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Following the recent preprints arXiv:1903.09650 and arXiv:1906.04654 wecomment on the feasibility of implementation of autodifferentiation in standardtensor network toolkits by briefly walking through the steps to do so. Thetotal implementation effort comes down to fewer than 1000 lines of additionalcode. We furthermore summarise the current status when the method is applied tocases where the underlying scalars are complex, not real and the final resultis a real-valued scalar. It is straightforward to generalise most operations(addition, tensor products and also the QR decomposition) to this case andafter the initial submission of these notes, also the adjoint of the complexSVD has been found.

Use and implementation of autodifferentiation in tensor network methods with complex scalars