Posted by **Gyanno** on Thursday, March 21, 2013 at 1:31pm.

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

(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.

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