This paper introduces a novel two-dimensional triangle function combined with a discrete chaotic map (2D-TFCDM) for secure quantum image communication. The proposed chaotic map is evaluated through various tests, including attractor plot, bifurcation diagram, sensitivity test, Lyapunov exponent, 0–1 Test, permutation entropy, and the NIST test suite. The map is combined with the Secure Hash Algorithm (SHA) to enhance image cryptography. The encrypted image is then communicated using the novel enhanced quantum representation (NEQR) method, leveraging the IBM quantum computer (Qiskit) to utilize the principles of quantum mechanics for data security. The paper discusses the limitations of existing chaotic maps and highlights the effectiveness of the proposed method in resisting various attacks. The authors also review recent advancements in chaotic maps and quantum image representation techniques, emphasizing the importance of multimedia security in various domains.This paper introduces a novel two-dimensional triangle function combined with a discrete chaotic map (2D-TFCDM) for secure quantum image communication. The proposed chaotic map is evaluated through various tests, including attractor plot, bifurcation diagram, sensitivity test, Lyapunov exponent, 0–1 Test, permutation entropy, and the NIST test suite. The map is combined with the Secure Hash Algorithm (SHA) to enhance image cryptography. The encrypted image is then communicated using the novel enhanced quantum representation (NEQR) method, leveraging the IBM quantum computer (Qiskit) to utilize the principles of quantum mechanics for data security. The paper discusses the limitations of existing chaotic maps and highlights the effectiveness of the proposed method in resisting various attacks. The authors also review recent advancements in chaotic maps and quantum image representation techniques, emphasizing the importance of multimedia security in various domains.