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Similar to what is done classically to preserve the sparsity of the LU decomposition, it might be possible to limit the number of circuit in the Pauli decomposition by reordering the matrix columns/rows.
Explore the literature to see if that's been solved
Explore a few reordering schemes to see if that makes a difference
Similar to what is done classically to preserve the sparsity of the LU decomposition, it might be possible to limit the number of circuit in the Pauli decomposition by reordering the matrix columns/rows.