 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2020/quantum-information/3/c/solution

The phase oracle multiplies an unmarked basis vector by

+ 1

and a marked one by

- 1

. Thus the state after the oracle is

V_{f} ∣ e_{0} ⟩ = \frac{1}{N} (∣ A_{0} ⟩ - ∣ A_{1} ⟩) .

Its squared norm is

(S_{0} + S_{1}) / N = 1

. All computational outcomes would still have probability

1/ N

if measured at this point: the oracle has changed the relative phase, not the magnitudes of the amplitudes. The following reflection converts that phase information into a changed probability distribution through quantum interference.

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