Explicit quantum implementation of nonlinear activation functions

Construct an explicit quantum implementation of nonlinear activation functions for quantum graph convolutional networks, in order to extend the implemented architectures beyond the activation-free linear models studied in the paper.

Background

The quantum graph convolutional construction requires nonlinear activation functions to reproduce the full multilayer graph-convolutional architecture. The paper discusses the Nonlinear Transformation of Complex Amplitudes technique and related proposals, but omits activation functions in the implemented models because their quantum realization introduces substantial computational cost.

References

In our case, an explicit quantum implementation of nonlinear activation functions is left for future work.

— Quantum Graph Convolutional Networks: Implementation and Trainability Analysis  (2609.19983 - Sein et al., 17 Sep 2026) in Section 4, Layer-wise transformation