Quantum Analytic Descent

TL;DR

Quantum Analytic Descent offers a method to efficiently optimize variational quantum algorithms by classically approximating the local energy landscape, enabling direct jumps to estimated minima with minimal quantum resource use.

Contribution

The paper introduces Analytic Descent, a novel approach that uses classical models to approximate quantum energy landscapes for efficient optimization.

Findings

Supports the approach with rigorous complexity-theoretic arguments

Derives an optimal measurement strategy for the method

Shows the resource cost is equivalent to a single gradient evaluation

Abstract

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 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 analyse this approximate function in order 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.