Work

Mitigating Barren Plateaus via Domain Decomposition in Variational Quantum Algorithms for Nonlinear PDEs

Year: 2026

Type: preprint

Abstract: Barren plateaus present a major challenge in the training of variational quantum algorithms (VQAs), particularly for large-scale discretizations of nonlinear partial differential equations. In this work, we introduce a domain decomposition framework to mitigate barren plateaus by localizing the cost functional. Our strategy is based on partitioning the spatial domain into overlapping subdomains, each associated with a localized parameterized quantum circuit and measurement operator. Numerical results for the time-independent Gross-Pitaevskii equation show that the domain-decomposed formulation, allowing subdomain iterations to be interleaved with optimization iterations, exhibits improved solution accuracy and stable optimization compared to the global VQA formulation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.24523

Authors: Busaleh, Laila S., Kwon, Jeonghyeuk, Zang, Orlane, Hassan, Muhammad, Maday, Yvon

Institutions: Imam Abdulrahman Bin Faisal University, Kyung Hee University, Université de Picardie Jules Verne, Technical University of Munich, Centre National de la Recherche Scientifique, Université Paris Cité, Sorbonne Université, Laboratoire Jacques-Louis Lions, King Abdullah University of Science and Technology

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche, King Abdullah University of Science and Technology, Imam Abdulrahman Bin Faisal University

Awards: G1190173965, G2361257913, Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés, G7683707404

OpenAlex ID: W7140613352

Cites: 1

Cited by: 1

Related to: 10