Image preparations of multi-mode quantum image representation and their application on quantum image reproduction

doi:10.1016/j.ijleo.2021.168321

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Volume 251, February 2022, 168321

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Abstract

Efficient and general quantum image representation and preparation are the precondition of quantum image processing. The multi-mode quantum image representation is compatible with many important color modes. Studying image preparation and image processing will help to further improve the universality of quantum image on different application fields. In this paper, we improve the multi-mode quantum image representation to reduce the difficulty of entanglement preparation. We give a detailed image preparation process and algorithm based on this proved representation. Then, to reduce the number of Not-gates in preparation circuits, the optimal preparation is proposed. Furthermore, we give the reproduction circuit based on these preparations. The preparation and reproduction experiments are performed on the IBM Quantum lab platform. The circuits and the Bell-state statistic histograms of the measurement collapse are given. The results show that the preparations and reproduction are correct and efficient.

Introduction

With the development of quantum computing and quantum information, some researches have focused on high-performance and efficient quantum image processing [1]. How to extend the classical digital image algorithms to the quantum field deserves to be studied. In general, if the image representations are different, the preparations and the processing algorithms will be great different. Therefore, general quantum image representation and efficient preparation are the premise of good quantum image processing algorithm [2].

The first quantum image representation, Qubit lattice [3] was proposed by Venegas-Anraca et al. and this model uses a qubit to store each pixel of the classical image. Subsequently, Latorre et al. proposed the Real Ket quantum image representation model [4]. With the help of the characteristics of the balanced quadtree, each leaf node (a pixel) of the balanced quadtree is stored in n qubits. Le et al. proposed and modified the FRQI (Flexible Representation of Quantum Images) [5]. $N$ qubits are used to represent the horizontal (vertical) coordinate, and 1 qubit is used to represent the color, so the total number of qubits is $2 N + 1$ . Then MCQI [6] was put forward to support color mode, in which the coordinate information does not change, and the RGB color channels are represented with 3 qubits, so the total number of qubits is $2 N + 3$ . These two quantum image representations in literature [5], [6] are the basic models in the field of quantum image, and perform well in image storage and collection. Inspired by these kinds of models, some quantum image representations are proposed for different image modes, such as grayscale image, color image, infrared image, etc. In these models, color information is encoded on phase or basis state. Only color information encoded on basis state can accurately be restored through limited measurement operations, while the former can only obtain the probability of color information. Therefore, we focus on the quantum image representation encoding color information on the basis state.

Although there are many quantum image representations, most of them are only suitable for specific image modes. There are 3 types of color mode conversion for classical image: (i) Color mode can be directly converted to grayscale mode; (ii) Other modes are converted to bitmap mode, in which grayscale mode is the necessary intermediary; (iii) RGB (Red Green Blue) mode is converted to CMYK (Cyan Magenta Yellow Black) mode, and Lab (Lightness-ab) is a necessary mediator. Therefore, grayscale mode, RGB mode and Lab mode are basic and important. The multi-mode quantum image representation(MQIR) is compatible with these important color modes [7].

In quantum image field, how to construct the representation to store the image information carried by quantum is the most basic process. The key of both image storing and quantum computing is the preparation of multi-qubit entanglement. The scholars have developed a quantum chip with 20 superconducting qubits [8], which they successfully manipulated and realized global quantum entanglement. This study was published in journal Science, which once set a new world record for generating 20-qubit entangled states in solid-state quantum devices. In other words, the technology of multi-qubit entanglement is very difficult. In order to make full use of the supercoordinate and entanglement properties of quantum states, it is necessary to reduce the number of entanglement qubits in quantum image and study the quantum image preparation.

Therefore, in this paper, the related works are introduced in Section 2. We improve our previously proposed MQIR [7], and the improved multi-mode quantum image representation is shown in Section 3. Furthermore, based on this new representation, the preparation, optimal preparation, and their application on quantum image reproduction are introduced in Section 4. These experiments are implemented on IBM Quantum Lab platform [9] to verify the efficiency and correctness. The experimental analysis is presented in Section 5. Finally, the conclusion is given in Section 6.

Section snippets

Related works

If the color information is represented as basis state, the quantum image can be prepared by controlled NOT gate (CNOT gate). Since the quantum basis states are orthogonal to each other, the pixel values of the quantum image can be distinguished by quantum measurement [10]. Then the color information can be accurately retrieved through a limited number of measurement operations. Therefore, in this part, we mainly introduce the quantum image representations and related preparations in which the

