Fig. 4: The 3D preimage contours which show topological links for the Hopf insulator with h = 0.5. | Nature Communications

Fig. 4: The 3D preimage contours which show topological links for the Hopf insulator with h = 0.5.

From: Experimental demonstration of adversarial examples in learning topological phases

Fig. 4: The 3D preimage contours which show topological links for the Hopf insulator with h = 0.5.

a Topological link, obtained from two spin states with Bloch sphere representations \({{{{{{{\bf{S}}}}}}}}=(-1,-1,0)/\sqrt{2}\) (blue) and \((0,1,-1)/\sqrt{2}\) (orange), for a legitimate sample in the stereographic coordinates of \({{\mathbb{S}}}^{3}\), between two spin states on the Bloch sphere. Solid lines are curves from numerically calculated directions Sth and the stars are experimentally measured spin orientations Sexp. The deviation ∣Sexp − Sth∣≤0.25(0.35) for the blue (orange) curve. b The topological link for an adversarial example with deviation ∣Sexp − Sth∣≤0.25 for blue and orange curves.

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