  Recent simulations have shown that a high-energy proton bunch can excite
strong plasma wakefields and accelerate a bunch of electrons to the energy
frontier in a single stage of acceleration. It therefore paves the way towards
a compact future collider design using the proton beams from existing
high-energy proton machines, e.g. Tevatron or the LHC. This paper addresses
some key issues in designing a compact electron-positron linear collider and an
electron-proton collider based on existing CERN accelerator infrastructure.
