Graph Kernels Encoding Features of All Subgraphs by Quantum Superposition

Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to the best of our knowledge there is no existing graph kernel that uses some features explicitly extracted from all subgraphs to measure similarity. We propose a novel graph kernel that applies a quantum computer to measure the similarity obtained from all subgraphs by fully exploiting the power of quantum superposition to encode every subgraph into a feature of particular form. For the construction of the quantum kernel, we develop an efficient protocol that clears the index information of the subgraphs encoded in the quantum state. We also prove that the quantum computer requires less query complexity to construct the feature vector than the classical sampler used to approximate the same vector. A detailed numerical simulation of a bioinformatics problem is presented to demonstrate that, in many cases, the proposed quantum kernel achieves better classification accuracy than existing graph kernels.