In the domain of Internet of Things (IoT) applications, quantum computers offer the promise of addressing complex computational issues that traditional cryptographic methods find challenging. The unparalleled computational power of quantum computers makes existing cryptographic schemes, tailored to mitigate computational complexity, ineffective. This research introduces a robust encryption scheme designed specifically for digital data exchanged between IoT devices such as smartphones, smart sensors, and smart health monitoring devices. The proposed encryption framework is based on bit-plane extraction-based encryption, the chaotic sine model, the hyperchaotic map, the quantum baker map, and quantum operations such as quantum selective scrambling. The proposed methodology involves three key phases: the first and last phase related to permutation, which is performed at the bit level based on discrete bit-plane scrambling, bit-plane extraction, and hyperchaotic mapping. However, the second phase is based on diffusion, which depends on the chaotic sine model. During the initial stage, creating correlations among image pixels, along with a couple of chaotic sequences using a quantum baker map, is accomplished through a superposition of quantum-states. Before applying diffusion, the pixels of the grayscale image are encoded using a single qubit, and quantum operations are based on a quantum circuit featuring swap gates. To introduce pixel-level permutation, a hyperchaotic map generates random sequences within the range of 0 to 255. A circular shift further shuffles the pixel rows and pixel columns of the permuted image pixels. To enhance the digital image security further, bit-planes are extracted from the permuted bit-planes. Then, the bits within each bit plane are scrambled using a random sequence generated by the hyperchaotic map. Finally, the encoded bit planes are merged to produce a final encrypted image. Experimental results demonstrate the effectiveness of the proposed methodology, with security parameters such as correlation, entropy, and key space measuring at 0.0001, 7.999, and >2100, respectively. Furthermore, to assess performance in relation to computational complexity, a detailed analysis of computational time is conducted. The results reveal that the proposed encryption scheme can execute all encryption steps presented in the proposed method in less than one second. These findings demonstrate the secure transmission of digital data between IoT devices and show the suitability of the proposed encryption scheme for real-time applications.