Locality and entanglement properties across the many-body spectrum in a 4x4 array of superconducting qubits (part 1): Theory*

The spectrum of a strongly interacting system can display properties of localization and entanglement that cannot be understood in terms of single-particle physics. In this work, we use a two-dimensional 4x4 array of superconducting transmon qubits as a quantum simulator to explore these properties in the strongly-interacting hard-core Bose-Hubbard model. Using the simultaneous control and readout capability of our system, we generate non-thermal, coherent excited states in the lattice, and probe its many-body spectrum and properties to observe the transition between local and delocalized many-body modes. In this part of the talk we discuss the theoretical background and experimental concept.