Barren plateaus in variational quantum computing

Variational quantum computing offers a flexible computational approach with a broad range of applications. 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 if they are ill-suited. As BPs strongly impact 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 exchanging ideas with other fields such as quantum optimal control, tensor networks and learning theory. This article provides a review of the current understanding of the BP phenomenon.