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I was just curious; when do the qubits get entangled? Do the qubits get entangled right after initialization or do they get entangled when we apply Hadamard Gates to the qubits?

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As mentioned before, qubits are only entangled by means of 2-qubit gates and not by 1-qubit gates, which only cause a rotation of the qubit state in question. Therefore, 2-qubit gates are needed to provide anything meaningful on a quantum computer other than pure random number generation. Practically, 2-qubit gates (typically a CX - gate) are harder to realize than 1-qubit gates, which also leads to a significantly larger quantum error.

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