Classification of patterns representing Apples and Oranges in three-qubit system

The study of the classification of Apples and Oranges in a warehouse has been undertaken in a three-qubit system using the method of repeated iterations in Grover’s algorithm and Ventura’s algorithm separately. Operator describing an inversion about average has been constructed as a square matrix of order eight, the phase inversion operators and corresponding iteration operators for patterns separately representing Apples and Oranges have been derived, and various possible superpositions as the choice for search states for the classification of these patterns have been obtained for starting states consisting of two patterns and a single pattern, respectively. It has been demonstrated that on the second iteration of the exclusion superposition by the corresponding iteration operators, the patterns Apples and Oranges, respectively, are most suitably classified using the Grover’s algorithm. The probabilities of classifications of Apples have also been calculated by using Ventura’s algorithm (Ventura and Martinez in Inf Sci 124:273–296, 2000; Found Phys Lett 12:547–559, 1999) for all the possible superpositions as the search states, and the results have been compared with those of Grover’s algorithm and it has been demonstrated that in general for classification of a given pattern (Apples) in three-qubit system, the Grover’s and Ventura’s algorithms are effective in the cases where the number of patterns in the stored database is larger or smaller, respectively.