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

Abstract

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.

11 pages, 1 figure; include reference to recently found adjoint of SVD

References in corpus (3)

• Differentiable Programming Tensor Networks
• Auto-Differentiating Linear Algebra
• Automatic Differentiation for Complex Valued SVD

Cited by in corpus (4)

• Automatic Differentiable Monte Carlo: Theory and Application
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• QR and LQ Decomposition Matrix Backpropagation Algorithms for Square, Wide, and Deep -- Real or Complex -- Matrices and Their Software Implementation
• Differentiate Everything with a Reversible Embeded Domain-Specific Language