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Is there a way to view the even/odd extensions for Neumann/dirichlet boundary conditions as cosine/sine transformations respectively as opposed to the Fourier transform representation used for periodic boundary conditions?
You may be interested in results from quantum algorithms on the quantum approximate optimization algorithm, which similar to the product you wrote, is a product of "driving (ZZ)" and "mixing ( X)" terms. The difficulty in this problem is determining the phase angles. arxiv.org/abs/2106.15645
