A flexible representation of quantum images for polynomial preparation, image compression, and processing operations

Abstract

A Flexible Representation of Quantum Images (FRQI) is proposed to provide a representation for images on quantum computers in the form of a normalized state which captures information about colors and their corresponding positions in the images. A constructive polynomial preparation for the FRQI state from an initial state, an algorithm for quantum image compression (QIC), and processing operations for quantum images are combined to build the whole process for quantum image processing on FRQI. The simulation experiments on FRQI include storing, retrieving of images and a detection of a line in binary images by applying quantum Fourier transform as a processing operation. The compression ratios of QIC between groups of same color positions range from 68.75 to 90.63% on single digit images and 6.67-31.62% on the Lena image. The FRQI provides a foundation not only to express images but also to explore theoretical and practical aspects of image processing on quantum computers.

Quantum image processing: A review of advances in its security technologies

“…The innovative representations 8,9 to encode images on the quantum computing framework set the stage for Le et al to propose the FRQI 11 (i.e.°exible representation for quantum images) that truly kick-started research in the context of present day descriptions of QIP. This could be attributed to the°exible manner it supports the integration of the quantum image into a normalized state, which facilitates auxiliary transformations on the content of the image.…”

“…In 2011, Le et al proposed the FRQI, 11 which has since burgeoned into the most widely used QIR. The FRQI captures the essential information about the colors as well as the corresponding positions of every point in an image and integrates them into a normalized quantum state.…”

A Novel Quantum Image Compression Method Based on JPEG

“…Different quantum image representations may have different preparation methods. Researchers have proposed a number of quantum image representation schemes, such as Qubit Lattice [1], Real Ket [2], Entangled Image [3], FRQI (the flexible representation of quantum images) [4], MCQI (the RGB multi-channel representation for quantum images) [5], NEQR (the novel enhanced quantum representation of digital images) [6], QUALPI (the quantum representation for log-polar images) [7], QSMC&QSNC (quantum states for M colors and quantum states for N coordinates) [8], NAQSS (the normal arbitrary quantum superposition state) [9], INEQR (the improved NEQR) [10], GQIR (the generalized quantum image representation) [11], and etc. A number of papers have summarized and compared them [11][12].…”

“…Quantum image compression is the procedure that reduces the quantum resources used to prepare quantum images [4]. The main resource in quantum preparation is the number of quantum gates instead of the number of qubits, because as stated previously, the number of qubits used in quantum images (i.e., h + w + q) has been very fewer than the number of bits used in classical images (i.e., HW q).…”

“…[4] and [6], the minimization of Boolean expressions is used to compress the image preparation. We call it Boolean expression compression (BEC) method and will introduce it in detail in Section 2.1.…”