Evaluation of a Quantum Kernel for Graph Classification on Neutral Atoms Quantum Computer

This work merges two cutting-edge fields of study, Machine Learning and Quantum Computing, combined for solving the graph classification problem. Machine learning is the study of models and algorithms that “learn” through experience to solve problems, mimicking human intelligence. Quantum Computing is an emerging field of study, that overturns the classical information and computation paradigm by incorporating Quantum Mechanics principles. Both technologies have the potential to change the world, and their future development is still unpredictable. However, we are currently in the Noisy Intermediate-Scale Quantum era(NISQ), with quantum computers not able to perform error correction, and a medium number of quantum bits, not enough for quantum advantage. In this context, the hybrid quantum-classical algorithms have emerged, with the possibility of classical post-processing of the quantum results. An example are Variational Quantum Eigensolver(VQE), Quantum Machine Learning algorithm(QML), and Quantum Approximate Optimization Algorithm(QAOA). Under technology side, Neutral Atoms Quantum Computer has emerged as a technology that allows to simulation of Hamiltonians that incorporate problem specifications in their structure. In the proposed setting, the evolution of a quantum state can be an interesting source of information for a graph, thanks to the possibility of building Hamiltonians that reflect graph topologies and properties. After the time evolution, a proper observable is measured, and a probability distribution is obtained. By computing a distance between the distribution, a graph kernel can be defined and used to make classification(using a Support Vector Machine). The method is benchmarked against a classical graph kernel, using different metrics, in particular F1, more affordable in case of class imbalance. The Quantum Kernel slightly outperforms the classical one. Finally, the method is analyzed in the case of real, noisy quantum hardware, in the case of a dataset that cannot be emulated on a classical machine. Also in these settings, the methods show robustness, reaching better results than the emulated one.