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Concise quantum associative memories with nonlinear search algorithm

The model of Quantum Associative Memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou et al. which uses the quantum matrix with the binary decision diagram put forth by David Rosenbaum and the Abrams and Lloyd's nonlinear search algorithm . Our model gives the possibility to retrieve one of the sought states in multi‐values retrieving scheme when a measurement is done on the first register in O(c−r) time complexity. It is better than Grover's algorithm and its modified form which need O(2nm) steps when they are used as the retrieval algorithm. n is the number of qubits of the first register and m the number of x values for which f(x)=1 . As the nonlinearity makes the system highly susceptible to the noise, an analysis of the influence of the single qubit noise channels on the Nonlinear Search Algorithm of our model of QAM shows a fidelity of about 0.7 whatever the number of qubits existing in the first register, thus demonstrating the robustness of our model.