  Variational quantum algorithms is one of the most representative algorithms
in quantum computing, which has a wide range of applications in quantum machine
learning, quantum simulation and other related fields. However, they face
challenges associated with the barren plateau phenomenon, especially when
dealing with large numbers of qubits, deep circuit layers, or global cost
functions, making them often untrainable. In this paper, we propose a novel
parameter initialization strategy based on Gaussian Mixture Models. We
rigorously prove that, the proposed initialization method consistently avoids
the barren plateaus problem for hardware-efficient ansatz with arbitrary length
and qubits and any given cost function. Specifically, we find that the gradient
norm lower bound provided by the proposed method is independent of the number
of qubits $N$ and increases with the circuit depth $L$. Our results strictly
highlight the significance of Gaussian Mixture model initialization strategies
in determining the trainability of quantum circuits, which provides valuable
guidance for future theoretical investigations and practical applications.
