Fig. 3: Measured stabilizer values and topological entanglement entropy for a Floquet eigenstate.
From: Long-lived topological time-crystalline order on a quantum processor
a Measured expectation values of plaquette operators {Ap} and {Bq} for the Floquet eigenstate \(\vert {E}_{+}^{(0)}\rangle\) are shown in the left panel. Expectation values of string operators \(\{{X}_{{L}_{i}},{Z}_{{L}_{i}}\}\) are plotted in the right panel with solid (hollow) bars representing experimental (theoretical) results. b Measuring topological entanglement entropy (TOPO, Stopo) on four- and six-qubit subsystems. The division of subsystems and corresponding experimental results are shown in the upper and lower panels, respectively. Blue squares (red circles) represent entanglement entropy (region fidelities F(ρi)). The topological entanglement entropy is extracted from the measured von Neumann entropy for the regions Si. The error bars, obtained by repeated measurements, are very small and not shown here. The black rhombus markers are theoretical predictions for Stopo and Si, which agree well with the corresponding experimental results.
