In our efforts to construct a secure quantum image encryption algorithm, we first propose a quantum 3-D Baker map to scramble a 3-D quantum representation of an image. To have this 3-D quantum representation, we harness the NEQR model for a \(2^n \times 2^n\) grayscale image. In the second step of the proposed encryption scheme, we implement a substitution routine which starts by implementing the generalized gray code on the permuted image and concludes with selected intra bit-XOR-ing and XOR-ing with the pseudorandom sequence generated by the Fractional Chen’s system. The encryption scheme utilizes the basic quantum gates like C-NOT, Toffoli, and Ripple-carry adder due to their computational efficiency. The theoretical and numerical simulation results show that the algorithm has the potential to be used as an image encryption algorithm on quantum computers.

在构建安全的量子图像加密算法的过程中，我们首先提出了一个量子3-D Baker映射图来对图像的3-D量子表示进行加扰。为了具有这种3-D量子表示，我们利用NEQR模型获得\（2 ^ n \ times 2 ^ n \）灰度图像。在拟议的加密方案的第二步中，我们实现了一个替换例程，该例程首先在置换后的图像上实施广义格雷码，然后以分数级Chen生成的伪随机序列以选定的内部位XOR-ing和XOR-ing结束系统。由于它们的计算效率，加密方案利用了诸如C-NOT，Toffoli和Ripple-carry加法器之类的基本量子门。理论和数值模拟结果表明，该算法具有作为量子计算机图像加密算法的潜力。