Flat-band (de)localization emulated with a superconducting qubit array

Arrays of coupled superconducting qubits can be used as analog quantum simulators of tight-binding models with broadly adjustable model parameters. These simulators can therefore be used to study parameter regimes that are difficult to access or tune in natural materials, for example regimes with multiple competing energy scales. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the bandwidth of the system and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of universal scaling behavior.