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We present the new mathematical formalisms of Cognitive Quantum Number (CQN), as unified validation logic in human minds and machines. Though our theory is general, on study we concentrate in logic formation in the field of quantum computing specially for information processing in nano-scale devices. Our proposed logic not only allows us to derive the results of quantum state, but also permits their generalization of making available new techniques of logic inference, establishes a direct dynamical link between memory and processing part naturally. We consider quantum logic and cognition of mind in general as Eigen value problems. The role of molecular magnets in the field of quantum computation and mechanism for using it as qubits in the context of quantum phenomenon of spin tunneling in presence of external magnetic fields is formulated. Synthesis and spectral response of nano-particle towards quantum dot formation is also studied. We showed that the spectrum of logic operators and cognition of minds is in exact correspondence of the fundamentals alphabet of logic truth-values. The basic gate for quantum logic operations is also derived.