Pair-Wise Classifications of Patterns in a Two-Qubits System

Carrying out the classification of pairs of patterns in a two-qubit system by separately using Grover’s and Ventura’s algorithms on different possible superposition, it has been shown that the exclusion superposition and the phase-invariance superposition are the most suitable search states obtained from two- pattern start-states and one-pattern start-states, respectively, for the simultaneous classifications of patterns. The higher effectiveness of Grover’s algorithm for large search states has been verified but the higher effectiveness of Ventura’s algorithm for smaller data base has been contradicted in two- qubit systems and it has been demonstrated that the unknown patterns (not present in the concerned start state or the date base) are classified more efficiently than the known ones (present in the data-base) in Grover’s algorithm.It has also been shown that all possible pairs of Singh-Rajput MES are the most suitable choice as the search states obtained from the corresponding single-pattern start-states for the classification of respective pairs of patterns of a two-qubit system. It has been further demonstrated that the pairs of consecutive states of Singh-Rajput MES are most suitable search states for the classification of pairs of class 𝐶1 with minimum Hamming separations while the pairs of alternative states of these MES are suitable for the simultaneous classification of patterns of pairs of class 𝐶3 with intermediate Hamming separation and the pair of the first and last states of these MES classify most efficiently the patterns of class 𝐶2 with maximum Hamming separation.

Keywords: Pattern Classification; Entanglement; Qubits; Iterations; Search States; Grover’s Algorithm.