Nuclear magnetic resonance implementation of the Deutsch–Jozsa algorithm using different initial states

Abstract

The Deutsch–Jozsa algorithm distinguishes constant functions from balanced functions with a single evaluation. In the first part of the work, we present simulations of the nuclear magnetic resonance application of the Deutsch–Jozsa algorithm to a 3-spin system for all possible balanced functions. Three different kinds of initial states are considered: a thermal state, a pseudopure state, and a pair (difference) of pseudopure states. Then, simulations of several balanced functions and the two constant functions of a 5-spin system are described. Finally, corresponding experimental spectra obtained by using a 16-frequency pulse to create an input equivalent to either a constant function or a balanced function are presented, and the results are compared with those obtained from computer simulations.