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Note that BE contractor exploits sparsity in the tensors by reducing the number of indices to range over in cases where terms corresponding to most index combinations are zero. This arises very often in quantum circuits where a lot of tensors are diagonal.
Treewidth sets the lower bound for contraction complexity.
This should work fairly well on quantum circuits and SAT tensor network. For the other types, a lot depends on the tensors, but note that performing SVD on an edge does introduce a diagonal tensor that BE contractor can exploit.
Bucket elimination is a fast algorithm that works well for networks with small "tree width".
Positive examples include: TTN, quantum circuits, MPS, and MERA.
Negative examples include: SAT TensorNetwork.
Seeing how most of our work involves the former, we should implement this algorithm asap. @viathor has been working on a first version.
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