Quantum correlations in Deutsch-Jozsa algorithm via deterministic quantum computation with one qubit model

Abstract: Quantum correlations have been pointed out as the most likely source of the speed-up in quantum computation. Here we analyzed the presence of quantum correlations in the implementation of Deutsch-Jozsa algorithm running in the DQC1 and DQCp models of quantum computing. For some balanced functions, the qubits in DQC1 model are quantum correlated just in the intermediate steps of the algorithm for a given decomposition into one and two qubits gates. In the DQCp model the final state is strongly quantum correlated for some balanced functions, so that the pairwise entanglement between blocks scales with the system size. Although the Deutsch-Jozsa algorithm is efficiently implemented in both models of computation, the presence of quantum correlations is not a sufficient property for computational gain in this case, since the performance of the classical probabilistic algorithm is better than the quantum ones. The measurement of other qubits than the control one showed to be inefficient to turn the algorithm deterministic.