Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state

Multi-dimensional color image processing has two difficulties: One is that a large number of bits are needed to store multi-dimensional color images, such as, a three-dimensional color image of \(1024 \times 1024 \times 1024\) needs \(1024 \times 1024 \times 1024 \times 24\) bits. The other one is that the efficiency or accuracy of image segmentation is not high enough for some images to be used in content-based image search. In order to solve the above problems, this paper proposes a new representation for multi-dimensional color image, called a \((n\,+\,1)\)-qubit normal arbitrary quantum superposition state (NAQSS), where \(n\) qubits represent colors and coordinates of \({2^n}\) pixels (e.g., represent a three-dimensional color image of \(1024 \times 1024 \times 1024\) only using 30 qubits), and the remaining 1 qubit represents an image segmentation information to improve the accuracy of image segmentation. And then we design a general quantum circuit to create the NAQSS state in order to store a multi-dimensional color image in a quantum system and propose a quantum circuit simplification algorithm to reduce the number of the quantum gates of the general quantum circuit. Finally, different strategies to retrieve a whole image or the target sub-image of an image from a quantum system are studied, including Monte Carlo sampling and improved Grover’s algorithm which can search out a coordinate of a target sub-image only running in \(O(\sqrt{N/r} )\) where \(N\) and \(r\) are the numbers of pixels of an image and a target sub-image, respectively.