Analysis and improvement of the quantum Arnold image scrambling

We investigate the quantum Arnold image scrambling proposed by Jiang et al. (Quantum Inf Process 13(5):1223–1236, 2014). It is aimed to realize Arnold and Fibonacci image scrambling in quantum computer. However, the algorithm does not perceive the particularities of “mod $$2^{n}$$2n,” multiply by 2, and subtraction in binary arithmetic. In this paper, a possible simplified version is presented based on 3 theorems and a corollary which represent the particularities of binary arithmetic. The theoretical analysis indicates that the network complexity is dropped from 140n$$\sim $$∼168n to 28n$$\sim $$∼56n and the unitarity of circuits is not destroyed.