Quantum Inf Process DOI 10.1007/s11128-016-1472-z Classification of patterns representing Apples and Oranges in three-qubit system Manu Pratap Singh 1 · Kishori Radhey 1 · V. K. Saraswat 1 · Sandeep Kumar 1 Received: 6 June 2016 / Accepted: 8 November 2016 © Springer Science+Business Media New York 2016 Abstract 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 inver- sion about average has been constructed as a square matrix of order eight, the phase inversion operators and corresponding iteration operators for patterns separately rep- resenting 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 classifica- tions 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 Ven- B Kishori Radhey k.radhey2011@gmail.com Manu Pratap Singh manu_p_singh@hotmail.com V. K. Saraswat vk.saraswat@gmail.com Sandeep Kumar sandeepvertical@gmail.com 1 Department of Computer Science, Dr. B R. Ambedkar University, Agra, U.P. 282002, India 123