AG-CoT: Verified Algorithmic Traces for LLM Program Synthesis on Clifford Circuits

Lu Wei, Yufeng Wang, Chenfeng Cao, Lu Pang, Haibin Ling

Scientific code generation can produce executable programs that fail to compute the intended scientific object. We study this problem in language-model synthesis of Clifford circuits, which prepare the stabilizer states used in quantum error correction and admit exact classical verification. In our target-conditioned framework, each target is given as compact signed stabilizer generators, and an exact verifier checks the generated OpenQASM circuits. We supervise models with Aaronson-Gottesman chain-of-thought (AG-CoT) traces checked by the verifier, and continue training on model generations that the verifier accepts. Across two independently trained model families (3B and 7B), AG-CoT supervision multiplies greedy-decode state-equivalence accuracy by four to six times over circuit-only baselines, and verifier-filtered continuation training adds a further consistent gain atop both. A complementary 32B study shows that supervised models achieve near-perfect syntax and Clifford validity while the strongest direct model reaches 6.14% state equivalence per target, rising to over 10% under verifier-guided selection with multiple candidates. These results show that algorithmic trace…