VQNE: Variational Quantum Network Embedding with Application to Network Alignment

Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.