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Concise Quantum Associative Memories with Nonlinear Search Algorithm | | J.-P. Tchapet Njafa
; S. G. Nana Engo
; P. Woafo
; | | Date: |
30 Nov 2012 | | Abstract: | 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, $pleq2^n$ the number of stored patterns, $qleq p$
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), $mleq q$ 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. | | Source: | arXiv, 1211.7187 | | Services: | Forum | Review | PDF | Favorites | |
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