Barren plateaus in variational quantum computing

Abstract

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. Barren plateaus are widely considered as one of the main limitations for variational quantum algorithms. This Review summarizes the latest understandings of barren plateaus, indicating its causes, architecture that will suffer from this phenomenon, and discusses strategies that can — and cannot — avoid it. Variational quantum algorithms (VQAs) — this hybrid computational approach aims at training a quantum learning model (usually a parametrized quantum circuit) to solve a given task. The parameters in the model are trained by minimizing a loss function that encodes the degree to which the problem has been solved. Barren plateaus — a phenomenon in which the gradients of the loss landscape of VQAs get exponentially suppressed. Currently, this issue is understood as a form of curse of dimensionality arising from operating in an unstructured manner in an exponentially large Hilbert space. Trainability — in the context of VQAs, trainability refers to the ability to optimize parameters of a model and minimize the loss function. Barren plateaus are one of the main barriers to the trainability of VQAs. Variational quantum algorithms (VQAs) — this hybrid computational approach aims at training a quantum learning model (usually a parametrized quantum circuit) to solve a given task. The parameters in the model are trained by minimizing a loss function that encodes the degree to which the problem has been solved. Barren plateaus — a phenomenon in which the gradients of the loss landscape of VQAs get exponentially suppressed. Currently, this issue is understood as a form of curse of dimensionality arising from operating in an unstructured manner in an exponentially large Hilbert space. Trainability — in the context of VQAs, trainability refers to the ability to optimize parameters of a model and minimize the loss function. Barren plateaus are one of the main barriers to the trainability of VQAs.