physics

posted by .

Suppose 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⟩.
If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial state), what is the resulting superposition? Note that you can describe the superposition by specifying two numbers, αy and αx for x≠y. You may use K to denote the total number of elements. (K should be uppercase.) HINT: You may want to review Problems 2, 3, and 5 of Assignment 6.
Now if we run for another m steps, what is the resulting superposition?
What about after yet another m+1 steps?

  • Quantum Physics -

    This is fairly simple. You just need to remember that Grover's algorithm is cyclical

    You start out with an equal superposition for both the y x answers

    0 steps: ay = 1/sqrt(K), ax = 1/sqrt(k)


    then after m steps, you solve it

    @m steps: ay - 1, ax = o

    Since you started from 0 instead of 1, it takes M+1 steps to get it back to the original position, but it's inverted

    @2m+1 steps: ay = -1/sqrt(K), ax = -1/sqrt(k)

    Then it takes another m steps to find the answer (but inverted)
    @3m+1 steps: ay = -1, ax = 0

    and then m+1 steps later, you're back to the initial position.

    @4m+2 steps: ay = 1/sqrt(K), ax = 1/sqrt(k)

    and the cycle repeats.

    @5m+2 steps: ay = 1, ax = 0
    @6m+3 steps: ay = -1/sqrt(K), ax = -1/sqrt(k)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Quantum 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 ?
  2. physics

    n 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?
  3. Quantum Physics

    Suppose 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?
  4. Quantum Physics

    Suppose 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?
  5. Quantum Physics

    Suppose 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⟩. If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial …
  6. quantum physics

    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?
  7. physics

    Suppose 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⟩. If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial …
  8. Quantum computers

    PROBLEM 5 Suppose 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⟩. PROBLEM 5A (4 points possible) If we run for m+1 additional steps (i.e. …
  9. Algebra

    Yazmin decided to get some exercise by taking the stairs from the first to the fifth floor in her apartment building. The first time she went up the entire flight, she walked up some steps and ran up 16 steps. This took a total of …
  10. Math

    azmin decided to get some exercise by taking the stairs from the first to the fifth floor in her apartment building. The first time she went up the entire flight, she walked up some steps and ran up 16 steps. This took a total of 60 …

More Similar Questions