Using the coefficients introduced by Bargmann and Moshinsky for the reduction of the su( $3$ ) algebra of Cartesian three-dimensional oscillator multiplet states into so( $3$ ) angular momentum submultiplets, we implement unitary rotations of three-dimensional Cartesian arrays that form finite pixellated "volume images." Transforming between the Cartesian and spherical bases, the subgroup of rotations in the latter is converted into rotations of the former, allowing for proper concatenation and inversion of these unitary transformations, which entail no loss of information.Using the coefficients introduced by Bargmann and Moshinsky for the reduction of the su($3$) algebra of Cartesian three-dimensional oscillator multiplet states into so($3$) angular momentum submultiplets, we implement unitary rotations of three-dimensional Cartesian arrays that form finite pixellated "volume images." Transforming between the Cartesian and spherical bases, the subgroup of rotations in the latter is converted into rotations of the former, allowing for proper concatenation and inversion of these unitary transformations, which entail no loss of information.

arXiv:2207.13308Jul 27, 20220 citations

Geometric Operations of Quantum Images

Zhixin Zhang, Xianhua Song, Ahmed A. Abd El‐Latif +2 more

To achieve a certain desired visual effect, the pixel positions of the input image are mapped to positions different from the original ones so as to change the display effect of the original image. This process is called the geometric transformation of the image. Geometric transformations mainly include geometric correction of the image and spatial transformations (scaling transformation, rotation, and affine transformation) [ 1 – 26 ] . This chapter proposes the geometric transformations of the QIRHSI quantum color image, including basic geometric transformations and scaling operations, and further studies the unitary operators of geometric transformations and the corresponding quantum circuits.To achieve a certain desired visual effect, the pixel positions of the input image are mapped to positions different from the original ones so as to change the display effect of the original image. This process is called the geometric transformation of the image. Geometric transformations mainly include geometric correction of the image and spatial transformations (scaling transformation, rotation, and affine transformation) [ 1 – 26 ] . This chapter proposes the geometric transformations of the QIRHSI quantum color image, including basic geometric transformations and scaling operations, and further studies the unitary operators of geometric transformations and the corresponding quantum circuits.

CRC Press eBooksMay 15, 20260 citations

Unitary Rotations

IMPERIAL COLLEGE PRESS eBooksJun 12, 20120 citations

Searching for a pixel's position in a grayscale quantum image with Grover's algorithm

Amor Gueddana

This work proposes a circuit implementation of the encoding circuit for an N × N grayscale-based Flexible Representation of Quantum Images (FRQI). The implementation is tested on the Qiskit simulator before being executed on real IBM Quantum hardware. The encoded FRQI, with a searched pixel encoded by a single qubit, is considered an unsorted database with a single table, where the key of the table represents the pixel’s position (x, y). The other columns represent the grayscale level at this position and the searched grayscale level, which are encoded by rotation angles and implemented using several multi-controlled rotation gates along the y-axis. Subsequently, Grover ’s algorithm is used to retrieve the position from the FRQI after performing a comparison with the given grayscale level of an individual pixel. The physical constraints associated with the IBM quantum device used are discussed, and the limitations of Grover ’s algorithm for searching the pixel are addressed.This work proposes a circuit implementation of the encoding circuit for an N × N grayscale-based Flexible Representation of Quantum Images (FRQI). The implementation is tested on the Qiskit simulator before being executed on real IBM Quantum hardware. The encoded FRQI, with a searched pixel encoded by a single qubit, is considered an unsorted database with a single table, where the key of the table represents the pixel’s position (x, y). The other columns represent the grayscale level at this position and the searched grayscale level, which are encoded by rotation angles and implemented using several multi-controlled rotation gates along the y-axis. Subsequently, Grover ’s algorithm is used to retrieve the position from the FRQI after performing a comparison with the given grayscale level of an individual pixel. The physical constraints associated with the IBM quantum device used are discussed, and the limitations of Grover ’s algorithm for searching the pixel are addressed.

Quantum Communications and Quantum ImagingOct 4, 20241 citation

Rotation Matrices - I

Springer eBooksJan 1, 20021 citation

Using the coefficients introduced by Bargmann and Moshinsky for the reduction of the su(

3

) algebra of Cartesian three-dimensional oscillator multiplet states into so(

3

) angular momentum submultiplets, we implement unitary rotations of three-dimensional Cartesian arrays that form finite pixellated "volume images." Transforming between the Cartesian and spherical bases, the subgroup of rotations in the latter is converted into rotations of the former, allowing for proper concatenation and inversion of these unitary transformations, which entail no loss of information.