In the paper, function projective synchronization of quantum cellular neural network with uncertain system parameters and Lorenz hyperchaotic system is studied. The adaptive controllers are proposed to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function. We also present the relevant proof by applying Lyapunov stability theory. Moreover, linear independence of coefficient vector of uncertain system parameters in quantum cellular neural network is analyzed theoretically, which aims to realize the unknown parameter identification and estimation. Numerical simulations are made to show the effectiveness of the function projective synchronization and parameter estimation.