Quantum-information processing using strongly dipolar coupled nuclear spins

Dipolar coupled homonuclear spins present challenging, yet useful systems for quantum-information processing. In such systems, the eigenbasis of the system Hamiltonian is the appropriate computational basis and coherent control can be achieved by specially designed strongly modulating pulses. In this paper we describe the first experimental implementation of the quantum algorithm for numerical gradient estimation by nuclear magnetic resonance, using the eigenbasis of a four spin system.