AVOIDING BARREN PLATEAUS VIA GAUSSIAN MIXTURE MODEL

Yun Shang

Keywords: Barren plateaus, Gaussian mixture model, Quantum circuits, Variational quantum algorithms

TL;DR: We propose a novel parameter initialization strategy based on Gaussian Mixture Models which can avoids the barren plateaus problem for hardware-efficient ansatz with arbitrary length and qubits and any given cost function.

Abstract:

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.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 4396