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

Abstract

In recent years the quantum entanglement [1] has played important role in the fields of quantum information theory[2,3], quantum computers [4], universal quantum computing network [5], teleportation[6], dense coding [7,8], geometric quantum computation [9,10] and quantum cryptography[11-13]. From physical point of view, entanglement is still little understood. What makes it too powerful is the fact that since quantum states exist as superposition, the correlations between different qubits exist in superposition as well and when superposition is destroyed, the proper correlation is somehow communicated between the qubits [14]. It is this communication that is the crux of entanglement. We have recently explored [15] the entanglement as one of the key resources required for quantum neural network (QNN), constructed the complete set of new maximally entangled states (Singh-Rajput MES), different from Bell’s MES, in a two-qubit system and established [16] the functional dependence of the entanglement measures on spin correlation functions. We have also performed the pattern association (quantum associative memory) [17,18,19] and pattern classifications [20] by employing the method of Grover’s iteration [21] on Bell’s MES [22] and Singh-Rajput MES [15,16] in two-qubit system and demonstrated that, for all the related processes in a two-qubit system, Singh-Rajput MES provide the most suitable choice of memory states and the search states. Applying the method of Grover’s repeated iterations on three different superposition in three-qubit system, we have shown [23] that the state corresponding to exclusive superposition is the most suitable choice as the search state for the desired pattern classifications.