  Variational quantum algorithms (VQAs), which classically optimize a
parametrized quantum circuit to solve a computational task, promise to advance
our understanding of quantum many-body systems and improve machine learning
algorithms using near-term quantum computers. Prominent challenges associated
with this family of quantum-classical hybrid algorithms are the control of
quantum entanglement and quantum gradients linked to their classical
optimization. Known as the barren plateau phenomenon, these quantum gradients
may rapidly vanish in the presence of volume-law entanglement growth, which
poses a serious obstacle to the practical utility of VQAs. Inspired by recent
studies of measurement-induced entanglement transition in random circuits, we
investigate the entanglement transition in variational quantum circuits endowed
with intermediate projective measurements. Considering the Hamiltonian
Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz
(HEA), we observe a measurement-induced entanglement transition from volume-law
to area-law with increasing measurement rate. Moreover, we provide evidence
that the transition belongs to the same universality class of random unitary
circuits. Importantly, the transition coincides with a "landscape transition"
from severe to mild/no barren plateaus in the classical optimization. Our work
paves an avenue for greatly improving the trainability of quantum circuits by
incorporating intermediate measurement protocols in currently available quantum
hardware.
