NQQR: scalable qutrit image representation

Abstract

Abstract Ternary quantum image processing (TQIP) integrates qutrit-based quantum computing with image representation, offering a promising pathway for efficient image encoding models. This paper introduces Novel Qutrit Quantum Representation (NQQR) model, a scalable and optimized ternary model for representing grayscale and RGB images of size $$3^n \times 3^n$$ in a ternary quantum system. The proposed model encodes pixel positions using the superposition of 2 n qutrits and assigns grayscale or color intensity values using 6 qutrits, while an additional color qutrit and an ancilla qutrit are employed to reduce the complexity of multi-controlled N -qutrit gates, thereby lowering the overall quantum cost. Experimental results show that the NQQR achieves a time complexity of $$O(n3^{2n})$$ and the optimized NQQR model significantly reduces quantum cost, with improvements up to $$99.36\%$$ for grayscale images and $$99.33\%$$ for RGB images when compared to equivalent non-optimized qubit/qutrit-based encoding models. In addition, the performance of the proposed model is evaluated under quantum depolarizing noise using MSE and PSNR metrics computed between the original and reconstructed images under different noise levels. These results demonstrate the efficiency and scalability of the proposed NQQR model at the representation level and suggest its potential as a building block for future research in TQIP.