Mitigating Barren Plateaus via Domain Decomposition in Variational Quantum Algorithms for Nonlinear PDEs
This addresses a major challenge in quantum computing for scientific simulations, but it is incremental as it builds on existing VQA methods.
The paper tackled the problem of barren plateaus in training variational quantum algorithms for nonlinear PDEs by introducing a domain decomposition framework, resulting in improved solution accuracy and stable optimization for the Gross-Pitaevskii equation.
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.