Experimental demonstration of the Deutsch-Jozsa algorithm in homonuclear multispin systems

Despite early experimental tests of the Deutsch-Jozsa (DJ) algorithm, there have been only a very few nontrivial balanced functions tested for register number $n>3$. In this paper, we experimentally demonstrate the DJ algorithm in four- and five-qubit homonuclear spin systems by the nuclear-magnetic-resonance technique, by which we encode the one function evaluation into a long shaped pulse with the application of the gradient ascent algorithm. Our work, dramatically reducing the accumulated errors due to gate imperfections and relaxation, demonstrates a better implementation of the DJ algorithm.