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I want to implement the Grover iteration instead of the multi-control qubit implemented as in this picture:

enter image description here

I want to implement them like in this example of five qubits: enter image description here

I mean how can I decompose them in the circuit (picture1)?

This is my attempt but I failed to get the amplitude increases for the state |1111> (after measuring the wires 1,2,3 and 6)

If you could do it in the Quirk simulator, that will be too helpful.

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  • $\begingroup$ I'm not sure what you're struggling with. What's stopping you from just taking the second picture and creating it in Quirk? $\endgroup$
    – Craig Gidney
    May 20 '20 at 1:04
  • $\begingroup$ Actually I did but I don't get the same chance of finding the state |1111>. I don't know where I'm wrong in my implementation. $\endgroup$
    – walid
    May 20 '20 at 1:07
  • $\begingroup$ Well in the second picture there are 5 control qubits whereas in the first there are 4. Maybe that's the difference? $\endgroup$
    – Craig Gidney
    May 20 '20 at 1:48
  • $\begingroup$ Yes I know but this not the problem, the seconde picture is just an example on how I want the multi control for 4 qubits and 3 qubits in the first picture to look like, I mean to decompose them in an approprite way. $\endgroup$
    – walid
    May 20 '20 at 2:12
  • $\begingroup$ Hi @Craig Gidney pls see the edited question, I added a link to my attempt if you could figure out my error :). And thank you. $\endgroup$
    – walid
    May 20 '20 at 18:49
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In the second half of the circuit you're mixing up which qubits are your ancillae and which are the ones you want to operate on. You can't use one of your system qubits as an ancilla.

enter image description here

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  • $\begingroup$ Awesome! That was clear. Thank you so much. $\endgroup$
    – walid
    May 21 '20 at 14:39

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