<p>With the rapid advancement of quantum computing, traditional image steganography confronts significant security vulnerabilities against quantum attacks, rendering quantum image steganography an indispensable research direction for secure communication in the quantum era. Existing quantum image steganographic algorithms often suffer from insufficient security due to simplistic chaotic systems, excessive quantum circuit complexity, or unstable embedding payloads. To mitigate these challenges, this paper extends the quantum Logistic map to the complex domain (CQLM) for generating high-randomness key sequences, proposes an encrypted matrix coding scheme integrated with a chessboard sharing mechanism to balance security and payload stability, and design a low-complexity quantum circuit for efficient implementation. Simulation results demonstrate that the proposed algorithm achieves an average PSNR of 54.16 dB, SSIM of 0.9925, and stable payload of ~ 0.5 bit/pixel, while reducing quantum gate count by 51.5% and qubit usage by 44.8% compared to state-of-the-art schemes. It outperforms existing methods in imperceptibility while maintaining robust security, with a key space exceeding 2²⁹⁸ to resist quantum attacks.</p>