This research proposes a new two-dimensional chaotic map based encryption method for secure quantum image communication. The proposed 2D-TFCDM map is tested on various criteria such as attractor plot, bifurcation diagram, sensitivity test, Lyapunov exponent, 0–1 Test, permutation entropy and NIST test suite. The map is combined with the Secure Hash Algorithm (SHA) for image cryptography applications. The encrypted image is communicated using the novel enhanced quantum representation (NEQR) method with the qasm_simulator of IBM quantum computer (Qiskit) to utilize the benefits of the laws of physics to secure data. Numerical analyses and simulation results are compared with recent techniques, showing the effectiveness of the image encryption method in resisting various attacks. Chaos-based cryptosystems require extremely nonlinear chaotic maps with many chaotic regions. Quantum computers efficiently provide speed and security in image communication. The research gap found in the last few years is that existing chaotic maps exhibit weak complexity and easy prediction of the signal. A new hyper-chaotic system with complete control and conditional symmetry is proposed. Triangular chaotic maps provide a full chaotic population over infinite control parameters. Many new 2D-TFCDM are highly sensitive to initial conditions, offering extreme randomness. Multimedia information security is an emerging and challenging domain in the growing digital world. High data is communicated from one end to another, becoming highly vulnerable to attacks. Therefore, multimedia security is crucial in medical, military and personal use. Developing a 2D sine-Henson alteration map-based image encryption technique uses the two chaotic signals to diffuse and confuse the image pixels. Researchers proposed an image encryption algorithm that uses XOR diffusion, a laser chaos system, and Joseph's double-layer scrambling method. Shor created a quantum integer factoring algorithm in 1994 to search the secret code efficiently in polynomial time. Grover developed a quantum search technique in 1996 that might provide quadratic speed-up searches. Once these methods were represented, digital data processed and communicated through classical computation became vulnerable to attacks; on the other hand, these researches have motivated many scholars to explore the excellent properties of quantum computing. In recent years, numerous methods have been developed to utilise quantum mechanics in representing digital images to quantum images. Among the many techniques, Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum image Representation (NEQR) are the most common and effective techniques to use quantum mechanics for converting a classical image to a quantum image. Controlled-NOT gates diffuse classical images in the quantum circuit with a quantum-represented encryption key. To overcome the effects of Shor's and Grover's algorithm, the image is encrypted in the classical computer and transferred using qubits (quantum bits) to the receiver. Qiskit is a quantum lab developed by IBM with various simulators to utilise quantum properties in multiple applications. Researchers addressed the literature gap and improved the existing quantum image representation techniques inThis research proposes a new two-dimensional chaotic map based encryption method for secure quantum image communication. The proposed 2D-TFCDM map is tested on various criteria such as attractor plot, bifurcation diagram, sensitivity test, Lyapunov exponent, 0–1 Test, permutation entropy and NIST test suite. The map is combined with the Secure Hash Algorithm (SHA) for image cryptography applications. The encrypted image is communicated using the novel enhanced quantum representation (NEQR) method with the qasm_simulator of IBM quantum computer (Qiskit) to utilize the benefits of the laws of physics to secure data. Numerical analyses and simulation results are compared with recent techniques, showing the effectiveness of the image encryption method in resisting various attacks. Chaos-based cryptosystems require extremely nonlinear chaotic maps with many chaotic regions. Quantum computers efficiently provide speed and security in image communication. The research gap found in the last few years is that existing chaotic maps exhibit weak complexity and easy prediction of the signal. A new hyper-chaotic system with complete control and conditional symmetry is proposed. Triangular chaotic maps provide a full chaotic population over infinite control parameters. Many new 2D-TFCDM are highly sensitive to initial conditions, offering extreme randomness. Multimedia information security is an emerging and challenging domain in the growing digital world. High data is communicated from one end to another, becoming highly vulnerable to attacks. Therefore, multimedia security is crucial in medical, military and personal use. Developing a 2D sine-Henson alteration map-based image encryption technique uses the two chaotic signals to diffuse and confuse the image pixels. Researchers proposed an image encryption algorithm that uses XOR diffusion, a laser chaos system, and Joseph's double-layer scrambling method. Shor created a quantum integer factoring algorithm in 1994 to search the secret code efficiently in polynomial time. Grover developed a quantum search technique in 1996 that might provide quadratic speed-up searches. Once these methods were represented, digital data processed and communicated through classical computation became vulnerable to attacks; on the other hand, these researches have motivated many scholars to explore the excellent properties of quantum computing. In recent years, numerous methods have been developed to utilise quantum mechanics in representing digital images to quantum images. Among the many techniques, Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum image Representation (NEQR) are the most common and effective techniques to use quantum mechanics for converting a classical image to a quantum image. Controlled-NOT gates diffuse classical images in the quantum circuit with a quantum-represented encryption key. To overcome the effects of Shor's and Grover's algorithm, the image is encrypted in the classical computer and transferred using qubits (quantum bits) to the receiver. Qiskit is a quantum lab developed by IBM with various simulators to utilise quantum properties in multiple applications. Researchers addressed the literature gap and improved the existing quantum image representation techniques in