Observation of exact quantum critical states

Anderson localization describes the suppression of wave transport in disordered media. In quantum systems, it gives rise to extended, localized and critical eigenstates, with the latter showing properties between the other two. Characterizing critical states is challenging because it requires analysis in the thermodynamic limit or a universal mechanism that identifies them. Here we experimentally realize critical states in a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials using a system of superconducting qubits. By measuring time-evolving observables, we identify coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which characterize the critical states. We map the transition from localized to critical behaviour and show that critical states persist until strong long-range couplings remove the quasiperiodic zeros. Finally, we resolve an energy-dependent transition between localized and critical states, revealing anomalous mobility edges. Anderson localization allows critical states between localized and extended regimes, but observing them is difficult. Now critical states are experimentally realized in a superconducting-qubit simulator implementing a quasiperiodic lattice model.