NMR tomography of the three-qubit Deutsch-Jozsa algorithm

The optimized version of the Deutsch-Jozsa algorithm proposed by Collins et al. was implemented using the three ${}^{19}\mathrm{F}$ nuclear spins of 2,3,4-trifluoroaniline as qubits. To emulate the behavior of pure quantum-mechanical states pseudopure states of the ensemble were prepared prior to execution of the algorithm. Full tomography of the density matrix was employed to obtain detailed information about initial, intermediate, and final states. Information, thus obtained, was applied to optimize the pulse sequences used. It is shown that substantial improvement of the fidelity of the preparation may be achieved by compensating the effects caused by the different relaxation behavior of the different substates of the density matrix. All manipulations of the quantum states were performed under the conditions of unresolved spin-spin interactions.