Novel quantum circuit for image compression utilizing modified Toffoli gate and quantized transformed coefficient alongside a novel reset gate
Ershadul Haque, Manoranjan Paul
TL;DR
The paper tackles the high gate-count problem in quantum image compression by introducing MTGSC, a scheme that uses a modified state-connection and a reset gate to map quantized DCT coefficients efficiently. It provides a formal complexity bound $O[3q+\log_2 S_x+\log_2 S_y+2q(\log_2 S_x+\log_2 S_y)]$ for a block size $2^{S_x}\times 2^{S_y}$ with $q$ nonzero coefficients and reports a ~44% gate reduction over DCTEFRQI while maintaining PSNR. Through block-partitioned coefficient mapping and a deterministic preparation pipeline, MTGSC demonstrates lower gates-per-pixel and competitive PSNR across standard grayscale images, outperforming JPEG-like references in the quantum setting. The approach scales to larger images with a compact qubit footprint (as low as 15 qubits for representation) and offers a practical, deterministic alternative to probabilistic quantum-image representations.
Abstract
Quantum image computing has emerged as a groundbreaking field, revolutionizing how we store and process data at speeds incomparable to classical methods. Nevertheless, as image sizes expand, so does the complexity of qubit connections, posing significant challenges in the efficient representation and compression of quantum images. In response, we introduce a modified Toffoli gate state connection using a quantized transform coefficient preparation process. This innovative strategy streamlines circuit complexity by modifying state connection from the state connection information. In our operational control gates, only input 1 impacts the output, allowing us to modify the state connection and dramatically enhance the efficiency of the proposed circuit. As a result, the proposed approach significantly reduces the number of gates required for both image compression and representation. Our findings reveal that it requires an impressive 44.21 percent fewer gates than existing techniques, such as the Direct Cosine Transform Efficient Flexible Representation of Quantum Images (DCTEFRQI), all while maintaining a consistent peak signal-to-noise ratio (PSNR). For an image block size of 2^Sx2^Sy with q gray levels, the complexity of our approach can be succinctly expressed as, O[3q+log2Sx+log2Sy+2q(log2Sx+log2Sy)]. Here, Sx and Sy represent the X and Y positional control gates while q indicates the non-zero transform coefficients. Moreover, experimental evaluations strongly demonstrate that it excels in both compressing and representing quantum images compared to the DCTEFRQI approach, particularly excelling in the essential metrics of gate requirements and PSNR performance. Embrace the future of quantum imaging with our innovative solution, where efficiency meets excellence.