This paper presents a quantum image encryption algorithm based on a novel 3D chaotic system and the quantum Rubik's cube principle. Initially, we propose a new 3D chaotic system for generating chaotic key sequences and chaotic images. Subsequently, we introduce the quantum Rubik's cube principle, which serves as a fundamental component of our encryption scheme. The scheme consists of two stages: In the first stage, chaotic key sequences control the operation of the quantum Rubik's cube principle, enabling pixel permutation in the encrypted image. In the second stage, the scrambled image undergoes bitwise XOR with the chaotic image, facilitating pixel diffusion through quantum bitwise XOR operations. By leveraging the chaotic system's sensitivity to initial values and its large key space, our proposed scheme effectively resists statistical attacks and noise interference. The time complexity of our scheme is exponential reduced compared to its classical counterpart. We also conduct experiments on both the IBM Qiskit platform and a classical computer and analyze the results.