In order to improve the security of quantum color images, this study proposes a novel algorithm for quantum color image encryption based on three-dimensional chaotic systems. The encrypted quantum color image is represented by the novel quantum image representation for color digital image model. The original image is first perturbed by the Arnold transform and then the RGB channel is perturbed separately from the chaotic sequence generated by the new three-dimensional chaotic system by the xor operation. Evaluation metrics such as histogram, information entropy, and correlation of neighboring pixels of the image are analyzed using MATLAB. The simulation results show that the pixel values of the encrypted image are uniformly distributed and the algorithm enhances the security of quantum color images. The specific quantum circuit diagram of the encryption algorithm is given in the paper. The superposition and entanglement properties of quantum physics greatly improve the efficiency of complex image processing algorithms, and the overall complexity of the circuit is [Formula: see text], which is efficient and implementable.

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Many fractional order calculus researchers believe that fractional order calculus is a good way to solve information processing as well as certain physical system modeling problems. In the training of neural networks, there is the problem of long convergence time. In order to shorten the convergence time of the network, an R-L gradient descent method is proposed in this study. The article begins with a theoretical proof of the convergence of fractional order derivatives using function approximation and interpolation inequality theorems. Finally, through multiple simulations, it can be obtained that the fractional-order neural network can maintain a higher accuracy rate compared with the integer-order neural network, and also can well solve the problem of longer convergence time of the neural network. The convergence time can be reduced by nearly 10% compared to the integer order.

The firefly algorithm (FA) is a popular swarm intelligence optimization algorithm. The FA is used to solve various optimization problems, but it still has some deficiencies, such as high complexity, slow convergence rate, and low accuracy of the solution. This paper proposes a highly efficient quantum firefly algorithm with stochastic search strategies (QSSFA). In QSSFA, individuals are generated in the way of quantum angle coding by introducing the laws of quantum physics and quantum gates, and combined with the random neighborhood attraction model, an adaptive step size strategy is also introduced in the optimization. The complexity of the algorithm is greatly reduced, and the global search ability of the algorithm is optimized. The convergence speed of the algorithm, the ability to jump out of the local optimum, and the algorithm accuracy are improved. The proposed QSSFA’s performance is tested on ten mathematical test functions. The obtained results show that the QSSFA algorithm is very competitive compared to the firefly algorithm and three other FA variants.

Most models of quantum neural networks are optimized based on gradient descent, and like classical neural networks, gradient descent suffers from the barren plateau phenomenon, which reduces the effectiveness of optimization. Therefore, this paper establishes a new QNN model, the optimization process adopts efficient quantum particle swarm optimization, and tentatively adds a quantum activation circuit to our QNN model. Our model will inherit the superposition property of quantum and the random search property of quantum particle swarm. Simulation experiments on some classification data show that the model proposed in this paper has higher classification performance than the gradient descent-based QNN.