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I have a quantum circuit as the following picture. Now I add the depolarizing error on the Hadamard gate using the following code in Qiskit.

prob_1 = 0.5
error_1 = noise.depolarizing_error(prob_1, 1)
noise_model = noise.NoiseModel()
noise_model.add_quantum_error(error_1, ['h'], [0])

The problem is that if I add depolarizing error on X gate instead on the same circuit, the output of the circuit is still noisy.

noise_model.add_quantum_error(error_1, ['x'], [0])

This makes me confused because I only have a Hadamard gate in the circuit. Why the output is noisy after I put the depolarizing error on X gate?

I am also confused about where the depolarizing error is added, before or after the Hadamard gate? I test both of these cases theoretically, but the results are not consistent with the outputs.

enter image description here

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  • $\begingroup$ I don't know exactly, but a promising direction would be to check the basis gates of the simulator and of the noise model. You can start by transpiling the circuit and check how the transpiled circuit looks like - my guess is that it contains X gates. $\endgroup$ Jun 29, 2023 at 12:45

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