Multi-mode quantum image representation based on 3-D coordinate

To reduce the number of qubits in quantum image, we proposed multi-mode quantum image representation (MQIR) [7]. A $2^{n} \times 2^{n}$ MQIR image can be shown as Eq. (1). $| I_{m} 〉 = \frac{1}{{\sqrt{2}}^{2 n + l}} \sum_{Z = 0}^{2^{l} - 1} \sum_{Y = 0}^{2^{n} - 1} \sum_{X = 0}^{2^{n} - 1} | m 〉 | C_{Z Y X}^{} 〉 | Z Y X 〉,$ where $| Z Y X 〉 = | Z 〉 | Y 〉 | X 〉 = | z_{l - 1} z_{l - 2} \dots z_{0} 〉 | y_{n - 1} y_{n - 2} \dots y_{0} 〉 | x_{n - 1} x_{n - 2} \dots x_{0} 〉$ , $l = ⌈ l o g_{2} b ⌉$ , $b$ is the number of binary bits representing the color/gray level, $z_{k}, y_{i}, x_{j} \in {0, 1}$ , $i, j \in {0, 1, \dots, n - 1}$ , $k \in [0 l - 1]$ , The mode control qubit $| m 〉 = cos \frac{θ}{2} | 0 〉 + e^{i ϕ} sin \frac{θ}{2} | 1 〉$ . $| m 〉$ is introduced to distinguish different color modes and

TMQIR image preparations and their application

To prepare TMQIR image, it is the key that how to set the binary value in $Z$ -axis of 3-D coordinates. The gray value or true color value in traditional 2-D coordinates are binarized into the pixel sequence. Then the coordinates in the pixel sequence are binarized, respectively. This binarization value is the value in $Z$ -axis. As a result, a 3-D coordinate space is formed, and the pixel value in 3-D coordinates is either 0 or 1. It is only necessary to prepare the pixel value 1 in 3-D coordinate

Consistency verifications of the TMQIR image preparation and reproduction

In order to verify the consistency of TMQIR preparation before and after optimization, the preparation circuit (i.e. Fig. 3) and the optimal preparation circuit (i.e. Fig. 5) of the quantum grayscale image in Fig. 1(a) are implemented using the Qiskit development kit provided by IBMQ. And the Bell state statistical histograms of measuring collapse are shown as Fig. 8.

In Fig. 8, the ordinate is the probability of measurement and the abscissa is a quantum sequence. Based on Eq. (1), in order to

Conclusion

In this paper, a TMQIR model is proposed to reduce the number of qubits required for 3-D coordinates. The TMQIR preparation process, algorithm, optimal algorithm, and their application on image reproduction are given. These experiments are implemented on the IBM quantum lab platform, and the TMQIR preparation circuit and optimal circuit are formed. Then the Bell-state statistical histograms of measuring collapse are given, which shown the efficiency and correctness of the TMQIR preparation and

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work is supported by the Fund of the Fundamental Research Funds for the Central Universities, China (No. 2019XD-A02).

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With the rapid development of multimedia technology, image scrambling technology is essential for the application of information hiding and digital watermarking. However, in the field of quantum image processing, there are few researches on image scrambling. An MQIR (Multimode Quantum Image Representation) takes less qubits to store images, which has certain advantages. It is very significant to research more secure scrambling algorithms on the superior quantum images. Therefore, we propose an MQIR image encryption scheme based on right-angle rotation and Gray code transformation. We give the MQIR image encryption and decryption circuit based on right-angle rotation and Gray code transformation. In the encryption process, the combination of the NOT gate and the swap gate acts on the qubits representing the horizontal and vertical coordinates in the sub-blocks of the MQIR image, and realizes different right-angle rotations of each sub-block in the MQIR image. Further, Gray code scrambling is performed on the three-dimensional coordinates of the MQIR image, and the double scrambling of the pixel position and pixel value of the MQIR image is completed. The encryption circuit is very simple to operate, saving a certain amount of quantum gates. This encryption method is simulated on the IBM quantum cloud platform and matlab. Experimental results show that the encryption method has certain effectiveness. This method not only disrupts the histogram distribution of the original image, but also has a good scrambling effect. Finally, we give the scrambled image and histogram with the best encryption effect in the scrambling period.
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Original Research ArticleImage preparations of multi-mode quantum image representation and their application on quantum image reproduction

Abstract

Introduction

Section snippets

Related works

Multi-mode quantum image representation based on 3-D coordinate

TMQIR image preparations and their application

Consistency verifications of the TMQIR image preparation and reproduction

Conclusion

Declaration of Competing Interest

Acknowledgment

Optik

Opt. Commun.

Chem. Phys. Lett. X

Phys. Lett. A

The Feynman processor: Quantum entanglement and the computing revolution [Book Review]

Nature

An improved novel quantum image representation and its experimental test on IBM quantum experience

Sci. Rep.

Storing, processing, and retrieving an image using quantum mechanics

Image compression and entanglement

A flexible representation and invertible transformations for images on quantum computers

An RGB multi-channel representation for images on quantum computers

J. Adv. Comput. Intell. Intell. Inform.

A multimode quantum image representation and its encryption scheme

Quantum Inf. Process.

Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits

Science

IBM quantum experience

NEQR: a novel enhanced quantum representation of digital images

Quantum Inf. Process.

Original Research Article
Image preparations of multi-mode quantum image representation and their application on quantum image reproduction