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

TL;DR

This paper discusses the implementation of autodifferentiation in tensor network methods with complex scalars, showing it requires minimal additional code and can be generalized to complex cases.

Contribution

It demonstrates that autodifferentiation can be efficiently integrated into tensor network toolkits, including for complex scalar cases, with minimal implementation effort.

Findings

Implementation requires fewer than 1000 lines of code

Most tensor operations can be generalized to complex scalars

The adjoint of the complex SVD has been derived

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.