Variational quantum algorithms are among the most prominent methods in quantum computing,with applications in quantum machine learning, quantum simulation, and related fields. However,as the number of qubits grows, these algorithms often encounter the barren-plateau phenomenon,which severely limits their scalability. In this work, we introduce a novel parameter-initializationstrategy based on Gaussian mixture models. We rigorously prove that for a hardware-efficientansatz initialized in the |0⟩⊗N state, our scheme avoids barren plateaus regardless of circuit depth,qubit count, or choice of cost function. Specifically, the lower bound on the initial gradient normprovided by our method remains independent of the number of qubits Building on thisfoundation, we validate our theoretical results through numerical experiments, includingvariational ground-state searches for Hamiltonians, to demonstrate the practical effectiveness ofour approach. Our findings highlight the critical role of Gaussian mixture model-basedinitialization in enhancing the trainability of quantum circuits and offer valuable guidance forfuture theoretical and experimental advances in quantum machine learning.

Publication:

New J. Phys. 27 (2025) 104501

http://dx.doi.org/10.1088/1367-2630/ae0823

Author:

Xiao Shi

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’sRepublic of China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

Yun Shang

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’sRepublic of China

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing,100190, People’s Republic of China

Author to whom any correspondence should be addressed

E-mail: shangyun@amss.ac.cn