Graph kernels encoding features of all subgraphs by quantum superposition

TL;DR

This paper introduces a novel quantum graph kernel that encodes all subgraphs simultaneously using quantum superposition, leading to improved classification accuracy in bioinformatics applications.

Contribution

It develops a quantum-based graph kernel that considers all subgraphs at once and demonstrates its efficiency and superior performance over classical kernels.

Findings

Quantum kernel requires fewer queries than classical methods.

Proposed kernel achieves better classification accuracy in bioinformatics.

Efficient protocol removes subgraph index information from quantum states.

Abstract

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 considers all subgraphs to measure similarity. We propose a novel graph kernel that applies a quantum computer to measure the graph similarity taking all subgraphs into account by fully exploiting the power of quantum superposition to encode every subgraph into a feature. For the construction of the quantum kernel, we develop an efficient protocol that removes the index information of 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.