Asked by imath
In this problem, we will carry out some steps of the quantum factoring algorithm for N=21.
(a) What is the period k of the periodic superposition set up by the quantum factoring algorithm if it chooses x=2? In other words, what is the period of f(j)=2^j (mod 21).
(b) Assume that we found this k using period finding algorithm. Use k to find a non-trivial square root of 1(mod 21). Write your answer as an integer between 0 and 21.
(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.
(a) What is the period k of the periodic superposition set up by the quantum factoring algorithm if it chooses x=2? In other words, what is the period of f(j)=2^j (mod 21).
(b) Assume that we found this k using period finding algorithm. Use k to find a non-trivial square root of 1(mod 21). Write your answer as an integer between 0 and 21.
(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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