  The model of quantum associative memories (QAM) we propose here consists in
simplifying and generalizing that of Rigui Zhou \etal \cite{zhou2012} who uses
the quantum matrix with binary decision diagram and nonlinear search algorithm
in his model. It is worth noting that David Rosenbaum put forth the quantum
matrix with binary decision diagram \cite{Rosenbaum2010} and Abrams and Llyod
did the nonlinear algorithm. \cite{Abrams1998} Our model gives the possibility
to retrieve one of the sought states in multi-values retrieving scheme when a
measure on the first register is done. It is better than Grover's algorithm and
its modified form which need $\mathcal{O}(\sqrt{\frac{2^n} {m}})$ steps when
they are used as the retrieval algorithm. $n$ is the number of qubit of the
first register and $m$ the number of values $x$ for which $f(x)=1$. As the
nonlinearity makes the system highly susceptible to 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 present in the first register.
