  Analog quantum simulation offers a hardware-specific approach to studying
quantum dynamics, but mapping a model Hamiltonian onto the available device
parameters requires matching the hardware dynamics. We introduce a paradigm for
quantum Hamiltonian simulation that leverages digital decomposition techniques
and optimal control to perform analog simulation. We validate this approach by
constructing the optimal analog controls for a superconducting transmon device
to emulate the dynamics of an extended Bose-Hubbard model. We demonstrate the
role of control time, digital error, and pulse complexity, and we explore the
accuracy and robustness of these controls. We conclude by discussing the
opportunity for implementing this paradigm in near-term quantum devices.
