Fig. 1: Experimental setup.

a Circuit diagram of the superconducting processor, consisting of ten transmon qubits, Q1–Q10, and nine couplers C1–C9, each of which is placed between every two nearest-neighbor qubits. b Schematic representation of the GAAH model with both the on-site and off-diagonal quasi-periodic modulations. The darkness of the double-headed arrows above the qubits indicates the variation of nearest-neighbor coupling strength Ji,i+1, and the sinusoidal curve below the qubits shows the on-site potential hj with modulation amplitude V. c Phase diagram of the GAAH model, divided into extended (E), localized (L), and critical (C) phases. The heatmap shows the inverse participation ratio (IPR) averaged over all eigenstates and 100 configurations of δ for system size L = 1000. d Experimental pulse sequences for observing localization properties of the GAAH model.