Data for Figure2

There are six sub floders, listed as Figure2a, Figure2b, Figure2c, Figure2d, Figure2e and Figure2f in the compressed file entitled 'Figure2.rar'.In floder Figure2a, the file named "20210812_30qubits_sample_B26d_allConfig_optPhase12MHz_Les_order2_tStop_1000_5922_6081_q8.mat" contains all the information (including 'datasets', 'fouriers_mat', 'freq', 'les', 'phis', 'sigmaxs', 'sigmays', 'times') needed for plotting squared FT (Fourier transformation) magnitudes |A₈|² when using Q_8,↑ as target qubitin the main text (Figure 2a). 'datasets' is the raw file names saved on our disk; 'fouriers_mat' demonstrates all the FT magnitudes |A₈|2 corresponding to all modulation phase <i>ϕ</i>; 'freq' shows the frequency of after FT; 'phis' is a list of different modulation phase <i>ϕ</i>; 'times' is the evolution time in unit 'ns'; 'sigmaxs' is the measured expected values of σ_<em>x</em>; 'sigmays' is the measured expected values of σ_y; 'les' donates response functions σ_{<em>x </em>}<i>+ i</i>σ_<em>y.</em>In floder Figure2b, there are 15 files, e.g., "20210812_30qubits_sample_B26d_allConfig_optPhase12MHz_Les_order2_tStop_1000_4122_4289_q1.mat", which contain all the information (including 'datasets', 'fouriers_mat', 'freq', 'les', 'phis', 'sigmaxs', 'sigmays', 'times') needed for plotting squared FT (Fourier transformation) magnitudes |A_j|² when using all 15 qubits as target qubitin the main text (Figure 2b). 'datasets' is the raw file names saved on our disk; 'fouriers_mat' demonstrates all the FT magnitudes |A_j|2 corresponding to all qubits for all modulation phase <i>ϕ</i>; 'freq' shows the frequency of after FT; 'phis' is a list of different modulation phase <i>ϕ</i>; 'times' is the evolution time in unit 'ns'; 'sigmaxs' is the measured expected values of σ_<em>x</em>; 'sigmays' is the measured expected values of σ_y; 'les' donates response functions σ_{<em>x </em>}<i>+ i</i>σ_<em>y.</em>Files in floder Figure2c are same as Figure2b, one can plot Figure 2c by summing the squared FT magnitudes over 15 qubits for <i>ϕ </i>= 2π/3.Folder Figure2d contains the numerical data, named as "4.7-0.012-15_1D_numerical_spec.mat" (including 'spec', 'phi'), needed for plotting the band structure of the 2D Chern insulator for b = 1/3 and Δ/2π = 12 MHz with 15 sites along the x-direction and periodic along the y direction. 'phis' is a list of different modulation phase <i>ϕ</i>; 'spec' is the numerical spectroscopy data for all qubits.Files in floder Figure2e are same as Figure2b and Figure2c, one can plot the experimentally measured data for <i>ϕ</i> varied from 0 to 2π.Folder Figure2f contains the simulation data, named as "-4.7-0.012-Allphi-[0.0 1000.0]Loschmidt_echo_simuq1q2q3q4q5q6q7q8q9q10q11q12q13q14q15.mat" (including 'data', 'freq' and 'phis'), needed for plotting the band structure of the 2D Chern insulator for b = 1/3 and Δ/2π = 12 MHz with 15 sites along the x-direction and periodic along the y direction. 'phis' is a list of different modulation phase <i>ϕ</i>; 'freq' is the frequency after FT; 'data' is the simulated spectroscopy data for all qubits.