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Figure 6 | EPJ Quantum Technology

Figure 6

From: Fock state-enhanced expressivity of quantum machine learning models

Figure 6

Binary classification of the moon dataset of Fig. 4 using the two mode linear quantum photonic circuit of Fig. 2(c) which implements a quantum-enhanced random kitchen sink with 10 input photons, base (single input photon) resolution \(\gamma = 1\), regularization parameter \(\alpha = 0.2\), and random Fourier feature dimensions \(R = 1, 10, 100\). The circuit with 10 input photons can probe 10 different kernel resolutions simultaneously, i.e: \(\sigma = \{1/n | 1 \leq n \leq 10\}\); six resolutions are illustrated here. When \(R = 1\) the feature vectors reduce to a cosine-like kernel whose frequency increases with the number of input photons and k. The classification results improve with R because the kernels are better approximated by random Fourier features of higher dimension with \(\sigma = 0.25\) and \(1/7\) (\(R = 100\)), which are the optimal resolutions for the moon dataset. For a given R, the decision boundaries for higher resolutions are noisier because the corresponding approximated kernel has a narrower peak, thus meaningful predictions cannot be made for points that are far (relative to the kernel resolution) from the training set

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