Efficient block encoding of graph adjacency matrices

Develop efficient quantum circuit implementations for block-encoding sparse and structured graph adjacency matrices, including the normalized adjacency matrices used by Quantum Simplified Graph Convolutional Networks.

Background

The Quantum Simplified Graph Convolutional Network requires a block encoding of a normalized adjacency matrix or its powers. The paper notes that the potential complexity advantages of the quantum architecture depend on implementing this block encoding efficiently, while current methods remain incomplete for general sparse or structured matrices.

References

The efficient circuit implementation of the block-encoding protocol is still an open and active research area.

— Quantum Graph Convolutional Networks: Implementation and Trainability Analysis  (2609.19983 - Sein et al., 17 Sep 2026) in Section 4.1, Simplified Graph Convolutional Network