An improved flexible representation of quantum images

Abstract

Quantum image representations are the models that are used to represent digital images on to the quantum computers. They also allow to perform various image processing operations on these images and to store on to the quantum system. For storing images on to the quantum computers, QIR models use qubits. The FRQI and NEQR are well-known models used for capturing and processing quantum images. But these models have some weaknesses especially they suffer from time and space complexity respectively. Therefore, in this research, we establish that the complexity of image preparation in FRQI model is O(n2 2n ), which is linear in the size of image. Moreover, by analyzing the FRQI and NEQR models, we propose an improved flexible representation of quantum images (IFRQI) which takes p qubits to encode gray-scale values of pixels of a 2p-bit-deep image. The gray-scale values are encoded by employing rotation matrices corresponding to chosen values of angles which assist in accurate retrieval of original image information through projective measurements. The quantum image compression algorithm and basic image processing operations are discussed in detail to establish the effectiveness of IFRQI model. The performance analysis in respect of time and space complexity exhibits that the IFRQI model is comparable to FRQI and NEQR models.