Project: Quantum Image Processing

The goal of Quantum Image Processing $($QIP$)$ is to design algorithms for image encoding

and processing that exploit quantum advantage. These quantum implementations often re$-$

sult in an exponential advantage in terms of memory usage and$/$or an exponential advantage

in processing time via the Quantum Fourier Transform. QIP can also be employed in the

implementation of fast algorithms for geometric transformations and computer graphics in

general.

In this project, you will explore a common way of encoding digital images into quantum

states called Flexible Representation of Quantum Images $($FRQI$).$ In this encoding, a black$-$

and$-$white image of size $2^n{2}^n-$pixels is given as a matrix $I=(lo{n}_{ij}{)}_{i,j}=0,2^n-1,$ where $lo{n}_{ij}in\{0,1\}$

represents a black $(0)$ or white $(1)$ pixel in position $(i,j),$ and it is then encoded as a quantum

superposition

$|I$:

For example, a black$-$and$-$white image consisting of a grid of $22$ pixels $(n=1)$ can be

encoded using $3$ qubits, as shown below:

$=\frac{1}{2}(|1$:$)|00$:

Design a quantum circuit to encode each of the following images using FRQI and

implement them in QisKit