I was going through the qiskit textbook and in this chapter, i came across a statement under the topic "Kickback with the T-gate" related to the Controlled-Z gate that "the controlled-Z rotation gates are symmetrical in fashion (two controls instead of a control and a target). There is no clear control or target qubit for all cases." What does it imply exactly?

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  • $\begingroup$ A releted answer. $\endgroup$ – Davit Khachatryan Aug 31 at 17:39
  • 2
    $\begingroup$ CZ(control=i,target=j)=CZ(control=j,target=i)...maybe a bit surprising at first...so you can pick either bit for control/target $\endgroup$ – unknown Aug 31 at 17:50

For the mathematical explanation, check here: Why is the action of controlled-Z unaltered by exchanging target control qubits?

Maybe it would help you to see CZ in a different (symmetric) notation, like its current representation in Qiskit:

from qiskit import *
circuit = QuantumCircuit(2)

a CZ gate represented as a symmetric gate

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