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 supervision gives a large, statistically significant gain in both model families and that verifier-filtered continuation adds a further repeated gain. The persistent gap between Clifford validity and state equivalence confirms that exact verification is necessary: a circuit can be syntactically and physically valid yet prepare the wrong quantum state.

翻译：暂无翻译