Orlane Zang

Laila S. Busaleh, Jeonghyeuk Kwon, Orlane Zang et al.

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.

Orlane Zang, Grégoire Barrué, Tony Quertier

Data encoding plays a fundamental and distinctive role in Quantum Machine Learning (QML). While classical approaches process data directly as vectors, QML may require transforming classical data into quantum states through encoding circuits, known as quantum feature maps or quantum embeddings. This step leverages the inherently high-dimensional and non-linear nature of Hilbert space, enabling more efficient data separation in complex feature spaces that may be inaccessible to classical methods. This encoding part significantly affects the performance of the QML model, so it is important to choose the right encoding method for the dataset to be encoded. However, this choice is generally arbitrary, since there is no "universal" rule for knowing which encoding to choose based on a specific set of data. There are currently a variety of encoding methods using different quantum logic gates. We studied the most commonly used types of encoding methods and benchmarked them using different datasets.