controlled-Z rotation gates in symmetrical fashion

Question

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?

luciano · Answer

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)
circuit.cz(0,1)
circuit.draw('mpl')

controlled-Z rotation gates in symmetrical fashion

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