Quantum Simulation of Bose-Hubbard Phases with a Superconducting Transmon Lattice

The Hubbard model underpins the behavior of lattices of particles, and offers the ability to study transitions between insulating and conducting behavior in solid state systems. In the case where these particles have bosonic statistics, this becomes the Bose-Hubbard model which describes the natural time evolution of superconducting qudit lattices. Characterization of the many-body nature of a transmon lattice offers both a method of benchmarking larger lattices, for which performing qubit-by-qubit characterization is infeasible, and a platform for studying Hubbard physics in a highly controllable quantum system. In this talk, we will discuss progress towards performing multi-level analog quantum simulation of the Bose-Hubbard model using transmons. In order to have tunable interactions between lattice sites, we use additional transmon qubits as tunable couplers. This addition, as well as the operation of transmons beyond a two-level system, adds complexity to both control and modeling. We will provide an overview of our methods for circumventing this complexity and calibrating our 21-transmon system. Finally, we will discuss measurement of order parameters on this platform and what they elucidate about the phases in our system.