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

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arxiv 1907.13422 v2 pith:5BO2WTCL submitted 2019-07-31 cond-mat.str-el

Claudius Hubig This is my paper · ORCID
classification cond-mat.str-el
keywords compleximplementationtensorarxivautodifferentiationnetworkscalarsaddition
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Following the recent preprints arXiv:1903.09650 and arXiv:1906.04654 we comment on the feasibility of implementation of autodifferentiation in standard tensor network toolkits by briefly walking through the steps to do so. The total implementation effort comes down to fewer than 1000 lines of additional code. We furthermore summarise the current status when the method is applied to cases where the underlying scalars are complex, not real and the final result is a real-valued scalar. It is straightforward to generalise most operations (addition, tensor products and also the QR decomposition) to this case and after the initial submission of these notes, also the adjoint of the complex SVD has been found.

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  1. Automatic Differentiation for Complex Valued SVD

    math.NA 2019-09 conditional novelty 6.0 of 10

    A new backpropagation formula for complex-valued SVD is derived, with the key contribution a novel diagonal term absent from the real SVD case.

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