Fig. 2: Schematic of effect of exponential concentration and shot noise on training and generalization performance. | Nature Communications

Fig. 2: Schematic of effect of exponential concentration and shot noise on training and generalization performance.

From: Exponential concentration in quantum kernel methods

Fig. 2: Schematic of effect of exponential concentration and shot noise on training and generalization performance.

For the unseen (test) data, the behavior depends on how kernel values are statistically estimated. In the case of the Loschmidt Echo test, the model predictions are zero with high probability. On using the SWAP test, the model predictions fluctuate around zero (due to shot noise). On the other hand, for the training data, the training labels are effectively hard-coded by the optimization process. (For simplicity we here consider the limit of no regularization).

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