A Survey of Methods for Mitigating Barren Plateaus for Parameterized Quantum Circuits

TL;DR

This survey reviews various methods to mitigate barren plateaus in parameterized quantum circuits, addressing a key obstacle in quantum algorithms by exploring their origins, mathematical frameworks, and techniques involving cost functions, entanglement, and initialization.

Contribution

It provides a comprehensive overview of the causes, mathematical formalism, and mitigation strategies for barren plateaus in quantum circuits, bridging classical and quantum perspectives.

Findings

Different genesis of barren plateaus identified

Mathematical formalism of barren plateau phenomena

Techniques involving cost functions, entanglement, and initialization discussed

Abstract

Barren Plateaus are a formidable challenge for hybrid quantum-classical algorithms that lead to flat plateaus in the loss function landscape making it difficult to take advantage of the expressive power of parameterized quantum circuits with gradient-based methods. Like in classical neural network models, parameterized quantum circuits suffer the same vanishing gradient issue due to large parameter spaces with non-convex landscapes. In this review, we present an overview of the different genesis for barren plateaus, mathematical formalisms of common themes around barren plateaus, and dives into gradients. The central objective is to provide a conceptual perspective between classical and quantum interpretations of vanishing gradients as well as dive into techniques involving cost functions, entanglement, and initialization strategies to mitigate barren plateaus. Addressing barren plateaus paves the way towards feasibility of many classically intractable applications for quantum simulation, optimization, chemistry, and quantum machine learning.