Quantum analytic descent

Abstract

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