  In a quantum processor, the device design and external controls together
contribute to the quality of the target quantum operations. As we continuously
seek better alternative qubit platforms, we explore the increasingly large
device and control design space. Thus, optimization becomes more and more
challenging. In this work, we demonstrate that the figure of merit reflecting a
design goal can be made differentiable with respect to the device and control
parameters. In addition, we can compute the gradient of the design objective
efficiently in a similar manner to the back-propagation algorithm and then
utilize the gradient to optimize the device and the control parameters jointly
and efficiently. This extends the scope of the quantum optimal control to
superconducting device design. We also demonstrate the viability of
gradient-based joint optimization over the device and control parameters
through a few examples.
