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This paper addresses the function projective synchronization problem between 3-cell Quantum cellular neural network hyperchaotic system and 6th-order cellular neural network system in the presence of unknown system parameters. Quantum-CNN systems produce nanoscale chaotic controllers under certain conditions. Based on Lyapunov stability theory the adaptive control law and the parameter update law are proposed to make the states of the 3-cell Quantum-CNN hyperchaotic system and 6th-order cellular neural network system asymptotically synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization schemes.