Quantum program generation demands mathematical precision incompatible with the statistical reasoning carried out by large language models (LLMs). Hallucinations are mathematically inevitable, instead of engineering problems solvable by scale. We argue that architectures prioritizing verification are necessary for quantum copilots and AI automation in domains governed by constraints. Our position rests on three points: verified training data enables models to internalize precise constraints as learned structure rather than statistical approximation; verification must constrain generation rather than filter outputs, as valid designs occupy exponentially shrinking subspaces; and domains where physical laws impose correctness criteria require verification embedded as architectural primitives. Early experiments show LLMs with verification knowledge achieve more than 79% accuracy on circuit optimization. Our positions are formulated as quantum computing and AI4Research community imperatives, calling for elevating verification from afterthought to architectural foundation in AI4Research.