm benchmark, with LAD consistently improving performance, providing evidence that verified libraries can strengthen domain-specific proof agents. Notably, the results pinpointed specific areas where current AI agents struggle, including quantum simulation, quantum learning, quantum information measures, and entanglement theory. Monetary and time costs per score point also varied significantly between models, revealing important trade-offs between capability and efficiency. The team anticipates these benchmarks will establish a reproducible baseline for developing more capable and reliable proof agents and advance quantum information science.

QudeLeap Research, a Shanghai-based artificial intelligence firm, is applying automated theorem proving to the complex field of quantum computing. Each task within the benchmarks is designed to be machine-checkable, meaning every step of the proof can be verified by a computer, a crucial requirement for building reliable quantum systems. The research team evaluated four leading language models, GPT-5.5. LAD provides the AI with access to a verified domain library, allowing it to consult existing, formally proven theorems.

This approach equips AI with a foundation of established, error-free knowledge, rather than simply tasking it with solving problems in isolation. The team introduced two new benchmarks, Lean-QuantumAlg-Bench and Lean-QIT-Bench, containing 36 and 40 theorem-completion tasks for quantum algorithms and quantum information theory, respectively. These benchmarks assess an AI’s ability to complete proofs within the domains of quantum algorithms and quantum information theory. Evaluation focused on four leading language models, GPT-5. Results showed that “LAD improves both score and completion rate in all eight model–benchmark comparisons, with gains of up to 15.9 points,” indicating a clear advantage from leveraging pre-verified information. The highest difficulty-weighted scores achieved were 60.4 out of 100 on the quantum-algorithm benchmark and 59.6 out of 100 on the quantum-information benchmark.

The assumption that automated theorem proving is easily applied across all mathematical domains proves inaccurate when tested against the complexities of quantum computing. The highest difficulty-weighted scores are 60.4 out of 100 on the quantum-algorithm benchmark and 59.6 out of 100 on the quantum-information benchmark, respectively, indicating significant challenges remain.

QudeLeap Research, based in Shanghai, is assessing the capabilities of artificial intelligence in the demanding field of formal quantum theorem proving. These benchmarks are not merely assessing whether an AI can arrive at a correct answer, but whether it can construct a proof, a critical step towards building truly reliable quantum systems. Analysis of four leading models, GPT-5.5, showed that while the highest difficulty-weighted score achieved was 60.4 on the quantum-algorithm benchmark and 59.6 on the quantum-information benchmark, the study highlighted considerable variation in both monetary and wall-clock costs per score point between models, revealing important capability and efficiency trade-offs.