Barren Plateaus in Variational Quantum Computing

TL;DR

Barren Plateaus significantly hinder the trainability of variational quantum algorithms by creating flat optimization landscapes, and understanding their causes is crucial for advancing quantum computing applications.

Contribution

This paper provides a comprehensive review of the current understanding of the Barren Plateau phenomenon in variational quantum computing.

Findings

Barren Plateaus cause exponential flatness in optimization landscapes.

Various factors like ansatz, initial state, and noise can induce BPs.

Research efforts focus on understanding and mitigating BPs to improve trainability.

Abstract

Variational quantum computing offers a flexible computational paradigm with applications in diverse areas. However, a key obstacle to realizing their potential is the Barren Plateau (BP) phenomenon. When a model exhibits a BP, its parameter optimization landscape becomes exponentially flat and featureless as the problem size increases. Importantly, all the moving pieces of an algorithm -- choices of ansatz, initial state, observable, loss function and hardware noise -- can lead to BPs when ill-suited. Due to the significant impact of BPs on trainability, researchers have dedicated considerable effort to develop theoretical and heuristic methods to understand and mitigate their effects. As a result, the study of BPs has become a thriving area of research, influencing and cross-fertilizing other fields such as quantum optimal control, tensor networks, and learning theory. This article provides a comprehensive review of the current understanding of the BP phenomenon.