  A Higgs Factory is considered the highest priority next collider project by
the high-energy physics community. Very advanced designs based on
radio-frequency cavities exist, and variations on this approach are still being
developed. Recently, an option based on electron-bunch driven plasma wakefield
acceleration has also been proposed. In this article, we discuss a further
option based on proton-driven plasma wakefield acceleration. This option has
significant potential advantages due to the high energy of the plasma wakefield
driver, simplifying the plasma acceleration stage. Its success will depend on
further developments in producing compact high-energy proton bunches at a high
rate, which would also make possible a broad range of synergistic
particle-physics research.
