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Information Sciences

Quantum associative memory with distributed queries

Alexandr Alexandrovich Ezhov, A.V. Nifanova, Dan A. Ventura

Published Oct 1, 2000• 53 citations
Publisher
DOI
10.1016/s0020-0255(00)00057-8

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New set of maximally entangled states (Singh-Rajput MES), constituting orthonormal eigen bases, has been revisited and its superiority and suitability in the processes of quantum associative memory (QuAM) have been demonstrated. Using these MES as memory states in the evolutionary process of pattern storage, the suitability and superiority of these MES over Bell’s MES have been demonstrated and it has been shown that, under the operations of all the possible memorization operators for a two-qubit system, the first two states of Singh-Rajput MES are useful for storing the pattern ǀ11 > and the last two of these MES are useful in storing the pattern ǀ10 > while Bell’s MES are not much suitable as memory states in a valid memorization process. Recall operations of quantum associate memory (QuAM) have been conducted through evolutionary process in terms of unitary operators by separately choosing Singh-Rajput MES and Bell’s MES as memory states for various queries and it has been shown that in each case the choices of Singh-Rajput MES as valid memory states are much more suitable than those of Bell’s MES.
Quantum associative memories are derived from the Hopfleld memory model under the assumption that the elements of the correlation weight matrix W are stochastic variables. The probability density function of each weight is given as a solution of Schrodinger's diffusion equation. Spectral analysis of quantum associative memories follows previous studies on the wavelets' energy spectrum. Spectral analysis shows that (i) the basis functions of the stochastic weights express the distribution of energy with respect to the weights' values, (ii) the stochastic weights satisfy the principle of uncertainty.