We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels' ability to separate points, i.e., their "resolution," under the constraint of finite, fixed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature.

Department of Physics The University of Michigan Ann Arbor MI 48109 1040 USA

Faculty of Physics Adam Mickiewicz University 61 614 Poznan Poland

RCPTM Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences 17 listopadu 12 771 46 Olomouc Czech Republic

Theoretical Quantum Physics Laboratory RIKEN Cluster for Pioneering Research Wako shi 351 0198 Japan

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