  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.
