Building a Quantum Software and Games [unitaryhack] ( Quantum Euclidean Distance for Two Images using Quantum Fourier Transform) from the Idea 2

[divshacker]

Notebook written by Miguel de Jesús Martínez Felipe and Divyanshu Singh

Quantum Euclidean Distance for Two Images

Miguelillnino and divshacker
fixes #12

[MaldoAlberto]

Hi @divshacker @Miguelillnino

According to the issue you are going to have your work accepted with half of the bounty, being this $50, but you must make, several corrections, these are described in the following comments.

Comments:

1- Why do they say Square L^2 Norm, just to say an equivalence of the Euclidean distance, or are they going to talk about other L^p spaces and their equivalences, since if there is an L2 there is an L1 or an L0.

2- Your explanation of Drapper is missing an equation, before eq 3 is when you apply QFT to |a>, check this resource https://docs.microsoft.com/en-us/azure/quantum/user-guide/libraries/standard/algorithms

3- This part has a conflict "remember that using the CU1 Gate we have", where is CU1? mentioned. It would be clearer that in the fourier transform the X-basis is used and rotation changes are made in the Z-axis, so based on eq 4 the U-gate is used, but for this it is important to know the general Drapper scheme.

4- The structure of the implementation is not very clear, they mention the Drapper adder and then talk about how to encode the data, it would be more logical to talk about the order:

• Representation of numbers as encoding bases.
• Algorithm and its theory. They can add a diagram of the Drapper algorithm, since they mention the equations, but it is not clear when they talk about the gates, e.g.

So for the most significant value (q1) we rotate cu1(pi/8,q0,q8)
(8 times)

-Explain the encoding of a pixel to 4 qubits.

• Explain the quantum equivalence with the classical equivalence of the Euclidean distance, they do not confirm it, they only show the code.

Your PR will not be accepted until you have the changes, therefore it would not be complete, in case you finish the untiaryhack and you have not made the changes it will not be valid to claim your $50.