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We compare pseudopure state ensemble implementations, quantified by theirinitial polarization and ensemble size, of Grover's search algorithm toprobabilistic classical sequential search algorithms in terms of their successand failure probabilities. We propose a criterion for quantifying the resourcesused by the ensemble implementation via the aggregate number of oracleinvocations across the entire ensemble and use this as a basis for comparisonwith classical search algorithms. We determine bounds for a criticalpolarization such that the ensemble algorithm succeeds with a greaterprobability than the probabilistic classical sequential search. Our resultsindicate that the critical polarization scales as N^(-1/4) where N is thedatabase size and that for typical room temperature solution state NMR, thepolarization is such that the ensemble implementation of Grover's algorithmwould be advantageous for N > 10^22

Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches