Pattern Classifications Using Grover’s and Ventura’s Algorithms in a Two-qubits System

• Published in: International journal of theoretical physics Vol. 57; no. 3; pp. 692 - 705
• Main Authors: Singh, Manu Pratap, Radhey, Kishori, Rajput, B. S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2018; Springer Nature B.V
• Subjects: Algorithms; Classification; Elementary Particles; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Searching; Superposition (mathematics); Theoretical; Singh-Rajput MES; Pattern classification; Search states; Ventura’s algorithm; Entanglement; Iterations; Qubits; Grover’s algorithm; Maximally entangled states (MES)
• ISSN: 0020-7748; 1572-9575
• DOI: 10.1007/s10773-017-3601-6

Carrying out the classification 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 data-base) are classified more efficiently than the known ones (present in the data-base) in both the algorithms. It has also been demonstrated that different states of Singh-Rajput MES obtained from the corresponding self-single- pattern start states are the most suitable search states for the classification of patterns |00>,|01 >, |10> and |11> respectively on the second iteration of Grover’s method or the first operation of Ventura’s algorithm.