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Homework Help: Quantum Mechanics and Quantum Computation

  1. Aug 29, 2013 #1
    1. The problem statement, all variables and given/known data
    q1]] Which of the following pairs of quantum gates commute? Select all that apply. (Gates A and B commute if and only if for any input applying A and then B gives the same results as applying B and then A. This is the same as saying that the unitary transformations commute.)

    a) I and X
    b) X and Z
    c) H and X
    d) CNOT and X applied to the target
    e) qubit Real rotation by 30∘ and real rotation by 45∘

    q2]] 1] What is ZX applied to |0>?
    2] What is ZX applied to H|0>?
    3] Suppose we have a qubit in the state |ψ⟩. We know that if we measure it in the standard basis, the probability of getting a 0 is 29. Now, if we instead first apply a Hadamard gate and then measure the resulting qubit H|ψ⟩ in the sign basis, what is the probability of getting a +?
    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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