Fig. 2. Observation of diffusive transport.

a Experimental verification of preparing the states via the time evolution of participation entropy. Here, we chose Q_R = {Q_1,↑, Q_2,↑, …, Q_12,↑, Q_2,↓, Q_3,↓, …, Q_12,↓} with total 23 qubits. The inset of (a) shows the corresponding quantum circuit. The dotted horizontal line represents the participation entropy for Haar-random states, i.e., $S_{\mathrm{PE}}^{\mathrm{T}}\simeq 15.519$. b Experimental results of the autocorrelation function C_1,1(t) for the qubit ladder with L = 12, which are measured by performing the quantum circuit shown in Fig. 1c, d. Here, we consider the state generated from ${\widehat{U}}_R\left(t_R\right)$ with t_R = 200 ns, which is approximate to a Haar-random state. Markers are experimental data. The solid line is the numerical simulation of the correlation function C_1,1 at infinite temperature. The dashed line represents a power-law decay t^−1/2. Error bars represent the standard deviation.