Quantum analytic descent

Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must a certain simple form in local region around any reference point, it can be efficiently approximated its entirety by classical model -- support these observations with rigorous, complexity-theoretic arguments. One classically analyse this approximate function order to directly `jump' (estimated) minimum, before determining more refined if necessary. We derive an optimal measurement strategy and generally prove asymptotic resource cost of corresponds only single gradient vector evaluation.