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

Abstract: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.

Machine Learning (cs.LG); Computation and Language (cs.CL); Quantum Physics (quant-ph)

arXiv:2609.33192 [cs.LG]

(or arXiv:2609.33192v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.33192 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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