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Quantum Information Processing

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

Hai-Sheng Li, Qingxin Zhu, Ri‐Gui Zhou, Lan Song, Yang Xing-jiang

Published Dec 6, 2013• 157 citations
Publisher
DOI
10.1007/s11128-013-0705-7

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RGB multi channel representation is proposed for images on quantum computers (MCQI) that captures information about colors (RGB channels) and their corresponding positions in an image in a normalized quantum state. The proposed representation makes it possible to store the RGB information about an image simultaneously by using 2n+3 qubits for encoding 2n× 2npixel images, whereas pixel-wise processing is necessary in many other quantum image representations, e.g., qubit lattice, grid qubit, and quantum lattice. Simulation of storage and retrieval of MCQI images using human facial images demonstrated that 15 qubits are required for encoding 64 × 64 colored images, and encoded information is retrieved by measurement. Perspectives of designing quantum image operators are also discussed based onMCQI representation, e.g., channel of interest, channel swapping, and restrict version of color transformation.
A novel method is proposed in this paper to store and retrieve images in entangled quantum systems, i.e., we employ a 2-qubit (or 3-qubit) entangled quantum state to represent the colors of 3 pixels (or 5 pixels) of color or gray images, and design quantum circuits to store images in entangled quantum systems, in addition, illustrate how to retrieve images stored in entangled quantum systems and analyze that the number of measurement is needed at most to retrieve a correct entangled quantum state. Simulation results on the Lena image shows compression ratio is 5.7 when PSNR is 32.8DB by Fourier transform while compression ratio of 2-qubit entangled coding (i.e., 2-qubit entangled quantum states represent image colors) is 12 without losing any information of the image. Due to take advantage of the superposition and entanglement properties of quantum states, our method improves the ability of image compression.
In this study, an important geometric transformation, multidimensional color image scaling based on an n-qubit normal arbitrary superposition state (NASS), is put forward. In order to reduce the complexity of implementation of image scaling in a quantum system, nearest neighbor interpolation algorithm is chosen to implement image scaling up. And the corresponding quantum circuit of implementation is proposed. Finally, we discuss measurements of the part qubits of a NASS state to realize image scaling down. The paper explores theoretical and practical aspects of image processing on a quantum computer.