Abstract
Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.
Highlights
Richard Feynman examined the role quantum mechanics can play in the development of future computer hardware and demonstrated [1] that time evolution of an arbitrary quantum state was intrinsically more powerful computationally than the evolution of logical classical state
Entanglement is one of the key resources required for quantum computation and the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers
Starting with the theoretical basis of quantum computing in the present paper, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of Quantum Neural Networks (QNN) has been emphasized
Summary
Richard Feynman examined the role quantum mechanics can play in the development of future computer hardware and demonstrated [1] that time evolution of an arbitrary quantum state was intrinsically more powerful computationally than the evolution of logical classical state. Starting with the theoretical basis of quantum computing in the present paper, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Two different sets of maximally entangled two-qubit states have been obtained and it has been shown that the set of Bell states [26] is not the only eigen basis (magic eigen basis) of the space of two-qubit system, another set of MES constitutes a very powerful and reliable eigen basis of two-qubit systems This is the new eigen basis, being introduced for the first time, and to differentiate it from the already known Bell’s basis, it has been named as Singh-Rajput basis for its possible use in future in the literature. It has been shown that in neural networks the integrity of a stored pattern (bases states) is due to entanglement and the quantum associate memory (Qu AM) is the realization of the extreme condition of many Hopfield networks each storing a single pattern in parallel quantum universes
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