A quantum computer can be constructed from nuclear spins in a crystal latti
ce of a rare-earth monophosphide such as cerium-monophosphide (CeP), The 1/
2 spin of a P-31 nucleus can be used to represent a quantum bit ('qubit') w
ith a relatively long relaxation time. In a CeP crystal lattice, P-31 nucle
i are periodically situated in three dimensions at distances of about 6 Ang
strom. The application of a static magnetic field gradient in one direction
causes differences in the Zeeman frequencies of separate nuclei. This allo
ws thousands of distinct qubits to be individually addressed. Initializatio
ns of the qubits can be done efficiently by the Pound-Overhauser double res
onance effect on the nuclear spins and the antiferromagnetically ordered 4f
electron spins of cerium ions. Logic operations can be performed by simple
pulse sequences, and computational results after logic operations can be m
easured by the nuclear magnetic resonance of neighboring nuclei, or the ele
ctron resonance of neighboring 4f electrons of cerium ions.