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quantum physics

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ass 6
q6:Now, consider the case where N4 elements are marked instead of just one. If we run one iteration of Grover's algorithm and measure, what is the probability that we see a marked element?

q7: Which of the following observables correspond to a standard basis measurement?

q8: Which of the following observables correspond to a sign basis measurement?

q5: uppose we ran m steps of Grover's algorithm on some function f (which has one marked element y) and the resulting superposition was exactly |y⟩.

(a) What was the state after the (m−1)-th step? Note that you can describe the superposition by specifying two numbers, αy and αx for x≠y. Use K to denote the total number of elements. (Sorry for not using the conventional letter N, but EdX grader doesn't seem to allow the use of that letter.) Please fully simply your answer.
(b) Now, if we run one more step (total of m+1 steps), what is the resulting superposition?
(c) What if you now apply another phase inversion?

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