In this problem, we will carry out some steps of the quantum factoring algorithm for N = 15

Question

(a) What is the period k of the periodic superposition set up by the quantum factoring algorithm if it chooses x = 2 ?
(b) Assume that we found this k using period finding algorithm. Use k to find a non-trivial square root of 1(mod 15) . Write your answer as an integer between 0 and 15.
(c) Then, the algorithm proceeds by computing gcd (x,y) for some integers x and y . List these two numbers separated by a comma.

If there are more than one correct solution, provide any one of them.

Answer 1

a)4;b)4;c)(3,15) or (5,15)

Answer 2

thank you

Answer 3

Answer to Q 2,3,5?

Answer 4

q10