  Variational quantum circuits have been widely employed in quantum simulation
and quantum machine learning in recent years. However, quantum circuits with
random structures have poor trainability due to the exponentially vanishing
gradient with respect to the circuit depth and the qubit number. This result
leads to a general standpoint that deep quantum circuits would not be feasible
for practical tasks. In this work, we propose an initialization strategy with
theoretical guarantees for the vanishing gradient problem in general deep
quantum circuits. Specifically, we prove that under proper Gaussian initialized
parameters, the norm of the gradient decays at most polynomially when the qubit
number and the circuit depth increase. Our theoretical results hold for both
the local and the global observable cases, where the latter was believed to
have vanishing gradients even for very shallow circuits. Experimental results
verify our theoretical findings in the quantum simulation and quantum
chemistry.
