Avoiding barren plateaus using classical shadows

TL;DR

This paper introduces a method using classical shadow tomography to detect and avoid barren plateaus in variational quantum algorithms, enhancing the efficiency of quantum optimization on near-term devices.

Contribution

It proposes a novel approach to identify and circumvent barren plateaus using entropy-based measures and shadow tomography, improving variational quantum algorithm optimization.

Findings

Shadow tomography efficiently quantifies local entropy.

Avoiding WBPs ensures larger gradients at initialization.

Gradient step size reduction helps during optimization.

Abstract

Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ans\"atze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBP) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows to avoid WBPs during the optimization process. This paves the way for efficient barren plateau free optimization on near-term devices.