Quantum image processing (QIP) is a nascent domain that applies quantum computing perspectives to image processing challenges. NEQR: Novel Enhanced Quantum Representation is quantum representation model that transforms a classical image into a quantum state. Unlike classical image representations, NEQR allows quantum algorithms to process image data, enabling operations that can potentially surpass classical approaches in terms of efficiency. The Robert Cross (RC) operator edge detection technique is quick, straightforward, and efficient at identifying diagonal edges while preserving fine details with better clarity. Hence, in this proposed work, the RC operator is adapted to work on quantum-represented images (via NEQR). By operating on quantum-encoded images, the RC operator can extract edges by detecting significant changes in pixel intensity across the diagonals, just as in classical processing, but with the added benefits that quantum computing offer. The proposed hybrid model demonstrates a significant improvement in Peak Signal-to-Noise Ratio (PSNR) of around 6.76% compared to Kirsch operator, slight improvement of 1.70% compared to Laplacian operator and moderate improvement when compared with 4.50% Laplacian of Gaussian (LOG) operator.