Properties of multiqubit variational quantum states representing weighted graphs and their computing with quantum programming

This is a pure theoretical physics paper (arXiv preprint, 5 days old, 0 adoption signals) combining known quantum computing primitives (variational circuits, RZZ entanglement, graph representations) in a narrowly scoped mathematical analysis. The contribution is a closed-form derivation of entanglement properties for a specific circuit ansatz—intellectually sound but extremely specialized. No code repository exists, no users, no reproducible artifact. The novelty lies in the mathematical analysis connecting graph structure to entanglement geometry for this particular circuit class, but this is a niche theoretical result. Frontier labs have no incentive to productize this: it's not a practical algorithm, not a scalable architecture, and not a performance breakthrough. The result is academic rather than engineering-focused. Even for quantum software development, this doesn't provide a reusable component—it's a mathematical proof about properties of a specific ansatz. Defensibility is minimal: the insight, once published, is freely available and reproducible by anyone with quantum computing knowledge. Low frontier risk because this addresses pure theory (quantum physics research), not a productizable tool or platform capability.