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Is there an error on Qiskit.org textbook with the superdense coding section?

Quantum Computing Asked by E-H on March 7, 2021

The textbook on Qiskit.org has

When the H-gate is applied to first qubit, it creates superposition and we get the state $|0+rangle = frac{1}{sqrt{2}}(|00rangle + |01rangle)$

Shouldn’t it be:
$$|0+rangle = frac{1}{sqrt{2}}(|00rangle + |10rangle)$$

as explained in some answers here: (How do I apply the Hadamard gate to one qubit in a two-qubit pure state?)

One Answer

Qiskit's coding of the qubits is made such that Qiskit's least significant bit has the lowest index (0) and will be written at the right of the state, so instead of writing a qubit like $ |q_0 q_1 ... q_n rangle $, it will rather be $ |q_n q_{n-1} ... q_0 rangle $, explaining the difference between the Qiskit explanation and the explanation from the question you pointed. The first qubit is on the far right, so Hadamard will be applied on the one in the far right, thus you have the first result you pointed.

Hope this clears your question, if not please tell me :)

Correct answer by Lena on March 7, 2021

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