  Superconducting radio-frequency (SRF) cavities coupled to transmon circuits
have proven to be a promising platform for building high-coherence quantum
information processors. An essential aspect of this realization involves
designing high quality factor three-dimensional superconducting cavities to
extend the lifetime of quantum systems. To increase the computational
capability of this architecture, we are exploring a multimode approach. This
paper presents the design optimization process of a multi-cell SRF cavity to
perform quantum computation based on an existing design developed in the scope
of particle accelerator technology. We perform parametric electromagnetic
simulations to evaluate and optimize the design. In particular, we focus on the
analysis of the interaction between a nonlinear superconducting circuit known
as the transmon and the cavity. This parametric design optimization is
structured to serve as a blueprint for future studies on similar systems.
