Design an algorithm to decode a black$-$and$-$white FRQI image into a classical black$-$

and$-$white pixel image.

A greyscale image is encoded classically using $8$ bits for every pixel, where the greyscale

level corresponding to the pixel $(i,j)$ is an integer $g_{ij}in\{0,1,$dots,$255\}.$ In FRQI, a

greyscale image is encoded as a superposition

$|I$:

where ${}_{ij}in[0,\frac{}{2}]$ is an angle encoding the greyscale level. For example, we can let

${}_{ij}=\frac{}{2}*\frac{g_{ij}}{255}.$ Design a quantum circuit to encode a greyscale $22$ image consisting of

$4$ pixels with

$g_{00}=0,g_{01}=64,g_{10}=128,g_{11}=255$

and implement the circuit in QisKit.

Generalize your algorithm from part $(2)$ to decode a greyscale FRQI image into a

classical greyscale image.

How many qubits do you need to encode a $2^n{2}^n-$pixel image? How accurate is

your decoding algorithm? Guided by these two questions, discuss the advantages and

disavantages of FRQI vs$.$ classical image encoding.