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Certification cost of quantum models: measurement correlation, not parameter count

arXiv · AI, language, vision and robotics · article · Sep 13, 2026 · UTC

Reporting the Fisher geometry of a trained variational quantum model is routine; quoting the shot budget that would establish it is not. Certifying an empirical Fisher matrix to relative Frobenius error $\varepsilon$ under coordinate-wise parameter shift costs $Θ(B p^{2} V/(\varepsilon^{2} G))$ circuit executions, where $V$ is the measured readout variance and $G$ the measured squared gradient norm, with uniform allocation optimal in that class. One constant reproduces the cost of two circuit families whose exponents differ by a full power of $p$. The exponent is an identity in how $nV$ and $n

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