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I have a 8-qubits circuit whose final vector state may be for instance: $$ \frac{\sqrt{2}}{4} |00010101\rangle+\frac{\sqrt{2}}{4} |00101010\rangle+\frac{\sqrt{2}}{4} |01010110\rangle+\frac{\sqrt{2}}{4} |01101001\rangle+\frac{\sqrt{2}}{4} |10011010\rangle+\frac{\sqrt{2}}{4} |10100101\rangle+\frac{\sqrt{2}}{4} |11011001\rangle+\frac{\sqrt{2}}{4} |11100110\rangle $$ I'd like to apply the Grover search to amplify the states that are 11...... (the two last ones here)

I guess something like

problem = AmplificationProblem(oracle,state_preparation=circ, is_good_state=[6,7])
from qiskit.algorithms import Grover
from qiskit.primitives import Sampler

grover = Grover(sampler=Sampler())
result = grover.amplify(problem)

should work, but I don't know how to write the oracle. Any help would be welcome.

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1 Answer 1

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If I'm understanding correctly, you want an oracle that detects when the first two qubits are set to $|1\rangle$. You could do this using a Toffoli gate and an ancilla qubit as follows.

import qiskit

data    = qiskit.QuantumRegister(8, "d")
ancilla = qiskit.QuantumRegister(1, "anc")
qc      = qiskit.QuantumCircuit(data, ancilla)

qc.toffoli(data[0], data[1], ancilla[0])
          
d_0: ──■──
       │  
d_1: ──■──
       │  
d_2: ──┼──
       │  
d_3: ──┼──
       │  
d_4: ──┼──
       │  
d_5: ──┼──
       │  
d_6: ──┼──
       │  
d_7: ──┼──
     ┌─┴─┐
anc: ┤ X ├
     └───┘

So the ancilla qubit detects when q_0 and q_1 are both $|1\rangle$. Then, you can use this oracle in Grover's.

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    $\begingroup$ Thanks for your answer (and sorry to reply so late: I was in a "no Internet area" for a few days). I indeed finally used a mcx gate. $\endgroup$ Jun 13, 2023 at 8:21
  • $\begingroup$ No worries, glad I helped. Please consider accepting answers that solve your questions! $\endgroup$
    – epelaez
    Jun 13, 2023 at 12:27

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