  A proposal for a magnetic quantum processor that consists of individual
molecular spins coupled to superconducting coplanar resonators and transmission
lines is carefully examined. We derive a simple magnetic quantum
electrodynamics Hamiltonian to describe the underlying physics. It is shown
that these hybrid devices can perform arbitrary operations on each spin qubit
and induce tunable interactions between any pair of them. The combination of
these two operations ensures that the processor can perform universal quantum
computations. The feasibility of this proposal is critically discussed using
the results of realistic calculations, based on parameters of existing devices
and molecular qubits. These results show that the proposal is feasible,
provided that molecules with sufficiently long coherence times can be developed
and accurately integrated into specific areas of the device. This architecture
has an enormous potential for scaling up quantum computation thanks to the
microscopic nature of the individual constituents, the molecules, and the
possibility of using their internal spin degrees of freedom.
