# physics

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Let |α⟩=1M√∑M−1j=0αj|j⟩ and let |β⟩=1M√∑M−1j=0βj|j⟩ be its QFTM. Suppose we shift the superposition |α⟩ to produce |α′⟩=1M√∑M−1j=0αj|j+1(modM)⟩, and let |β′⟩=1M√∑M−1j=0βj′|j⟩ be the QFTM of |α′⟩. Derive an expression for β′j as a function of βj. You can use e, j, pi, and M in your response.

• physics -

Got this result for above question:
exp(2ðji/M)âj

However it is graded as wrong, can someone help?

• physics -

exp(2piji/M)beta j

• physics -

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.

• physics -

Let |α⟩=1M√∑M−1j=0αj|j⟩ and let |β⟩=1M√∑M−1j=0βj|j⟩ be its QFTM. Suppose we shift the superposition |α⟩ to produce |α′⟩=1M√∑M−1j=0αj|j+1(modM)⟩, and let |β′⟩=1M√∑M−1j=0βj′|j⟩ be the QFTM of |α′⟩. Derive an expression for β′j as a function of βj. You can use e, j, pi, and M in your response.

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