Simulating quantum transport and localization using a superconducting quantum processor*

Quantum transport plays an important role in electron and phonon conduction in interacting condensed matter systems in the presence of inelastic scattering. Using an array of superconducting qubits, we emulate a 1-dimesional and 2-dimentsional tight-binding lattice in various parameter regimes. We first observe ballistic transport in quantum random walks on a lattice with uniform site energies. Next, we study the absence of diffusion in a disordered lattice due to Anderson localization and experimentally extract the scaling of the inverse participation ratio as a proxy for the degree of localization. Finally, we simulate the tight-binding model in the presence of a dc-field, leading to Wannier-Stark localization and Bloch oscillations.