A quantum computer using nuclear spins in a crystal lattice requires a meth
od for addressing individual quantum bits. This identification can be achie
ved with a spatially varying magnetic field. Spins at different lattice sit
es can have distinguishable Zeeman frequencies allowing initialization, log
ic operations, and measurements to be performed through radio frequency (rf
) pulse techniques. Here, we present magnet designs that have gradients bet
ween 1 and 20 T/mu m, which are necessary to realize quantum computation wi
th particular crystals. PACS: 03.67.Lx; 76.60.Pc; 85.70.w.