Growth and preservation of entanglement in a many-body localized system

We use programmable superconducting qubit quantum processors to provide a detailed survey of the many-body localized (MBL) phase for both 1D and 2D lattice geometries. We demonstrate disorder induced ergodicity breaking by studying the transport properties of excitations as the system evolves under a Bose-Hubbard Hamiltonian. Further, we use interferometric techniques to establish effective non-local interactions in our localized system. Beyond demonstrating these defining features of MBL we directly observe the slow growth of von Neumann entanglement entropy. From density matrix measurements we also compute the entanglement of formation and use this information to provide a spatial and temporal map of entanglement. Finally, starting with a maximally entangled Bell state embedded in an MBL environment, we measure the capability of an MBL system to preserve this quantum correlation and characterize its degradation in response to a remote excitation.