Optimization of matrix products for block-sparse Hamiltonians

The following plot shows the number of matrix product per order of \tilde{H}^{AA} for input Hamiltonians with a different sparsity structure. The red curve corresponds to an input Hamiltonian with a single off-diagonal perturbation, which makes every odd order off \tilde{H}^{AA}=0. Still, the plot shows that odd orders are exactly as costly as even orders, suggesting that we could improve how we evaluate matrix products.