Questions tagged [phase-kickback]

For questions about phase kick-back. For a detailed description of the mechanism, go through https://quantumcomputing.stackexchange.com/questions/2565 and the answers therein.

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10
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3answers
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Why does the “Phase Kickback” mechanism work in the Quantum phase estimation algorithm?

I've probably read the chapter The quantum Fourier transform and its applications from Nielsen and Chuang (10 th anniversary edition) a couple of times before and this took this thing for granted, but ...
7
votes
2answers
133 views

Who discovered the phase kickback trick?

Was it David Deutsch? Can you say who was the first paper to mention the phase kickback trick?
7
votes
2answers
106 views

Equivalent unitary transformations

Suppose $x \in \{0,1\}^n$. The standard way to make a query is with an oracle $O_x$ that given an input $|i,b \rangle $ returns $|i,b \oplus x_i \rangle$. Via the phase kick-back trick, this can be ...
4
votes
2answers
69 views

Is the $|-\rangle$ state the only one that can do the trick for Grover's algorithm?

$\newcommand{\qr}[1]{|#1\rangle}$Grover algorithm's input is a superposition, representing the haystack, and the Bell state $\qr{-}$. The $\qr{-}$ seems utterly important: when I replaced $\qr{-}$ by,...
3
votes
1answer
19 views

Obtaining phases of all basis states

I’m wondering that is there a way to separate phases of basis states from the magnitudes (namely putting phases on some new basis states with the same probability magnitude) if the exact values of ...