  Hybrid quantum-classical variational algorithms are one of the most
propitious implementations of quantum computing on near-term devices, offering
classical machine learning support to quantum scale solution spaces. However,
numerous studies have demonstrated that the rate at which this space grows in
qubit number could preclude learning in deep quantum circuits, a phenomenon
known as barren plateaus. In this work, we implicate random entanglement as the
source of barren plateaus and characterize them in terms of many-body
entanglement dynamics, detailing their formation as a function of system size,
circuit depth, and circuit connectivity. Using this comprehension of
entanglement, we propose and demonstrate a number of barren plateau
ameliorating techniques, including: initial partitioning of cost function and
non-cost function registers, meta-learning of low-entanglement circuit
initializations, selective inter-register interaction, entanglement
regularization, the addition of Langevin noise, and rotation into preferred
cost function eigenbases. We find that entanglement limiting, both automatic
and engineered, is a hallmark of high-accuracy training, and emphasize that as
learning is an iterative organization process while barren plateaus are a
consequence of randomization, they are not necessarily unavoidable or
inescapable. Our work forms both a theoretical characterization and a practical
toolbox; first defining barren plateaus in terms of random entanglement and
then employing this expertise to strategically combat them.
