We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of t
heir strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper Pair Box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.
