Tailored quantum simulation with analog control optimization

Analog quantum simulation offers a highly efficient, hardware-specific approach to studying quantum dynamics in which external control of a device Hamiltonian simulates the dynamics of a target system. However, identifying the controls necessary to simulate a given target system varies with the physics of the device and goal of the simulations. We apply quantum optimal control theory to compile hardware-level controls that drive quantum dynamics of the Bose-Hubbard system within a model circuit-QED Hamiltonian. Our approach uses the GOAT algorithm in the presence of practical control constraints including bandwidth, geometry, and multi-level Hamiltonians to construct optimal controls that simulate time-dependent dynamics of the target system. We evaluate the accuracy and robustness of these controls using a series of numerical simulations.