In this work, an efficient robust control scheme is proposed for position control of induction motors based on field-oriented control (FOC). The proposed control scheme consists of three interior loops. In the outer loop, the central controller based on the nonsingular fast terminal sliding mode control (NFTSM) is designed. The objective of this loop is to provide the required stator current in the q-axis for regulating the electromagnetic torque. In the inner loops, two fractional-order PI (FOPI) controllers are designed to provide the stator voltages. Besides, since induction motors have a complex mathematical model, time-varying dynamics, and non-linear structure, to deal with these challenges in the controller design, the quantum neural network (QNN) is presented with a novel framework and employed to estimate the lumped uncertainties. This makes the main contribution of the paper. In addition, to further improve system performance, the parameters of the FOPI controllers are tuned by employing the artificial bee colony (ABC) optimization algorithm. The stability of the proposed control approach is proved by Lyapunov’s stability theory. According to the results of the comparative simulation, the superiority of this approach is confirmed.