Fig. 7: Graphical proof of the state-dependent reconstruction of the central ququart in Fig. 5c. | Nature Communications

Fig. 7: Graphical proof of the state-dependent reconstruction of the central ququart in Fig. 5c.

From: Holographic codes from hyperinvariant tensor networks

Fig. 7

a The ququart Pauli operator X is represented by the logical operator \(\bar{X}=X{X}^{2}{X}^{3}I\). After pushing the Pauli operators acting on internal indices through the B tensors (green dots), which exchanges X ↔ Z, we apply the stabilizer \({(Z{Z}^{2}ZI)}^{3}={Z}^{3}{Z}^{2}{Z}^{3}I\) on the left side and \({\bar{Z}}^{3}={({Z}^{3}ZII)}^{3}=Z{Z}^{3}II\) on the right, resulting in a physical operator represented only on boundary region A. b Similarly, we can push \(\bar{Z}={Z}^{3}ZII\) to the left, apply \({\bar{X}}^{3}={(X{X}^{2}{X}^{3}I)}^{3}={X}^{3}{X}^{2}XI\), and again arrive at a physical operator on A.

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