Quantum Computation in a One-Dimensional Crystal Lattice with Nuclear Magnetic Resonance Force Microscopy

A proposal for a quantum computer using a nuclear spin network in a crystal lattice is presented. Magnetic resonance force microscopy is used for readout of an ensemble of nuclear spins. Two systems are proposed: One uses fluorine nuclear spins in a natural solid crystal of fluorapatite [Ca₅F(PO₄)₃], which approximates a one-dimensional structure, while the other uses isotope engineering to construct a more idealized one-dimensional system of ²⁹Si (spin-1/2) nuclear spins in a ²⁸Si (spin-0) matrix.