The Role of Data in Projected Quantum Kernels: The Higgs Boson Discrimination

Abstract: The development of quantum machine learning is bridging the way to fault tolerant quantum computation by providing algorithms running on the current noisy intermediate scale quantum devices.However, it is difficult to find use-cases where quantum computers exceed their classical counterpart.The high energy physics community is experiencing a rapid growth in the amount of data physicists need to collect, store, and analyze within the more complex experiments are being conceived.Our work approaches the study of a particle physics event involving the Higgs boson from a quantum machine learning perspective.We compare quantum support vector machine with the best classical kernel method grounding our study in a new theoretical framework based on metrics observing at three different aspects: the geometry between the classical and quantum learning spaces, the dimensionality of the feature space, and the complexity of the ML models.We exploit these metrics as a compass in the parameter space because of their predictive power. Hence, we can exclude those areas where we do not expect any advantage in using quantum models and guide our study through the best parameter configurations.Indeed, how to select the number of qubits in a quantum circuits and the number of datapoints in a dataset were so far left to trial and error attempts.We observe, in a vast parameter region, that the used classical rbf kernel model overtakes the performances of the devised quantum kernels.We include in this study the projected quantum kernel - a kernel able to reduce the expressivity of the traditional fidelity quantum kernel by projecting its quantum state back to an approximate classical representation through the measurement of local quantum systems.The Higgs dataset has been proved to be low dimensional in the quantum feature space meaning that the quantum encoding selected is not enough expressive for the dataset under study.Nonetheless, the optimization of the parameters on all the kernels proposed, classical and quantum, revealed a quantum advantage for the projected kernel which well classify the Higgs boson events and surpass the classical ML model.