Variational quantum algorithm for node embedding.

Area of Science:

• Quantum Computing
• Machine Learning
• Graph Theory

Background:

• Quantum machine learning (QML) shows promise but often neglects initial state preparation complexity, hindering end-to-end application.
• Node embedding is crucial for representing graph structures in machine learning tasks.

Purpose of the Study:

• To propose an end-to-end quantum algorithm for node embedding.
• To encode topological graph structures into quantum embedding vectors.
• To ensure the quantum embedding state preserves quantum advantage for downstream QML tasks.

Main Methods:

• Developed a quantum algorithm utilizing $$ qubits to represent information for $$ nodes.
• Employed a parameterized quantum circuit of $$ depth for efficient quantum state generation.
• Investigated measurement complexity for parameter training and extended the algorithm for high-order neighborhood information.

Main Results:

• The proposed algorithm generates quantum embedding states usable as input for other QML algorithms.
• The quantum embedding state functions as an efficient quantum database due to its parameterized circuit.
• Experimental demonstration on a nuclear magnetic resonance quantum processor validated the algorithm's efficacy on a graph model.

Conclusions:

• The quantum node embedding algorithm offers an end-to-end solution, overcoming limitations of previous QML approaches.
• The efficient quantum database capability and preserved quantum advantage make it suitable for advanced QML applications.
• Successful experimental validation confirms the practical applicability of quantum node embedding.