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I am writing a piece of work on Grover's algorithm and I am looking for references on the phase-kickback trick to transform a state oracle in a phase oracle.

Is there any paper or there a part on it in Nielsen and Chuang ?

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  • $\begingroup$ The phase kickback trick transforms a state oracle to a phase oracle, not vice versa! $\endgroup$ Jan 3, 2021 at 21:01

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The IBM Qiskit text has a section on this that you may find useful.

For something more "academic" Mermin Sections 4.2-4.5, Schuld and Petruccione Sections 3.5.1-3.5.3, or Nielson and Chuang Sections 6.1-6.2 may have what you're looking for.

Schuld and Petruccione also have references at the end of each chapter, which could be worth looking into.

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    $\begingroup$ Ok, thanks ! I wanted to know if there was anything a bit more "academic" $\endgroup$ Jan 3, 2021 at 19:06
  • $\begingroup$ Got it, I just added a bit to my answer. I haven't read these sections myself in a while, so can't say for sure if they contain what you're looking for. But if these books covered phase-kickback in any detail, the above is where it would be. $\endgroup$
    – ryanhill1
    Jan 3, 2021 at 19:34
  • $\begingroup$ An update to the link, since I was looking for something similar and the former is not working: learn.qiskit.org/course/ch-gates/phase-kickback $\endgroup$
    – Pasamonte
    Jun 25, 2023 at 17:37

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