As the question says - how does the amplitude amplification in Grover's algorithm work?

I am fine with adding the negative phase on the winning state, but how does one generate the diffuser to increase the probability for some specific problem (that uses Grover's algorithm)? Is the diffuser always the same and, if it is, how does it look like?

  • 2
    $\begingroup$ Nielsen's book chap 6, the geometry of Grover's algorithm will help, some questions in the Stack Exchange will also help. $\endgroup$
    – narip
    Jul 29, 2021 at 7:49
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    $\begingroup$ By "the diffuser" do you mean the bit that reflects about the initial state? If so, that is specific to every case. Essentially, you need a unitary $U$ such that $U|0\rangle=|\psi$, your initial state. $\endgroup$
    – DaftWullie
    Jul 29, 2021 at 7:54
  • $\begingroup$ By "the diffuser" I mean the part of the circuit that does the amplitude amplification. I understand how to build the oracle that marks the "correct / winning" states. $\endgroup$
    – YoungBoi
    Jul 29, 2021 at 17:35
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    $\begingroup$ do these answer your question? quantumcomputing.stackexchange.com/a/4400/55, quantumcomputing.stackexchange.com/q/1613/55, and links therein $\endgroup$
    – glS
    Jul 29, 2021 at 22:28


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