J. -P. Tchapet Njafa, S. G. Nana Engo, P. Woafo
The model of quantum associative memories proposed here is quietly similar to that of Rigui Zhou et al based on quantum matrix with binary decision diagram and nonlinear search algorithm put forth by David Rosenbaum, and Abrams and Llyod respectively. Our model, that simplify and generalize that of Ref. [1], gives the possibility to retrieve one of desired states in multi-values retrieving, when a measure on the first register is done. If $n$ is the number of qubit of first register, $p\leq2^n$ the number of stored patterns, $q\leq p$ the number of stored patterns if the value of $t$ are known (i.e., $t$ qubits have been measure or are already be disentangled to others, or the oracle acts on a subspace of $(n-t)$ qubits), $m\leq q$ the number of values $x$ for which $f(x)=1$, $c=\mathtt{ceil}(\log_2 {q})$ the least integer greater or equal to $\log_2{q}$, and $r=\mathtt{int} (\log_2 {m})$ the integer part of $\log_2{m}$, then the time complexity of our algorithm is $\mathcal{O}(c-r)$. It is better than Grover's algorithm and the modified forms which need $\mathcal{O}(\sqrt{\frac{2^n} {m}})$ steps, when they are used as the retrieval algorithm.
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http://arxiv.org/abs/1211.7187
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