76 Quantum Theorems Completed by AI in New Lean 4 Benchmark

QudeLeap Research and the Hong Kong University of Science and Technology (Guangzhou) have achieved a new benchmark for automated reasoning by introducing a benchmark 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, which focus on quantum algorithms and quantum information theory. All tasks underwent deterministic proof checking and semantic review, establishing a standardized evaluation process for AI agents in this complex field. This research demonstrates the move toward formal verification in quantum computing, a critical step toward building reliable systems, and measures for the first time an AI agent’s ability to construct machine-checkable proofs. The highest difficulty-weighted scores were 60.4 out of 100 for the Quantum Algorithms Benchmark and 59.6 out of 100 for the Quantum Information Benchmark. The results highlight recurring weaknesses in fields such as quantum simulation and entanglement theory, as well as important trade-offs between model power and efficiency.

Lean-QuantumAlg-Bench and Lean-QIT-Bench Benchmark Suite

The ability of artificial intelligence to rigorously test quantum computations has long been a theoretical goal. Recent research has demonstrated tangible progress in this capability with the introduction of two new benchmark suites: Lean-QuantumAlg-Bench and Lean-QIT-Bench. The suite includes a total of 76 tasks, 36 of which focus 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 results to verifying the correctness of the process, a critical step in building reliable quantum systems. Researchers evaluated four models: GPT-5.5, Kimi K3, DeepSeek V4-Pro, and MiniMax M3 under two conditions: baseline task completion and a library-augmented-deduction (LAD) configuration that provides access to validated domain libraries.

The highest difficulty-weighted score achieved was 60.4 out of 100 on the Quantum Algorithm Benchmark, with LAD consistently improving performance and providing evidence that the validated library can power domain-specific proof agents. Remarkably, the results pinpointed specific areas where current AI agents struggle, including quantum simulation, quantum learning, quantum information measurement, and entanglement theory. The monetary and time costs per score point also varied significantly between models, revealing important trade-offs between functionality and efficiency. The research team hopes that these benchmarks will establish a reproducible baseline for developing more capable and reliable proof agents and advancing quantum information science.

QudeLeap Research, a Shanghai-based artificial intelligence company, applies automatic theorem proving to the complex field of quantum computing. Each task in the benchmark is designed to be machine-checkable. This means that every step of the proof can be verified by computer. This is a key requirement for building reliable quantum systems. The research team evaluated four major language models: GPT-5.5. LAD provides AI with access to verified domain libraries and allows it to reference existing formally proven theorems.

This approach ensures that AI has a well-established, error-free foundation of knowledge, rather than being solely responsible for solving problems in isolation. The team introduced two new benchmarks: Lean-QuantumAlg-Bench and Lean-QIT-Bench. It includes 36 and 40 theorem completion tasks for quantum algorithms and quantum information theory, respectively. These benchmarks evaluate AI’s ability to complete proofs within the realm of quantum algorithms and quantum information theory. The evaluation focused on four major language models: GPT-5. The results showed that “LAD improved both scores and completion rates across all eight model-benchmark comparisons, by up to 15.9 points,” demonstrating the clear benefits of leveraging pre-validated information. The highest difficulty-weighted scores achieved were 60.4 out of 100 for the Quantum Algorithms Benchmark and 59.6 out of 100 for the Quantum Information Benchmark.

The assumption that automated theorem proving is easily applicable to all mathematical domains turns out to be inaccurate when tested against the complexities of quantum computing. The highest difficulty-weighted scores were 60.4 out of 100 for the Quantum Algorithms Benchmark and 59.6 out of 100 for the Quantum Information Benchmark, respectively, indicating that significant challenges remain.

Shanghai-based QudeLeap Research evaluates the capabilities of artificial intelligence in the demanding field of formal quantum theorem proving. These benchmarks don’t just assess whether AI can arrive at the correct answer, but whether it can construct proofs, a critical step in building truly trustworthy quantum systems. Although analysis of four leading models, GPT-5.5, showed that the highest difficulty-weighted scores achieved were 60.4 for the Quantum Algorithms Benchmark and 59.6 for the Quantum Information Benchmark, this study highlighted considerable variation in both monetary and real-time costs per score point across models, revealing important feature and efficiency trade-offs.