NMR Quantum Logic Gates for Homonuclear Spin Systems

If NMR systems are to be used as practical quantum computers, the number of coupled spins will need to be so large that it is not feasible to rely on purely heteronuclear spin systems. The implementation of a quantum logic gate imposes certain constraints on the motion of those spins not directly involved in that gate, the so-called “spectator” spins; they must be returned to their initial states at the end of the sequence. As a result, a homonuclear spin system where there is appreciable coupling between every pair of spins would seem to require a refocusing scheme that doubles in complexity and duration for every additional spectator spin. Fortunately, for the more realistic practical case where long-range spin-spin couplings can be neglected, simpler refocusing schemes can be devised where the overall duration of the sequence remains constant and the number of soft pulses increases only linearly with the number of spectator spins. These ideas are tested experimentally on a six qubit system: the six coupled protons of inosine.